Nonlinear dynamical analysis of an aeroelastic system with multi-segmented moment in the pitch degree-of-freedom

NASA Astrophysics Data System (ADS)

Vasconcellos, Rui; Abdelkefi, Abdessattar

2015-01-01

The effects of a multi-segmented nonlinearity in the pitch degree of freedom on the behavior of a two-degree of freedom aeroelastic system are investigated. The aeroelastic system is free to plunge and pitch and is supported by linear translational and nonlinear torsional springs and is subjected to an incoming flow. The unsteady representation based on the Duhamel formulation is used to model the aerodynamic loads. Using modern method of nonlinear dynamics, a nonlinear characterization is performed to identify the system's response when increasing the wind speed. It is demonstrated that four sudden transitions take place with a change in the system's response. It is shown that, in the first transition, the system's response changes from simply periodic (only main oscillating frequency) to two periods (having the main oscillating frequency and its superharmonic of order 2). In the second transition, the response of the system changes from two periods (having the main oscillating frequency and its superharmonic of order 2) to a period-1. The results also show that the third transition is accompanied by a change in the system's response from simply periodic to two periods (having the main oscillating frequency and its superharmonic of order 3). After this transition, chaotic responses take place and then the fourth transition is accompanied by a sudden change in the system's response from chaotic to two periods (having the main oscillating frequency and its superharmonic of order 3). The results show that these transitions are caused by the tangential contact between the trajectory and the multi-segmented nonlinearity boundaries and with a zero-pitch speed incidence. This observation is associated with the definition of grazing bifurcation.

Analyses of Multishaft Rotor-Bearing Response

NASA Technical Reports Server (NTRS)

Nelson, H. D.; Meacham, W. L.

1985-01-01

Method works for linear and nonlinear systems. Finite-element-based computer program developed to analyze free and forced response of multishaft rotor-bearing systems. Acronym, ARDS, denotes Analysis of Rotor Dynamic Systems. Systems with nonlinear interconnection or support bearings or both analyzed by numerically integrating reduced set of coupledsystem equations. Linear systems analyzed in closed form for steady excitations and treated as equivalent to nonlinear systems for transient excitation. ARDS is FORTRAN program developed on an Amdahl 470 (similar to IBM 370).

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond.

PubMed

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-05-26

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 10(20) N m(-3). This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond

PubMed Central

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-01-01

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 1020 N m−3. This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics. PMID:27225287

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Scott A; Catalfamo, Simone; Brake, Matthew R. W.

2017-01-01

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratiomore » variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.« less

Nonlinear hybrid modal synthesis based on branch modes for dynamic analysis of assembled structure

NASA Astrophysics Data System (ADS)

Huang, Xing-Rong; Jézéquel, Louis; Besset, Sébastien; Li, Lin; Sauvage, Olivier

2018-01-01

This paper describes a simple and fast numerical procedure to study the steady state responses of assembled structures with nonlinearities along continuous interfaces. The proposed strategy is based on a generalized nonlinear modal superposition approach supplemented by a double modal synthesis strategy. The reduced nonlinear modes are derived by combining a single nonlinear mode method with reduction techniques relying on branch modes. The modal parameters containing essential nonlinear information are determined and then employed to calculate the stationary responses of the nonlinear system subjected to various types of excitation. The advantages of the proposed nonlinear modal synthesis are mainly derived in three ways: (1) computational costs are considerably reduced, when analyzing large assembled systems with weak nonlinearities, through the use of reduced nonlinear modes; (2) based on the interpolation models of nonlinear modal parameters, the nonlinear modes introduced during the first step can be employed to analyze the same system under various external loads without having to reanalyze the entire system; and (3) the nonlinear effects can be investigated from a modal point of view by analyzing these nonlinear modal parameters. The proposed strategy is applied to an assembled system composed of plates and nonlinear rubber interfaces. Simulation results have proven the efficiency of this hybrid nonlinear modal synthesis, and the computation time has also been significantly reduced.

Study on Nonlinear Vibration Analysis of Gear System with Random Parameters

NASA Astrophysics Data System (ADS)

Tong, Cao; Liu, Xiaoyuan; Fan, Li

2018-03-01

In order to study the dynamic characteristics of gear nonlinear vibration system and the influence of random parameters, firstly, a nonlinear stochastic vibration analysis model of gear 3-DOF is established based on Newton’s Law. And the random response of gear vibration is simulated by stepwise integration method. Secondly, the influence of stochastic parameters such as meshing damping, tooth side gap and excitation frequency on the dynamic response of gear nonlinear system is analyzed by using the stability analysis method such as bifurcation diagram and Lyapunov exponent method. The analysis shows that the stochastic process can not be neglected, which can cause the random bifurcation and chaos of the system response. This study will provide important reference value for vibration engineering designers.

On the dimension of complex responses in nonlinear structural vibrations

NASA Astrophysics Data System (ADS)

Wiebe, R.; Spottswood, S. M.

2016-07-01

The ability to accurately model engineering systems under extreme dynamic loads would prove a major breakthrough in many aspects of aerospace, mechanical, and civil engineering. Extreme loads frequently induce both nonlinearities and coupling which increase the complexity of the response and the computational cost of finite element models. Dimension reduction has recently gained traction and promises the ability to distill dynamic responses down to a minimal dimension without sacrificing accuracy. In this context, the dimensionality of a response is related to the number of modes needed in a reduced order model to accurately simulate the response. Thus, an important step is characterizing the dimensionality of complex nonlinear responses of structures. In this work, the dimensionality of the nonlinear response of a post-buckled beam is investigated. Significant detail is dedicated to carefully introducing the experiment, the verification of a finite element model, and the dimensionality estimation algorithm as it is hoped that this system may help serve as a benchmark test case. It is shown that with minor modifications, the method of false nearest neighbors can quantitatively distinguish between the response dimension of various snap-through, non-snap-through, random, and deterministic loads. The state-space dimension of the nonlinear system in question increased from 2-to-10 as the system response moved from simple, low-level harmonic to chaotic snap-through. Beyond the problem studied herein, the techniques developed will serve as a prescriptive guide in developing fast and accurate dimensionally reduced models of nonlinear systems, and eventually as a tool for adaptive dimension-reduction in numerical modeling. The results are especially relevant in the aerospace industry for the design of thin structures such as beams, panels, and shells, which are all capable of spatio-temporally complex dynamic responses that are difficult and computationally expensive to model.

An approximation technique for predicting the transient response of a second order nonlinear equation

NASA Technical Reports Server (NTRS)

Laurenson, R. M.; Baumgarten, J. R.

1975-01-01

An approximation technique has been developed for determining the transient response of a nonlinear dynamic system. The nonlinearities in the system which has been considered appear in the system's dissipation function. This function was expressed as a second order polynomial in the system's velocity. The developed approximation is an extension of the classic Kryloff-Bogoliuboff technique. Two examples of the developed approximation are presented for comparative purposes with other approximation methods.

Optimisation of the vibrational response of ultrasonic cutting systems

NASA Astrophysics Data System (ADS)

Cartmell, M. P.; Lim, F. C. N.; Cardoni, A.; Lucas, M.

2005-10-01

This paper provides an account of an investigation into possible dynamic interactions between two coupled non-linear sub-systems, each possessing opposing non-linear overhang characteristics in the frequency domain in terms of positive and negative cubic stiffnesses. This system is a two-degree-of-freedom Duffing oscillator in which certain non-linear effects can be advantageously neutralised under specific conditions. This theoretical vehicle has been used as a preliminary methodology for understanding the interactive behaviour within typical industrial ultrasonic cutting components. Ultrasonic energy is generated within a piezoelectric exciter, which is inherently non-linear, and which is coupled to a bar- or block-horn, and to one or more material cutting blades, for example. The horn/blade configurations are also non-linear, and within the whole system there are response features which are strongly reminiscent of positive and negative cubic stiffness effects. The two-degree-of-freedom model is analysed and it is shown that a practically useful mitigating effect on the overall non-linear response of the system can be created under certain conditions when one of the cubic stiffnesses is varied. It has also been shown experimentally that coupling of ultrasonic components with different non-linear characteristics can strongly influence the performance of the system and that the general behaviour of the hypothetical theoretical model is indeed borne out in practice. Further experiments have shown that a multiple horn/blade configuration can, under certain circumstances, display autoparametric responses based on the forced response of the desired longitudinal mode parametrically exciting an undesired lateral mode. Typical autoparametric response phenomena have been observed and are presented at the end of the paper.

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

PubMed

Altoè, Alessandro; Charaziak, Karolina K; Shera, Christopher A

2017-12-01

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

Relationships between nonlinear normal modes and response to random inputs

NASA Astrophysics Data System (ADS)

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

2017-02-01

The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.

Response phase mapping of nonlinear joint dynamics using continuous scanning LDV measurement method

NASA Astrophysics Data System (ADS)

Di Maio, D.; Bozzo, A.; Peyret, Nicolas

2016-06-01

This study aims to present a novel work aimed at locating discrete nonlinearities in mechanical assemblies. The long term objective is to develop a new metric for detecting and locating nonlinearities using Scanning LDV systems (SLDV). This new metric will help to improve the modal updating, or validation, of mechanical assemblies presenting discrete and sparse nonlinearities. It is well established that SLDV systems can scan vibrating structures with high density of measurement points and produc e highly defined Operational Deflection Shapes (ODSs). This paper will present some insights on how to use response phase mapping for locating nonlinearities of a bolted flange. This type of structure presents two types of nonlinearities, which are geometr ical and frictional joints. The interest is focussed on the frictional joints and, therefore, the ability to locate which joint s are responsible for nonlinearity is seen highly valuable for the model validation activities.

Nonlinear dynamic response of a uni-directional model for the tile/pad space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Housner, J. M.; Edighoffer, H. H.; Park, K. C.

1980-01-01

A unidirectional analysis of the nonlinear dynamic behavior of the space shuttle tile/pad thermal protection system is developed and examined for imposed sinusoidal and random motions of the shuttle skin and/or applied tile pressure. The analysis accounts for the highly nonlinear stiffening hysteresis and viscous behavior of the pad which joins the tile to the shuttle skin. Where available, experimental data are used to confirm the validity of the analysis. Both analytical and experimental studies reveal that the system resonant frequency is very high for low amplitude oscillations but decreases rapidly to a minimum value with increasing amplitude. Analytical studies indicate that with still higher amplitude the resonant frequency increases slowly. The nonlinear pad is also responsible for the analytically and experimentally observed distorted response wave shapes having high sharp peaks when the system is subject to sinusoidal loads. Furthermore, energy dissipation in the pad is studied analytically and it is found that the energy dissipated is sufficiently high to cause rapid decay of dynamic transients. Nevertheless, the sharp peaked nonlinear responses of the system lead to higher magnification factors than would be expected in such a highly damped linear system.

Nonlinear system identification technique validation

NASA Astrophysics Data System (ADS)

Rudko, M.; Bussgang, J. J.

1982-01-01

This final technical report describes the results obtained by SIGNATRON, Inc. of Lexington MA on Air Force Contract F30602-80-C-0104 for Rome Air Development Center. The objective of this effort is to develop a technique for identifying system response of nonlinear circuits by measurements of output response to known inputs. The report describes results of a study into the system identification technique based on the pencil-of-function method previously explored by Jain (1974) and Ewen (1979). The procedure identified roles of the linear response and is intended as a first step in nonlinear response and is intended as a first step in nonlinear circuit identification. There are serious implementation problems associated with the original approach such as loss of accuracy due to repeated integrations, lack of good measures of accuracy and computational iteration to identify the number of poles.

Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

NASA Astrophysics Data System (ADS)

Rahman, M. A.; Ahmed, U.; Uddin, M. S.

2013-08-01

A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

A comprehensive study of the delay vector variance method for quantification of nonlinearity in dynamical systems

PubMed Central

Mandic, D. P.; Ryan, K.; Basu, B.; Pakrashi, V.

2016-01-01

Although vibration monitoring is a popular method to monitor and assess dynamic structures, quantification of linearity or nonlinearity of the dynamic responses remains a challenging problem. We investigate the delay vector variance (DVV) method in this regard in a comprehensive manner to establish the degree to which a change in signal nonlinearity can be related to system nonlinearity and how a change in system parameters affects the nonlinearity in the dynamic response of the system. A wide range of theoretical situations are considered in this regard using a single degree of freedom (SDOF) system to obtain numerical benchmarks. A number of experiments are then carried out using a physical SDOF model in the laboratory. Finally, a composite wind turbine blade is tested for different excitations and the dynamic responses are measured at a number of points to extend the investigation to continuum structures. The dynamic responses were measured using accelerometers, strain gauges and a Laser Doppler vibrometer. This comprehensive study creates a numerical and experimental benchmark for structurally dynamical systems where output-only information is typically available, especially in the context of DVV. The study also allows for comparative analysis between different systems driven by the similar input. PMID:26909175

Subharmonic response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random excitation.

PubMed

Haiwu, Rong; Wang, Xiangdong; Xu, Wei; Fang, Tong

2009-08-01

The subharmonic response of single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to narrow-band random excitation is investigated. The narrow-band random excitation used here is a filtered Gaussian white noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the applications of asymptotic averaging over the "fast" variables. The averaged stochastic equations are solved exactly by the method of moments for the mean-square response amplitude for the case of linear system with zero offset. A perturbation-based moment closure scheme is proposed and the formula of the mean-square amplitude is obtained approximately for the case of linear system with nonzero offset. The perturbation-based moment closure scheme is used once again to obtain the algebra equation of the mean-square amplitude of the response for the case of nonlinear system. The effects of damping, detuning, nonlinear intensity, bandwidth, and magnitudes of random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak amplitudes may be strongly reduced at large detunings or large nonlinear intensity.

Parametric Identification of Nonlinear Dynamical Systems

NASA Technical Reports Server (NTRS)

Feeny, Brian

2002-01-01

In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

Non-linear dynamic compensation system

NASA Technical Reports Server (NTRS)

Lin, Yu-Hwan (Inventor); Lurie, Boris J. (Inventor)

1992-01-01

A non-linear dynamic compensation subsystem is added in the feedback loop of a high precision optical mirror positioning control system to smoothly alter the control system response bandwidth from a relatively wide response bandwidth optimized for speed of control system response to a bandwidth sufficiently narrow to reduce position errors resulting from the quantization noise inherent in the inductosyn used to measure mirror position. The non-linear dynamic compensation system includes a limiter for limiting the error signal within preselected limits, a compensator for modifying the limiter output to achieve the reduced bandwidth response, and an adder for combining the modified error signal with the difference between the limited and unlimited error signals. The adder output is applied to control system motor so that the system response is optimized for accuracy when the error signal is within the preselected limits, optimized for speed of response when the error signal is substantially beyond the preselected limits and smoothly varied therebetween as the error signal approaches the preselected limits.

Relationships between nonlinear normal modes and response to random inputs

DOE PAGES

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

2016-07-25

The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). Here, this work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing.more » Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.« less

Step responses of a torsional system with multiple clearances: Study of vibro-impact phenomenon using experimental and computational methods

NASA Astrophysics Data System (ADS)

Oruganti, Pradeep Sharma; Krak, Michael D.; Singh, Rajendra

2018-01-01

Recently Krak and Singh (2017) proposed a scientific experiment that examined vibro-impacts in a torsional system under a step down excitation and provided preliminary measurements and limited non-linear model studies. A major goal of this article is to extend the prior work with a focus on the examination of vibro-impact phenomena observed under step responses in a torsional system with one, two or three controlled clearances. First, new measurements are made at several locations with a higher sampling frequency. Measured angular accelerations are examined in both time and time-frequency domains. Minimal order non-linear models of the experiment are successfully constructed, using piecewise linear stiffness and Coulomb friction elements; eight cases of the generic system are examined though only three are experimentally studied. Measured and predicted responses for single and dual clearance configurations exhibit double sided impacts and time varying periods suggest softening trends under the step down torque. Non-linear models are experimentally validated by comparing results with new measurements and with those previously reported. Several metrics are utilized to quantify and compare the measured and predicted responses (including peak to peak accelerations). Eigensolutions and step responses of the corresponding linearized models are utilized to better understand the nature of the non-linear dynamic system. Finally, the effect of step amplitude on the non-linear responses is examined for several configurations, and hardening trends are observed in the torsional system with three clearances.

Nonlinear normal modes modal interactions and isolated resonance curves

DOE PAGES

Kuether, Robert J.; Renson, L.; Detroux, T.; ...

2015-05-21

The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system. To this end, an energy balance technique is used to predict the amplitude of the harmonic forcing that is necessary to excite a specific nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip serves to illustrate the developments. Furthermore, the practical implications of isolated resonance curves are also discussed by computing the beam response to sine sweepmore » excitations of increasing amplitudes.« less

Grain size effects on stability of nonlinear vibration with nanocrystalline NiTi shape memory alloy

NASA Astrophysics Data System (ADS)

Xia, Minglu; Sun, Qingping

2017-10-01

Grain size effects on stability of thermomechanical responses for a nonlinear torsional vibration system with nanocrystalline superelastic NiTi bar are investigated in the frequency and amplitude domains. NiTi bars with average grain size from 10 nm to 100 nm are fabricated through cold-rolling and subsequent annealing. Thermomechanical responses of the NiTi bar as a softening nonlinear damping spring in the torsional vibration system are obtained by synchronised acquisition of rotational angle and temperature under external sinusoidal excitation. It is shown that nonlinearity and damping capacity of the NiTi bar decrease as average grain size of the material is reduced below 100 nm. Therefore jump phenomena of thermomechanical responses become less significant or even vanish and the vibration system becomes more stable. The work in this paper provides a solid experimental base for manipulating the undesired jump phenomena of thermomechanical responses and stabilising the mechanical vibration system through grain refinement of NiTi SMA.

Exact modelling of the optical bistability in ferroelectics via two-wave mixing: A system with full nonlinearity

NASA Astrophysics Data System (ADS)

Khushaini, Muhammad Asif A.; Ibrahim, Abdel-Baset M. A.; Choudhury, P. K.

2018-05-01

In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.

Robust fast controller design via nonlinear fractional differential equations.

PubMed

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

The effect of low velocity impact in the strength characteristics of composite materials laminates

NASA Technical Reports Server (NTRS)

Liebowitz, H.

1983-01-01

The nonlinear vibration response of a double cantilevered beam subjected to pulse loading over a central sector is studied. The initial response is generated in detail to ascertain the energetics of the response. The total energy is used as a gauge of the stability and accuracy of the solution. It is shown that to obtain accurate and stable initial solutions an extremely high spatial and time resolution is required. This requirement was only evident through an examination of the energy of the system. It is proposed, therefore, to use the total energy of the system as a necessary stability and accuracy criterion for the nonlinear response of conservative systems. The results also demonstrate that even for moderate nonlinearities, the effects of membrane forces have a significant influence on the system.

Structural stability of nonlinear population dynamics.

PubMed

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Structural stability of nonlinear population dynamics

NASA Astrophysics Data System (ADS)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Estimation of Sonic Fatigue by Reduced-Order Finite Element Based Analyses

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2006-01-01

A computationally efficient, reduced-order method is presented for prediction of sonic fatigue of structures exhibiting geometrically nonlinear response. A procedure to determine the nonlinear modal stiffness using commercial finite element codes allows the coupled nonlinear equations of motion in physical degrees of freedom to be transformed to a smaller coupled system of equations in modal coordinates. The nonlinear modal system is first solved using a computationally light equivalent linearization solution to determine if the structure responds to the applied loading in a nonlinear fashion. If so, a higher fidelity numerical simulation in modal coordinates is undertaken to more accurately determine the nonlinear response. Comparisons of displacement and stress response obtained from the reduced-order analyses are made with results obtained from numerical simulation in physical degrees-of-freedom. Fatigue life predictions from nonlinear modal and physical simulations are made using the rainflow cycle counting method in a linear cumulative damage analysis. Results computed for a simple beam structure under a random acoustic loading demonstrate the effectiveness of the approach and compare favorably with results obtained from the solution in physical degrees-of-freedom.

Efficient computational nonlinear dynamic analysis using modal modification response technique

NASA Astrophysics Data System (ADS)

Marinone, Timothy; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2012-08-01

Generally, structural systems contain nonlinear characteristics in many cases. These nonlinear systems require significant computational resources for solution of the equations of motion. Much of the model, however, is linear where the nonlinearity results from discrete local elements connecting different components together. Using a component mode synthesis approach, a nonlinear model can be developed by interconnecting these linear components with highly nonlinear connection elements. The approach presented in this paper, the Modal Modification Response Technique (MMRT), is a very efficient technique that has been created to address this specific class of nonlinear problem. By utilizing a Structural Dynamics Modification (SDM) approach in conjunction with mode superposition, a significantly smaller set of matrices are required for use in the direct integration of the equations of motion. The approach will be compared to traditional analytical approaches to make evident the usefulness of the technique for a variety of test cases.

Novel procedure for characterizing nonlinear systems with memory: 2017 update

NASA Astrophysics Data System (ADS)

Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

2017-05-01

The present article discusses novel improvements in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra or 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] . The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order and alleviate the Curse of Dimensionality (COD) in order to realize practical nonlinear solutions of scientific and engineering interest.

Study of cumulative fatigue damage detection for used parts with nonlinear output frequency response functions based on NARMAX modelling

NASA Astrophysics Data System (ADS)

Huang, Honglan; Mao, Hanying; Mao, Hanling; Zheng, Weixue; Huang, Zhenfeng; Li, Xinxin; Wang, Xianghong

2017-12-01

Cumulative fatigue damage detection for used parts plays a key role in the process of remanufacturing engineering and is related to the service safety of the remanufactured parts. In light of the nonlinear properties of used parts caused by cumulative fatigue damage, the based nonlinear output frequency response functions detection approach offers a breakthrough to solve this key problem. First, a modified PSO-adaptive lasso algorithm is introduced to improve the accuracy of the NARMAX model under impulse hammer excitation, and then, an effective new algorithm is derived to estimate the nonlinear output frequency response functions under rectangular pulse excitation, and a based nonlinear output frequency response functions index is introduced to detect the cumulative fatigue damage in used parts. Then, a novel damage detection approach that integrates the NARMAX model and the rectangular pulse is proposed for nonlinear output frequency response functions identification and cumulative fatigue damage detection of used parts. Finally, experimental studies of fatigued plate specimens and used connecting rod parts are conducted to verify the validity of the novel approach. The obtained results reveal that the new approach can detect cumulative fatigue damages of used parts effectively and efficiently and that the various values of the based nonlinear output frequency response functions index can be used to detect the different fatigue damages or working time. Since the proposed new approach can extract nonlinear properties of systems by only a single excitation of the inspected system, it shows great promise for use in remanufacturing engineering applications.

Theoretical and Analog Studies of the Effects of Nonlinear Stability Derivatives on the Longitudinal Motions of an Aircraft in Response to Step Control Deflections and to the Influence of Proportional Automatic Control

NASA Technical Reports Server (NTRS)

Curfman, Howard J , Jr

1955-01-01

Through theoretical and analog results the effects of two nonlinear stability derivatives on the longitudinal motions of an aircraft have been investigated. Nonlinear functions of pitching-moment and lift coefficients with angle of attack were considered. Analog results of aircraft motions in response to step elevator deflections and to the action of the proportional control systems are presented. The occurrence of continuous hunting oscillations was predicted and demonstrated for the attitude stabilization system with proportional control for certain nonlinear pitching-moment variations and autopilot adjustments.

Transfer function verification and block diagram simplification of a very high-order distributed pole closed-loop servo by means of non-linear time-response simulation

NASA Technical Reports Server (NTRS)

Mukhopadhyay, A. K.

1975-01-01

Linear frequency domain methods are inadequate in analyzing the 1975 Viking Orbiter (VO75) digital tape recorder servo due to dominant nonlinear effects such as servo signal limiting, unidirectional servo control, and static/dynamic Coulomb friction. The frequency loop (speed control) servo of the VO75 tape recorder is used to illustrate the analytical tools and methodology of system redundancy elimination and high order transfer function verification. The paper compares time-domain performance parameters derived from a series of nonlinear time responses with the available experimental data in order to select the best possible analytical transfer function representation of the tape transport (mechanical segment of the tape recorder) from several possible candidates. The study also shows how an analytical time-response simulation taking into account most system nonlinearities can pinpoint system redundancy and overdesign stemming from a strictly empirical design approach. System order reduction is achieved through truncation of individual transfer functions and elimination of redundant blocks.

A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis.

PubMed

Zhou, Shengxi; Yan, Bo; Inman, Daniel J

2018-05-09

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.

Optical nonlinearities in plasmonic metamaterials (Conference Presentation)

NASA Astrophysics Data System (ADS)

Zayats, Anatoly V.

2016-04-01

Metals exhibit strong and fast nonlinearities making metallic, plasmonic, structures very promising for ultrafast all-optical applications at low light intensities. Combining metallic nanostructures in metamaterials provides additional functionalities via prospect of precise engineering of spectral response and dispersion. From this point of view, hyperbolic metamaterials, in particular those based on plasmonic nanorod arrays, provide wealth of exciting possibilities in nonlinear optics offering designed linear and nonlinear properties, polarization control, spontaneous emission control and many others. Experiments and modeling have already demonstrated very strong Kerr-nonlinear response and its ultrafast recovery due to the nonlocal nature of the plasmonic mode of the metamaterial, so that small changes in the permittivity of the metallic component under the excitation modify the nonlocal response that in turn leads to strong changes of the metamaterial transmission. In this talk, we will discuss experimental studies and numerical modeling of second- and third-order nonlinear optical processes in hyperbolic metamaterials based on metallic nanorods and other plasmonic systems where coupling between the resonances plays important role in defining nonlinear response. Second-harmonic generation and ultrafast Kerr-type nonlinearity originating from metallic component of the metamaterial will be considered, including nonlinear magneto-optical effects. Nonlinear optical response of stand-alone as well as integrated metamaterial components will be presented. Some of the examples to be discussed include nonlinear polarization control, nonlinear metamaterial integrated in silicon photonic circuitry and second-harmonic generation, including magneto-optical effects.

Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form

NASA Astrophysics Data System (ADS)

Denis, V.; Jossic, M.; Giraud-Audine, C.; Chomette, B.; Renault, A.; Thomas, O.

2018-06-01

In this article, we address the model identification of nonlinear vibratory systems, with a specific focus on systems modeled with distributed nonlinearities, such as geometrically nonlinear mechanical structures. The proposed strategy theoretically relies on the concept of nonlinear modes of the underlying conservative unforced system and the use of normal forms. Within this framework, it is shown that without internal resonance, a valid reduced order model for a nonlinear mode is a single Duffing oscillator. We then propose an efficient experimental strategy to measure the backbone curve of a particular nonlinear mode and we use it to identify the free parameters of the reduced order model. The experimental part relies on a Phase-Locked Loop (PLL) and enables a robust and automatic measurement of backbone curves as well as forced responses. It is theoretically and experimentally shown that the PLL is able to stabilize the unstable part of Duffing-like frequency responses, thus enabling its robust experimental measurement. Finally, the whole procedure is tested on three experimental systems: a circular plate, a chinese gong and a piezoelectric cantilever beam. It enable to validate the procedure by comparison to available theoretical models as well as to other experimental identification methods.

PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

NASA Astrophysics Data System (ADS)

Liu, Haopeng; Zhu, Yunpeng; Luo, Zhong; Han, Qingkai

2017-09-01

In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

Tracing the transition of a macro electron shuttle into nonlinear response

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Chulki; Prada, Marta; Qin, Hua

We present a study on a macroscopic electron shuttle in the transition from linear to nonlinear response. The shuttle consists of a classical mechanical pendulum situated between two capacitor plates. The metallic pendulum enables mechanical transfer of electrons between the plates, hence allowing to directly trace electron shuttling in the time domain. By applying a high voltage to the plates, we drive the system into a controlled nonlinear response, where we observe period doubling.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Analytical simulation of nonlinear response to seismic test excitations of HDR-VKL (Heissdampfreaktor-Versuchskreislauf) piping system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Srinivasan, M.G.; Kot, C.A.; Mojtahed, M.

The paper describes the analytical modeling, calculations, and results of the posttest nonlinear simulation of high-level seismic testing of the VKL piping system at the HDR Test Facility in Germany. One of the objectives of the tests was to evaluate analytical methods for calculating the nonlinear response of realistic piping systems subjected to high-level seismic excitation that would induce significant plastic deformation. Two out of the six different pipe-support configurations, (ranging from a stiff system with struts and snubbers to a very flexible system with practically no seismic supports), subjected to simulated earthquakes, were tested at very high levels. Themore » posttest nonlinear calculations cover the KWU configuration, a reasonably compliant system with only rigid struts. Responses for 800% safe-shutdown-earthquake loading were calculated using the NONPIPE code. The responses calculated with NONPIPE were found generally to have the same time trends as the measurements but contained under-, over-, and correct estimates of peak values, almost in equal proportions. The only exceptions were the peak strut forces, which were underestimated as a group. The scatter in the peak value estimate of displacements and strut forces was smaller than that for the strains. The possible reasons for the differences and the effort on further analysis are discussed.« less

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Sensitivity of nonlinear photoionization to resonance substructure in collective excitation

PubMed Central

Mazza, T.; Karamatskou, A.; Ilchen, M.; Bakhtiarzadeh, S.; Rafipoor, A. J.; O'Keeffe, P.; Kelly, T. J.; Walsh, N.; Costello, J. T.; Meyer, M.; Santra, R.

2015-01-01

Collective behaviour is a characteristic feature in many-body systems, important for developments in fields such as magnetism, superconductivity, photonics and electronics. Recently, there has been increasing interest in the optically nonlinear response of collective excitations. Here we demonstrate how the nonlinear interaction of a many-body system with intense XUV radiation can be used as an effective probe for characterizing otherwise unresolved features of its collective response. Resonant photoionization of atomic xenon was chosen as a case study. The excellent agreement between experiment and theory strongly supports the prediction that two distinct poles underlie the giant dipole resonance. Our results pave the way towards a deeper understanding of collective behaviour in atoms, molecules and solid-state systems using nonlinear spectroscopic techniques enabled by modern short-wavelength light sources. PMID:25854939

Nonlinear random response prediction using MSC/NASTRAN

NASA Technical Reports Server (NTRS)

Robinson, J. H.; Chiang, C. K.; Rizzi, S. A.

1993-01-01

An equivalent linearization technique was incorporated into MSC/NASTRAN to predict the nonlinear random response of structures by means of Direct Matrix Abstract Programming (DMAP) modifications and inclusion of the nonlinear differential stiffness module inside the iteration loop. An iterative process was used to determine the rms displacements. Numerical results obtained for validation on simple plates and beams are in good agreement with existing solutions in both the linear and linearized regions. The versatility of the implementation will enable the analyst to determine the nonlinear random responses for complex structures under combined loads. The thermo-acoustic response of a hexagonal thermal protection system panel is used to highlight some of the features of the program.

Bandlimited computerized improvements in characterization of nonlinear systems with memory

NASA Astrophysics Data System (ADS)

Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

2016-05-01

The present article discusses some inroads in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] over many years of developmental research. The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms on the system are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order in order to combat and reasonably alleviate the curse of dimensionality.

Reduced-Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.

Reduced Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of an RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.

A nonlinear dynamics of trunk kinematics during manual lifting tasks.

PubMed

Khalaf, Tamer; Karwowski, Waldemar; Sapkota, Nabin

2015-01-01

Human responses at work may exhibit nonlinear properties where small changes in the initial task conditions can lead to large changes in system behavior. Therefore, it is important to study such nonlinearity to gain a better understanding of human performance under a variety of physical, perceptual, and cognitive tasks conditions. The main objective of this study was to investigate whether the human trunk kinematics data during a manual lifting task exhibits nonlinear behavior in terms of determinist chaos. Data related to kinematics of the trunk with respect to the pelvis were collected using Industrial Lumbar Motion Monitor (ILMM), and analyzed applying the nonlinear dynamical systems methodology. Nonlinear dynamics quantifiers of Lyapunov exponents and Kaplan-Yorke dimensions were calculated and analyzed under different task conditions. The study showed that human trunk kinematics during manual lifting exhibits chaotic behavior in terms of trunk sagittal angular displacement, velocity and acceleration. The findings support the importance of accounting for nonlinear dynamical properties of biomechanical responses to lifting tasks.

On the benefit of DMT modulation in nonlinear VLC systems.

PubMed

Qian, Hua; Cai, Sunzeng; Yao, Saijie; Zhou, Ting; Yang, Yang; Wang, Xudong

2015-02-09

In a visible light communication (VLC) system, the nonlinear characteristic of the light emitting diode (LED) in transmitter is a limiting factor of system performance. Modern modulation signals with large peak-to-power-ratio (PAPR) suffers uneven distortion. The nonlinear response directly impacts the intensity modulation and direct detection VLC system with pulse-amplitude modulation (PAM). The amplitude of the PAM signal is distorted unevenly and large signal is vulnerable to noise. Orthogonal linear transformations, such as discrete multi-tone (DMT) modulation, can spread the nonlinear effects evenly to each data symbol, thus perform better than PAM signals. In this paper, we provide theoretical analysis on the benefit of DMT modulation in nonlinear VLC system. We show that the DMT modulation is a better choice than the PAM modulation for the VLC system as the DMT modulation is more robust against nonlinearity. We also show that the post-distortion nonlinear elimination method, which is applied at the receiver, can be a reliable solution to the nonlinear VLC system. Simulation results show that the post-distortion greatly improves the system performance for the DMT modulation.

Nonlinear tapping dynamics of multi-walled carbon nanotube tipped atomic force microcantilevers

NASA Astrophysics Data System (ADS)

Lee, S. I.; Howell, S. W.; Raman, A.; Reifenberger, R.; Nguyen, C. V.; Meyyappan, M.

2004-05-01

The nonlinear dynamics of an atomic force microcantilever (AFM) with an attached multi-walled carbon nanotube (MWCNT) tip is investigated experimentally and theoretically. We present the experimental nonlinear frequency response of a MWCNT tipped microcantilever in the tapping mode. Several unusual features in the response distinguish it from those traditionally observed for conventional tips. The MWCNT tipped AFM probe is apparently immune to conventional imaging instabilities related to the coexistence of attractive and repulsive tapping regimes. A theoretical interaction model for the system using an Euler elastica MWCNT model is developed and found to predict several unusual features of the measured nonlinear response.

Spectral analysis for nonstationary and nonlinear systems: a discrete-time-model-based approach.

PubMed

He, Fei; Billings, Stephen A; Wei, Hua-Liang; Sarrigiannis, Ptolemaios G; Zhao, Yifan

2013-08-01

A new frequency-domain analysis framework for nonlinear time-varying systems is introduced based on parametric time-varying nonlinear autoregressive with exogenous input models. It is shown how the time-varying effects can be mapped to the generalized frequency response functions (FRFs) to track nonlinear features in frequency, such as intermodulation and energy transfer effects. A new mapping to the nonlinear output FRF is also introduced. A simulated example and the application to intracranial electroencephalogram data are used to illustrate the theoretical results.

A 1-D model of the nonlinear dynamics of the human lumbar intervertebral disc

NASA Astrophysics Data System (ADS)

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J.

2017-01-01

Lumped parameter models of the spine have been developed to investigate its response to whole body vibration. However, these models assume the behaviour of the intervertebral disc to be linear-elastic. Recently, the authors have reported on the nonlinear dynamic behaviour of the human lumbar intervertebral disc. This response was shown to be dependent on the applied preload and amplitude of the stimuli. However, the mechanical properties of a standard linear elastic model are not dependent on the current deformation state of the system. The aim of this study was therefore to develop a model that is able to describe the axial, nonlinear quasi-static response and to predict the nonlinear dynamic characteristics of the disc. The ability to adapt the model to an individual disc's response was a specific focus of the study, with model validation performed against prior experimental data. The influence of the numerical parameters used in the simulations was investigated. The developed model exhibited an axial quasi-static and dynamic response, which agreed well with the corresponding experiments. However, the model needs further improvement to capture additional peculiar characteristics of the system dynamics, such as the change of mean point of oscillation exhibited by the specimens when oscillating in the region of nonlinear resonance. Reference time steps were identified for specific integration scheme. The study has demonstrated that taking into account the nonlinear-elastic behaviour typical of the intervertebral disc results in a predicted system oscillation much closer to the physiological response than that provided by linear-elastic models. For dynamic analysis, the use of standard linear-elastic models should be avoided, or restricted to study cases where the amplitude of the stimuli is relatively small.

Comparison of heaving buoy and oscillating flap wave energy converters

NASA Astrophysics Data System (ADS)

Abu Bakar, Mohd Aftar; Green, David A.; Metcalfe, Andrew V.; Najafian, G.

2013-04-01

Waves offer an attractive source of renewable energy, with relatively low environmental impact, for communities reasonably close to the sea. Two types of simple wave energy converters (WEC), the heaving buoy WEC and the oscillating flap WEC, are studied. Both WECs are considered as simple energy converters because they can be modelled, to a first approximation, as single degree of freedom linear dynamic systems. In this study, we estimate the response of both WECs to typical wave inputs; wave height for the buoy and corresponding wave surge for the flap, using spectral methods. A nonlinear model of the oscillating flap WEC that includes the drag force, modelled by the Morison equation is also considered. The response to a surge input is estimated by discrete time simulation (DTS), using central difference approximations to derivatives. This is compared with the response of the linear model obtained by DTS and also validated using the spectral method. Bendat's nonlinear system identification (BNLSI) technique was used to analyze the nonlinear dynamic system since the spectral analysis was only suitable for linear dynamic system. The effects of including the nonlinear term are quantified.

Sensitivity of nonlinear photoionization to resonance substructure in collective excitation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mazza, T.; Karamatskou, A.; Ilchen, M.

Collective behaviour is a characteristic feature in many-body systems, important for developments in fields such as magnetism, superconductivity, photonics and electronics. Recently, there has been increasing interest in the optically nonlinear response of collective excitations. Here we demonstrate how the nonlinear interaction of a many-body system with intense XUV radiation can be used as an effective probe for characterizing otherwise unresolved features of its collective response. Resonant photoionization of atomic xenon was chosen as a case study. The excellent agreement between experiment and theory strongly supports the prediction that two distinct poles underlie the giant dipole resonance. Our results pavemore » the way towards a deeper understanding of collective behaviour in atoms, molecules and solid-state systems using nonlinear spectroscopic techniques enabled by modern short-wavelength light sources.« less

Sensitivity of nonlinear photoionization to resonance substructure in collective excitation

DOE PAGES

Mazza, T.; Karamatskou, A.; Ilchen, M.; ...

2015-04-09

Collective behaviour is a characteristic feature in many-body systems, important for developments in fields such as magnetism, superconductivity, photonics and electronics. Recently, there has been increasing interest in the optically nonlinear response of collective excitations. Here we demonstrate how the nonlinear interaction of a many-body system with intense XUV radiation can be used as an effective probe for characterizing otherwise unresolved features of its collective response. Resonant photoionization of atomic xenon was chosen as a case study. The excellent agreement between experiment and theory strongly supports the prediction that two distinct poles underlie the giant dipole resonance. Our results pavemore » the way towards a deeper understanding of collective behaviour in atoms, molecules and solid-state systems using nonlinear spectroscopic techniques enabled by modern short-wavelength light sources.« less

Nonlinear dynamics analysis of the spur gear system for railway locomotive

NASA Astrophysics Data System (ADS)

Wang, Junguo; He, Guangyue; Zhang, Jie; Zhao, Yongxiang; Yao, Yuan

2017-02-01

Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincaré maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

A nonlinear delayed model for the immune response in the presence of viral mutation

NASA Astrophysics Data System (ADS)

Messias, D.; Gleria, Iram; Albuquerque, S. S.; Canabarro, Askery; Stanley, H. E.

2018-02-01

We consider a delayed nonlinear model of the dynamics of the immune system against a viral infection that contains a wild-type virus and a mutant. We consider the finite response time of the immune system and find sustained oscillatory behavior as well as chaotic behavior triggered by the presence of delays. We present a numeric analysis and some analytical results.

Parametric system identification of resonant micro/nanosystems operating in a nonlinear response regime

NASA Astrophysics Data System (ADS)

Sabater, A. B.; Rhoads, J. F.

2017-02-01

The parametric system identification of macroscale resonators operating in a nonlinear response regime can be a challenging research problem, but at the micro- and nanoscales, experimental constraints add additional complexities. For example, due to the small and noisy signals micro/nanoresonators produce, a lock-in amplifier is commonly used to characterize the amplitude and phase responses of the systems. While the lock-in enables detection, it also prohibits the use of established time-domain, multi-harmonic, and frequency-domain methods, which rely upon time-domain measurements. As such, the only methods that can be used for parametric system identification are those based on fitting experimental data to an approximate solution, typically derived via perturbation methods and/or Galerkin methods, of a reduced-order model. Thus, one could view the parametric system identification of micro/nanosystems operating in a nonlinear response regime as the amalgamation of four coupled sub-problems: nonparametric system identification, or proper experimental design and data acquisition; the generation of physically consistent reduced-order models; the calculation of accurate approximate responses; and the application of nonlinear least-squares parameter estimation. This work is focused on the theoretical foundations that underpin each of these sub-problems, as the methods used to address one sub-problem can strongly influence the results of another. To provide context, an electromagnetically transduced microresonator is used as an example. This example provides a concrete reference for the presented findings and conclusions.

A method for the analysis of nonlinearities in aircraft dynamic response to atmospheric turbulence

NASA Technical Reports Server (NTRS)

Sidwell, K.

1976-01-01

An analytical method is developed which combines the equivalent linearization technique for the analysis of the response of nonlinear dynamic systems with the amplitude modulated random process (Press model) for atmospheric turbulence. The method is initially applied to a bilinear spring system. The analysis of the response shows good agreement with exact results obtained by the Fokker-Planck equation. The method is then applied to an example of control-surface displacement limiting in an aircraft with a pitch-hold autopilot.

Out-of-unison resonance in weakly nonlinear coupled oscillators

PubMed Central

Hill, T. L.; Cammarano, A.; Neild, S. A.; Wagg, D. J.

2015-01-01

Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems. PMID:25568619

The analysis on nonlinear control of the aircraft arresting system

NASA Astrophysics Data System (ADS)

Song, Jinchun; Du, Tianrong

2005-12-01

The aircraft arresting system is a complicated nonlinear system. This paper analyzes the mechanical-hydraulic structure of aircraft arresting system composed of electro hydraulic valve and establishes the dynamic equation of the aircraft arresting system. Based on the state-feedback linearization of nonlinear system, a PD-based controller is synthesized. Simulation studies indicate, while arresting the different type aircraft, the proposed controller has fast response, good tracking performance and strong robustness. By tuning the parameters of the PD controller, a satisfactory control performance can be guaranteed.

Nonlinear dynamic modeling of surface defects in rolling element bearing systems

NASA Astrophysics Data System (ADS)

Rafsanjani, Ahmad; Abbasion, Saeed; Farshidianfar, Anoushiravan; Moeenfard, Hamid

2009-01-01

In this paper an analytical model is proposed to study the nonlinear dynamic behavior of rolling element bearing systems including surface defects. Various surface defects due to local imperfections on raceways and rolling elements are introduced to the proposed model. The contact force of each rolling element described according to nonlinear Hertzian contact deformation and the effect of internal radial clearance has been taken into account. Mathematical expressions were derived for inner race, outer race and rolling element local defects. To overcome the strong nonlinearity of the governing equations of motion, a modified Newmark time integration technique was used to solve the equations of motion numerically. The results were obtained in the form of time series, frequency responses and phase trajectories. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The classical Floquet theory has been applied to the proposed model to investigate the linear stability of the defective bearing rotor systems as the parameters of the system changes. The peak-to-peak frequency response of the system for each case is obtained and the basic routes to periodic, quasi-periodic and chaotic motions for different internal radial clearances are determined. The current study provides a powerful tool for design and health monitoring of machine systems.

Dynamic analysis of nonlinear rotor-housing systems

NASA Technical Reports Server (NTRS)

Noah, Sherif T.

1988-01-01

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.

Characterizing driver-response relationships in marine pelagic ecosystems for improved ocean management.

PubMed

Hunsicker, Mary E; Kappel, Carrie V; Selkoe, Kimberly A; Halpern, Benjamin S; Scarborough, Courtney; Mease, Lindley; Amrhein, Alisan

2016-04-01

Scientists and resource managers often use methods and tools that assume ecosystem components respond linearly to environmental drivers and human stressors. However, a growing body of literature demonstrates that many relationships are-non-linear, where small changes in a driver prompt a disproportionately large ecological response. We aim to provide a comprehensive assessment of the relationships between drivers and ecosystem components to identify where and when non-linearities are likely to occur. We focused our analyses on one of the best-studied marine systems, pelagic ecosystems, which allowed us to apply robust statistical techniques on a large pool of previously published studies. In this synthesis, we (1) conduct a wide literature review on single driver-response relationships in pelagic systems, (2) use statistical models to identify the degree of non-linearity in these relationships, and (3) assess whether general patterns exist in the strengths and shapes of non-linear relationships across drivers. Overall we found that non-linearities are common in pelagic ecosystems, comprising at least 52% of all driver-response relation- ships. This is likely an underestimate, as papers with higher quality data and analytical approaches reported non-linear relationships at a higher frequency (on average 11% more). Consequently, in the absence of evidence for a linear relationship, it is safer to assume a relationship is non-linear. Strong non-linearities can lead to greater ecological and socioeconomic consequences if they are unknown (and/or unanticipated), but if known they may provide clear thresholds to inform management targets. In pelagic systems, strongly non-linear relationships are often driven by climate and trophodynamic variables but are also associated with local stressors, such as overfishing and pollution, that can be more easily controlled by managers. Even when marine resource managers cannot influence ecosystem change, they can use information about threshold responses to guide how other stressors are managed and to adapt to new ocean conditions. As methods to detect and reduce uncertainty around threshold values improve, managers will be able to better understand and account for ubiquitous non-linear relationships.

Nonlinear analysis of a rotor-bearing system using describing functions

NASA Astrophysics Data System (ADS)

Maraini, Daniel; Nataraj, C.

2018-04-01

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

Vortex-induced vibrations mitigation through a nonlinear energy sink

NASA Astrophysics Data System (ADS)

Dai, H. L.; Abdelkefi, A.; Wang, L.

2017-01-01

The passive suppression mechanism of the vortex-induced vibrations (VIV) of the cylinder by means of an essentially nonlinear element, the nonlinear energy sink (NES) is investigated. The flow-induced loads on the cylinder are modeled using a prevalent van der Pol oscillator which is experimentally validated, coupling to the structural vibrations in the presence of the NES structure. Based on the coupled nonlinear governing equations of motion, the performed analysis indicates that the mass and damping of NES have significant effects on the coupled frequency and damping of the aero-elastic system, leading to the shift of synchronization region and mitigation of vibration responses. It is demonstrated that the coupled system of flow-cylinder-NES behaves resonant interactions, showing periodic, aperiodic, and multiple stable responses which depend on the values of the NES parameters. In addition, it is found that the occurrence of multiple stable responses can enhance the nonlinear energy pumping effect, resulting in the increment of transferring energy from the flow via the cylinder to the NES, which is related to the essential nonlinearity of the sink stiffness. This results in a significant reduction in the VIV amplitudes of the primary circular cylinder for appropriate NES parameter values.

Periodic response of nonlinear systems

NASA Technical Reports Server (NTRS)

Nataraj, C.; Nelson, H. D.

1988-01-01

A procedure is developed to determine approximate periodic solutions of autonomous and non-autonomous systems. The trignometric collocation method (TCM) is formalized to allow for the analysis of relatively small order systems directly in physical coordinates. The TCM is extended to large order systems by utilizing modal analysis in a component mode synthesis strategy. The procedure was coded and verified by several check cases. Numerical results for two small order mechanical systems and one large order rotor dynamic system are presented. The method allows for the possibility of approximating periodic responses for large order forced and self-excited nonlinear systems.

Precluding nonlinear ISI in direct detection long-haul fiber optic systems

NASA Technical Reports Server (NTRS)

Swenson, Norman L.; Shoop, Barry L.; Cioffi, John M.

1991-01-01

Long-distance, high-rate fiber optic systems employing directly modulated 1.55-micron single-mode lasers and conventional single-mode fiber suffer severe intersymbol interference (ISI) with a large nonlinear component. A method of reducing the nonlinearity of the ISI, thereby making linear equalization more viable, is investigated. It is shown that the degree of nonlinearity is highly dependent on the choice of laser bias current, and that in some cases the ISI nonlinearity can be significantly reduced by biasing the laser substantially above threshold. Simulation results predict that an increase in signal-to-nonlinear-distortion ratio as high as 25 dB can be achieved for synchronously spaced samples at an optimal sampling phase by increasing the bias current from 1.2 times threshold to 3.5 times threshold. The high SDR indicates that a linear tapped delay line equalizer could be used to mitigate ISI. Furthermore, the shape of the pulse response suggests that partial response precoding and digital feedback equalization would be particularly effective for this channel.

Human middle-ear nonlinearity measurements using laser Doppler vibrometry

NASA Astrophysics Data System (ADS)

Gladiné, Kilian; Muyshondt, Pieter G. G.; Dirckx, Joris J. J.

2017-12-01

It has long been supposed that the middle-ear has near to perfect linear characteristics, and several attempts have been made to investigate this hypothesis. In conclusion, the middle-ear was regarded as a linear system at least up till sound pressure levels of 120 dB. Because of the linear relationship between Doppler shift of light and the vibration velocity of the object on which the light is reflected, laser Doppler vibrometry (LDV) is an intrinsically highly linear measurement technique. Therefore it allows straightforward detection of very small nonlinearities in a vibration response. In this paper, laser Doppler vibrometry and multisine stimulation are used to detect nonlinear distortions in the vibration response at the umbo of the tympanic membrane of seven human cadaver temporal bones. Nonlinear distortions were detected starting from sound pressure levels of 99 dB and measurements were performed up to 120 dB. These distortions can be subdivided into even degree (e.g. quadratic distortion tones) and odd degree nonlinear distortions (e.g. cubic distortion tones). We illustrate that with odd multisine stimulation the level of even and odd degree nonlinear distortions can be investigated separately. In conclusion, laser Doppler vibrometry is an adequate tool to detect nonlinear distortions in the middle-ear system and to quantify the level of such distortions even at 57 dB below the vibration response. The possibility to analyze even degree and odd degree nonlinear distortion levels separately can help in future work to pinpoint the source of the nonlinearity.

Nonlinear flow response of soft hair beds

NASA Astrophysics Data System (ADS)

Alvarado, José; Comtet, Jean; de Langre, Emmanuel; Hosoi, A. E.

2017-10-01

We are `hairy' on the inside: beds of passive fibres anchored to a surface and immersed in fluids are prevalent in many biological systems, including intestines, tongues, and blood vessels. These hairs are soft enough to deform in response to stresses from fluid flows. Yet fluid stresses are in turn affected by hair deformation, leading to a coupled elastoviscous problem that is poorly understood. Here we investigate a biomimetic model system of elastomer hair beds subject to shear-driven Stokes flows. We characterize this system with a theoretical model that accounts for the large-deformation flow response of hair beds. Hair bending results in a drag-reducing nonlinearity because the hair tip lowers towards the base, widening the gap through which fluid flows. When hairs are cantilevered at an angle subnormal to the surface, flow against the grain bends hairs away from the base, narrowing the gap. The flow response of angled hair beds is axially asymmetric and amounts to a rectification nonlinearity. We identify an elastoviscous parameter that controls nonlinear behaviour. Our study raises the hypothesis that biological hairy surfaces function to reduce fluid drag. Furthermore, angled hairs may be incorporated in the design of integrated microfluidic components, such as diodes and pumps.

A new method for analysis of limit cycle behavior of the NASA/JPL 70-meter antenna axis servos

NASA Technical Reports Server (NTRS)

Hill, R. E.

1989-01-01

A piecewise linear method of analyzing the effects of discontinuous nonlinearities on control system performance is described. The limit cycle oscillatory behavior of the system resulting from the nonlinearities is described in terms of a sequence of linear system transient responses. The equations are derived which relate the initial and the terminal conditions of successive transients and the boundary conditions imposed by the non-linearities. The method leads to a convenient computation algorithm for prediction of limit cycle characteristics resulting from discontinuous nonlinearities such as friction, deadzones, and hysteresis.

Characterizing Observed Limit Cycles in the Cassini Main Engine Guidance Control System

NASA Technical Reports Server (NTRS)

Rizvi, Farheen; Weitl, Raquel M.

2011-01-01

The Cassini spacecraft dynamics-related telemetry during long Main Engine (ME) burns has indicated the presence of stable limit cycles between 0.03-0.04 Hz frequencies. These stable limit cycles cause the spacecraft to possess non-zero oscillating rates for extended periods of time. This indicates that the linear ME guidance control system does not model the complete dynamics of the spacecraft. In this study, we propose that the observed limit cycles in the spacecraft dynamics telemetry appear from a stable interaction between the unmodeled nonlinear elements in the ME guidance control system. Many nonlinearities in the control system emerge from translating the linear engine gimbal actuator (EGA) motion into a spacecraft rotation. One such nonlinearity comes from the gear backlash in the EGA system, which is the focus of this paper. The limit cycle characteristics and behavior can be predicted by modeling this gear backlash nonlinear element via a describing function and studying the interaction of this describing function with the overall dynamics of the spacecraft. The linear ME guidance controller and gear backlash nonlinearity are modeled analytically. The frequency, magnitude, and nature of the limit cycle are obtained from the frequency response of the ME guidance controller and nonlinear element. In addition, the ME guidance controller along with the nonlinearity is simulated. The simulation response contains a limit cycle with similar characterstics as predicted analytically: 0.03-0.04 Hz frequency and stable, sustained oscillations. The analytical and simulated limit cycle responses are compared to the flight telemetry for long burns such as the Saturn Orbit Insertion and Main Engine Orbit Trim Maneuvers. The analytical and simulated limit cycle characteristics compare well with the actual observed limit cycles in the flight telemetry. Both have frequencies between 0.03-0.04 Hz and stable oscillations. This work shows that the stable limit cycles occur due to the interaction between the unmodeled nonlinear elements and linear ME guidance controller.

Nonlinear rotordynamics analysis. [Space Shuttle Main Engine turbopumps

NASA Technical Reports Server (NTRS)

Noah, Sherif T.

1991-01-01

Effective analysis tools were developed for predicting the nonlinear rotordynamic behavior of the Space Shuttle Main Engine (SSME) turbopumps under steady and transient operating conditions. Using these methods, preliminary parametric studies were conducted on both generic and actual HPOTP (high pressure oxygen turbopump) models. In particular, a novel modified harmonic balance/alternating Fourier transform (HB/AFT) method was developed and used to conduct a preliminary study of the effects of fluid, bearing and seal forces on the unbalanced response of a multi-disk rotor in the presence of bearing clearances. The method makes it possible to determine periodic, sub-, super-synchronous and chaotic responses of a rotor system. The method also yields information about the stability of the obtained response, thus allowing bifurcation analyses. This provides a more effective capability for predicting the response under transient conditions by searching in proximity of resonance peaks. Preliminary results were also obtained for the nonlinear transient response of an actual HPOTP model using an efficient, newly developed numerical method based on convolution integration. Currently, the HB/AFT is being extended for determining the aperiodic response of nonlinear systems. Initial results show the method to be promising.

A single-degree-of-freedom model for non-linear soil amplification

USGS Publications Warehouse

Erdik, Mustafa Ozder

1979-01-01

For proper understanding of soil behavior during earthquakes and assessment of a realistic surface motion, studies of the large-strain dynamic response of non-linear hysteretic soil systems are indispensable. Most of the presently available studies are based on the assumption that the response of a soil deposit is mainly due to the upward propagation of horizontally polarized shear waves from the underlying bedrock. Equivalent-linear procedures, currently in common use in non-linear soil response analysis, provide a simple approach and have been favorably compared with the actual recorded motions in some particular cases. Strain compatibility in these equivalent-linear approaches is maintained by selecting values of shear moduli and damping ratios in accordance with the average soil strains, in an iterative manner. Truly non-linear constitutive models with complete strain compatibility have also been employed. The equivalent-linear approaches often raise some doubt as to the reliability of their results concerning the system response in high frequency regions. In these frequency regions the equivalent-linear methods may underestimate the surface motion by as much as a factor of two or more. Although studies are complete in their methods of analysis, they inevitably provide applications pertaining only to a few specific soil systems, and do not lead to general conclusions about soil behavior. This report attempts to provide a general picture of the soil response through the use of a single-degree-of-freedom non-linear-hysteretic model. Although the investigation is based on a specific type of nonlinearity and a set of dynamic soil properties, the method described does not limit itself to these assumptions and is equally applicable to other types of nonlinearity and soil parameters.

Dynamic Nonlinear Elastic Stability of Helicopter Rotor Blades in Hover and in Forward Flight

NASA Technical Reports Server (NTRS)

Friedmann, P.; Tong, P.

1972-01-01

Equations for large coupled flap-lag motion of hingeless elastic helicopter blades are consistently derived. Only torsionally-rigid blades excited by quasi-steady aerodynamic loads are considered. The nonlinear equations of motion in the time and space variables are reduced to a system of coupled nonlinear ordinary differential equations with periodic coefficients, using Galerkin's method for the space variables. The nonlinearities present in the equations are those arising from the inclusion of moderately large deflections in the inertia and aerodynamic loading terms. The resulting system of nonlinear equations has been solved, using an asymptotic expansion procedure in multiple time scales. The stability boundaries, amplitudes of nonlinear response, and conditions for existence of limit cycles are obtained analytically. Thus, the different roles played by the forcing function, parametric excitation, and nonlinear coupling in affecting the solution can be easily identified, and the basic physical mechanism of coupled flap-lag response becomes clear. The effect of forward flight is obtained with the requirement of trimmed flight at fixed values of the thrust coefficient.

Application of the concept of dynamic trim control and nonlinear system inverses to automatic control of a vertical attitude takeoff and landing aircraft

NASA Technical Reports Server (NTRS)

Smith, G. A.; Meyer, G.

1981-01-01

A full envelope automatic flight control system based on nonlinear inverse systems concepts has been applied to a vertical attitude takeoff and landing (VATOL) fighter aircraft. A new method for using an airborne digital aircraft model to perform the inversion of a nonlinear aircraft model is presented together with the results of a simulation study of the nonlinear inverse system concept for the vertical-attitude hover mode. The system response to maneuver commands in the vertical attitude was found to be excellent; and recovery from large initial offsets and large disturbances was found to be very satisfactory.

Dynamic analysis of a flexible spacecraft with rotating components. Volume 1: Analytical developments

NASA Technical Reports Server (NTRS)

Bodley, C. S.; Devers, A. D.; Park, A. C.

1975-01-01

Analytical procedures and digital computer code are presented for the dynamic analysis of a flexible spacecraft with rotating components. Topics, considered include: (1) nonlinear response in the time domain, and (2) linear response in the frequency domain. The spacecraft is assumed to consist of an assembly of connected rigid or flexible subassemblies. The total system is not restricted to a topological connection arrangement and may be acting under the influence of passive or active control systems and external environments. The analytics and associated digital code provide the user with the capability to establish spacecraft system nonlinear total response for specified initial conditions, linear perturbation response about a calculated or specified nominal motion, general frequency response and graphical display, and spacecraft system stability analysis.

Nonlinear modal resonances in low-gravity slosh-spacecraft systems

NASA Technical Reports Server (NTRS)

Peterson, Lee D.

1991-01-01

Nonlinear models of low gravity slosh, when coupled to spacecraft vibrations, predict intense nonlinear eigenfrequency shifts at zero gravity. These nonlinear frequency shifts are due to internal quadratic and cubic resonances between fluid slosh modes and spacecraft vibration modes. Their existence has been verified experimentally, and they cannot be correctly modeled by approximate, uncoupled nonlinear models, such as pendulum mechanical analogs. These predictions mean that linear slosh assumptions for spacecraft vibration models can be invalid, and may lead to degraded control system stability and performance. However, a complete nonlinear modal analysis will predict the correct dynamic behavior. This paper presents the analytical basis for these results, and discusses the effect of internal resonances on the nonlinear coupled response at zero gravity.

Recent Applications of the Volterra Theory to Aeroelastic Phenomena

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Haji, Muhammad R; Prazenica, Richard J.

2005-01-01

The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in experimental aeroelasticity are reviewed. These results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the Active Aeroelastic Wing (AAW) aircraft.

Formulation of the aeroelastic stability and response problem of coupled rotor/support systems

NASA Technical Reports Server (NTRS)

Warmbrodt, W.; Friedmann, P.

1979-01-01

The consistent formulation of the governing nonlinear equations of motion for a coupled rotor/support system is presented. Rotor/support coupling is clearly documented by enforcing dynamic equilibrium between the rotor and the moving flexible support. The nonlinear periodic coefficient equations of motion are applicable to both coupled rotor/fuselage aeroelastic problems of helicopters in hover or forward flight and coupled rotor/tower dynamics of a large horizontal axis wind turbine (HAWT). Finally, the equations of motion are used to study the influence of flexible supports and nonlinear terms on rotor aeroelastic stability and response of a large two-bladed HAWT.

Experimental Modal Analysis and Dynamic Component Synthesis. Volume 2. Measurement Techniques for Experimental Modal Analysis

DTIC Science & Technology

1987-12-01

A- -- HZ LIN 3.0 . Be-I. •,% •4’ 20.. 0-p -4 -0 30a 4a j0 O0 100a 10 4140 iSo 130 20C. 2210 140 M* LIN g•" %g Figur 19. Cyli Avergin (N4,M 0 -3- 40...shows that the degree of nonlinearity of a structure varies according to the characteristics of the system. That is, welded structures will usually...exhibit a linear response; where a riveted or spot welded structure exhibits a very nonlinear response [52]. As an example of a nonlinear system

"NONLINEAR DYNAMIC SYSTEMS RESPONSE TO NON-STATIONARY EXCITATION USING THE WAVELET TRANSFORM"

DOE Office of Scientific and Technical Information (OSTI.GOV)

SPANOS, POL D.

2006-01-15

The objective of this research project has been the development of techniques for estimating the power spectra of stochastic processes using wavelet transform, and the development of related techniques for determining the response of linear/nonlinear systems to excitations which are described via the wavelet transform. Both of the objectives have been achieved, and the research findings have been disseminated in papers in archival journals and technical conferences.

Modeling off-resonant nonlinear-optical cascading in mesoscopic thin films and guest-host molecular systems

NASA Astrophysics Data System (ADS)

Dawson, Nathan J.; Andrews, James H.; Crescimanno, Michael

2013-12-01

A model for off-resonant microscopic cascading of (hyper)polarizabilities is developed using a self-consistent field approach to study mesoscopic systems of nonlinear polarizable atoms and molecules. We find enhancements in the higher-order susceptibilities resulting from geometrical and boundary orientation effects. We include an example of the dependence on excitation beam cross sectional structure and a simplified derivation of the microscopic cascading of the nonlinear-optical response in guest-host systems.

Robust approximation-free prescribed performance control for nonlinear systems and its application

NASA Astrophysics Data System (ADS)

Sun, Ruisheng; Na, Jing; Zhu, Bin

2018-02-01

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.

Identifying ultrasensitive HGF dose-response functions in a 3D mammalian system for synthetic morphogenesis.

PubMed

Senthivel, Vivek Raj; Sturrock, Marc; Piedrafita, Gabriel; Isalan, Mark

2016-12-16

Nonlinear responses to signals are widespread natural phenomena that affect various cellular processes. Nonlinearity can be a desirable characteristic for engineering living organisms because it can lead to more switch-like responses, similar to those underlying the wiring in electronics. Steeper functions are described as ultrasensitive, and can be applied in synthetic biology by using various techniques including receptor decoys, multiple co-operative binding sites, and sequential positive feedbacks. Here, we explore the inherent non-linearity of a biological signaling system to identify functions that can potentially be exploited using cell genome engineering. For this, we performed genome-wide transcription profiling to identify genes with ultrasensitive response functions to Hepatocyte Growth Factor (HGF). We identified 3,527 genes that react to increasing concentrations of HGF, in Madin-Darby canine kidney (MDCK) cells, grown as cysts in 3D collagen cell culture. By fitting a generic Hill function to the dose-responses of these genes we obtained a measure of the ultrasensitivity of HGF-responsive genes, identifying a subset with higher apparent Hill coefficients (e.g. MMP1, TIMP1, SNORD75, SNORD86 and ERRFI1). The regulatory regions of these genes are potential candidates for future engineering of synthetic mammalian gene circuits requiring nonlinear responses to HGF signalling.

Jump phenomena. [large amplitude responses of nonlinear systems

NASA Technical Reports Server (NTRS)

Reiss, E. L.

1980-01-01

The paper considers jump phenomena composed of large amplitude responses of nonlinear systems caused by small amplitude disturbances. Physical problems where large jumps in the solution amplitude are important features of the response are described, including snap buckling of elastic shells, chemical reactions leading to combustion and explosion, and long-term climatic changes of the earth's atmosphere. A new method of rational functions was then developed which consists of representing the solutions of the jump problems as rational functions of the small disturbance parameter; this method can solve jump problems explicitly.

Special class of nonlinear damping models in flexible space structures

NASA Technical Reports Server (NTRS)

Hu, Anren; Singh, Ramendra P.; Taylor, Lawrence W.

1991-01-01

A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

Nonlinear ultrafast optical response in organic molecular crystals

NASA Astrophysics Data System (ADS)

Rahman, Talat S.; Turkowski, Volodymyr; Leuenberger, Michael N.

2012-02-01

We analyze possible nonlinear excitonic effects in the organic molecule crystals by using a combined time-dependent DFT and many-body approach. In particular, we analyze possible effects of the time-dependent (retarded)interaction between different types of excitations, Frenkel excitons, charge transfer excitons and excimers, on the electric and the optical response of the system. We pay special attention to the case of constant electric field and ultrafast pulses, including that of four-wave mixing experiments. As a specific application we examine the optical excitations of pentacene nanocrystals and compare the results with available experimental data.[1] Our results demostrate that the nonlinear effects can play an important role in the optical response of these systems. [1] A. Kabakchiev, ``Scanning Tunneling Luminescence of Pentacene Nanocrystals'', PhD Thesis (EPFL, Lausanne, 2010).

Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play

NASA Astrophysics Data System (ADS)

Huang, Rui; Hu, Haiyan; Zhao, Yonghui

2013-10-01

In this paper, the effects of structural nonlinearity due to free-play in both leading-edge and trailing-edge outboard control surfaces on the linear flutter control system are analyzed for an aeroelastic model of three-dimensional multiple-actuated-wing. The free-play nonlinearities in the control surfaces are modeled theoretically by using the fictitious mass approach. The nonlinear aeroelastic equations of the presented model can be divided into nine sub-linear modal-based aeroelastic equations according to the different combinations of deflections of the leading-edge and trailing-edge outboard control surfaces. The nonlinear aeroelastic responses can be computed based on these sub-linear aeroelastic systems. To demonstrate the effects of nonlinearity on the linear flutter control system, a single-input and single-output controller and a multi-input and multi-output controller are designed based on the unconstrained optimization techniques. The numerical results indicate that the free-play nonlinearity can lead to either limit cycle oscillations or divergent motions when the linear control system is implemented.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

PubMed

Deng, Mao-Lin; Zhu, Wei-Qiu

2016-08-01

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn

2016-08-15

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

A method for reducing the order of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Masri, S. F.; Miller, R. K.; Sassi, H.; Caughey, T. K.

1984-06-01

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background

NASA Astrophysics Data System (ADS)

Triki, Houria; Porsezian, K.; Choudhuri, Amitava; Dinda, P. Tchofo

2016-06-01

A class of derivative nonlinear Schrödinger equation with cubic-quintic-septic-nonic nonlinear terms describing the propagation of ultrashort optical pulses through a nonlinear medium with higher-order Kerr responses is investigated. An intensity-dependent chirp ansatz is adopted for solving the two coupled amplitude-phase nonlinear equations of the propagating wave. We find that the dynamics of field amplitude in this system is governed by a first-order nonlinear ordinary differential equation with a tenth-degree nonlinear term. We demonstrate that this system allows the propagation of a very rich variety of solitary waves (kink, dark, bright, and gray solitary pulses) which do not coexist in the conventional nonlinear systems that have appeared so far in the literature. The stability of the solitary wave solution under some violation on the parametric conditions is investigated. Moreover, we show that, unlike conventional systems, the nonlinear Schrödinger equation considered here meets the special requirements for the propagation of a chirped solitary wave on a continuous-wave background, involving a balance among group velocity dispersion, self-steepening, and higher-order nonlinearities of different nature.

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

NASA Astrophysics Data System (ADS)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

Method for conducting nonlinear electrochemical impedance spectroscopy

DOEpatents

Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.

2015-06-02

A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.

Jump Resonance in Fractional Order Circuits

NASA Astrophysics Data System (ADS)

Buscarino, Arturo; Caponetto, Riccardo; Famoso, Carlo; Fortuna, Luigi

The occurrence of an hysteretic loop in the frequency response of a driven nonlinear system is a phenomenon deeply investigated in nonlinear control theory. Such a phenomenon, which is linked to the multistable behavior of the system, is called jump resonance, since the magnitude of the frequency response is subjected to an abrupt jump up/down with respect to the increasing/decreasing of the frequency of the driving signal. In this paper, we aim at investigating fractional order nonlinear systems showing jump resonance, that is systems in which the order of the derivative is noninteger and their frequency response has a magnitude that is a multivalued function in a given range of frequencies. Furthermore, a strategy for designing fractional order systems showing jump resonance is presented along with the procedure to design and implement an analog circuit based on the approximation of the fractional order derivative. An extensive numerical analysis allows one to assess that the phenomenon is robust to the difference in the derivative order, enlightening the first example of a system with order lower than two which is able to demonstrate a jump resonance behavior.

Localization and identification of structural nonlinearities using cascaded optimization and neural networks

NASA Astrophysics Data System (ADS)

Koyuncu, A.; Cigeroglu, E.; Özgüven, H. N.

2017-10-01

In this study, a new approach is proposed for identification of structural nonlinearities by employing cascaded optimization and neural networks. Linear finite element model of the system and frequency response functions measured at arbitrary locations of the system are used in this approach. Using the finite element model, a training data set is created, which appropriately spans the possible nonlinear configurations space of the system. A classification neural network trained on these data sets then localizes and determines the types of all nonlinearities associated with the nonlinear degrees of freedom in the system. A new training data set spanning the parametric space associated with the determined nonlinearities is created to facilitate parametric identification. Utilizing this data set, initially, a feed forward regression neural network is trained, which parametrically identifies the classified nonlinearities. Then, the results obtained are further improved by carrying out an optimization which uses network identified values as starting points. Unlike identification methods available in literature, the proposed approach does not require data collection from the degrees of freedoms where nonlinear elements are attached, and furthermore, it is sufficiently accurate even in the presence of measurement noise. The application of the proposed approach is demonstrated on an example system with nonlinear elements and on a real life experimental setup with a local nonlinearity.

Statistical Tests of System Linearity Based on the Method of Surrogate Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hunter, N.; Paez, T.; Red-Horse, J.

When dealing with measured data from dynamic systems we often make the tacit assumption that the data are generated by linear dynamics. While some systematic tests for linearity and determinism are available - for example the coherence fimction, the probability density fimction, and the bispectrum - fi,u-ther tests that quanti$ the existence and the degree of nonlinearity are clearly needed. In this paper we demonstrate a statistical test for the nonlinearity exhibited by a dynamic system excited by Gaussian random noise. We perform the usual division of the input and response time series data into blocks as required by themore » Welch method of spectrum estimation and search for significant relationships between a given input fkequency and response at harmonics of the selected input frequency. We argue that systematic tests based on the recently developed statistical method of surrogate data readily detect significant nonlinear relationships. The paper elucidates the method of surrogate data. Typical results are illustrated for a linear single degree-of-freedom system and for a system with polynomial stiffness nonlinearity.« less

Nonlinear dynamic analysis of rigid rotor supported by gas foil bearings: Effects of gas film and foil structure on subsynchronous vibrations

NASA Astrophysics Data System (ADS)

Guo, Zhiyang; Feng, Kai; Liu, Tianyu; Lyu, Peng; Zhang, Tao

2018-07-01

Highly nonlinear subsynchronous vibrations are the main causing factors of failure in gas foil bearing (GFB)-rotor systems. Thus, investigating the vibration generation mechanisms and the relationship between subsynchronous vibrations and GFBs is necessary to ensure the healthy operation of rotor systems. In this study, an integrated nonlinear dynamic model with the consideration of shaft motion, unsteady gas film, and deformations of foil structure is established to investigate the effect of gas film and foil structure on system subsynchronous response. One test rig of GFB-rotor system is developed for model comparison. High agreement is shown between the prediction and test data, especially in the frequency domain. The nonlinear dynamic response is analyzed using waterfall plots, operation deflection shapes, journal orbits, Poincaré maps, and fast Fourier transforms. The parameter studies reveal that subsynchronous vibrations are highly related to gas film and foil structure. Subsynchronous vibrations can be adjusted by parameters such as bump stiffness, nominal clearance, and static loads. Therefore, gas foil bearing parameters should be carefully adjusted by system manufacturers to achieve the best rotordynamic performance.

Nonlinear vibration of a coupled high- Tc superconducting levitation system

NASA Astrophysics Data System (ADS)

Sugiura, T.; Inoue, T.; Ura, H.

2004-10-01

High- Tc superconducting levitation can be applied to electro-mechanical systems, such as flywheel energy storage and linear-drive transportation. Such a system can be modeled as a magnetically coupled system of many permanent magnets and high- Tc superconducting bulks. It is a multi-degree-of-freedom dynamical system coupled by nonlinear interaction between levitated magnets and superconducting bulks. This nonlinearly coupled system, with small damping due to no contact support, can easily show complicated phenomena of nonlinear dynamics. In mechanical design, it is important to evaluate this nonlinear dynamics, though it has not been well studied so far. This research deals with forced vibration of a coupled superconducting levitation system. As a simple modeling of a coupled system, a permanent magnet levitated above a superconducting bulk is placed between two fixed permanent magnets without contact. Frequency response of the levitated magnet under excitation of one of the fixed magnets was examined theoretically. The results show typical nonlinear vibration, such as jump, hysteresis, and parametric resonance, which were confirmed in our numerical analyses and experiments.

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

NASA Astrophysics Data System (ADS)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Synthesis of nonlinear frequency responses with experimentally extracted nonlinear modes

NASA Astrophysics Data System (ADS)

Peter, Simon; Scheel, Maren; Krack, Malte; Leine, Remco I.

2018-02-01

Determining frequency response curves is a common task in the vibration analysis of nonlinear systems. Measuring nonlinear frequency responses is often challenging and time consuming due to, e.g., coexisting stable or unstable vibration responses and structure-exciter-interaction. The aim of the current paper is to develop a method for the synthesis of nonlinear frequency responses near an isolated resonance, based on data that can be easily and automatically obtained experimentally. The proposed purely experimental approach relies on (a) a standard linear modal analysis carried out at low vibration levels and (b) a phase-controlled tracking of the backbone curve of the considered forced resonance. From (b), the natural frequency and vibrational deflection shape are directly obtained as a function of the vibration level. Moreover, a damping measure can be extracted by power considerations or from the linear modal analysis. In accordance with the single nonlinear mode assumption, the near-resonant frequency response can then be synthesized using this data. The method is applied to a benchmark structure consisting of a cantilevered beam attached to a leaf spring undergoing large deflections. The results are compared with direct measurements of the frequency response. The proposed approach is fast, robust and provides a good estimate for the frequency response. It is also found that direct frequency response measurement is less robust due to bifurcations and using a sine sweep excitation with a conventional force controller leads to underestimation of maximum vibration response.

Non-linear shipboard shock analysis of the Tomahawk missile shock isolation system

NASA Technical Reports Server (NTRS)

Leifer, Joel; Gross, Michael

1987-01-01

The identification, quantification, computer modeling and verification of the Tomahawk nonlinear liquid spring shock isolation system in a surface ship Vertical Launch System (VLS) are discussed. The isolation system hardware and mode of operation is detailed in an effort to understand the nonlinearities. These nonlinearities are then quantified and modeled using the MSC/NASTRAN finite element code. The model was verified using experimental data from the Navel Ordnance Systems Center MIL-S-901 medium weight shock tests of August 1986. The model was then used to predict the Tomahawk response to the CG-53 USS Mobile Bay shock trials of May-June 1987. Results indicate that the model is an accurate mathematical representation of the physical system either functioning as designed or in an impaired condition due to spring failure.

Accuracy of three-dimensional seismic ground response analysis in time domain using nonlinear numerical simulations

NASA Astrophysics Data System (ADS)

Liang, Fayun; Chen, Haibing; Huang, Maosong

2017-07-01

To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.

Nonlinear flow response of soft hair beds

NASA Astrophysics Data System (ADS)

Alvarado, José

2017-11-01

We are hairy inside: beds of passive fibers anchored to a surface and immersed in fluids are prevalent in many biological systems, including intestines, tongues, and blood vessels. Such hairs are soft enough to deform in response to stresses from fluid flows. Fluid stresses are in turn affected by hair deformation, leading to a coupled elastoviscous problem which is poorly understood. Here we investigate a biomimetic model system of elastomer hair beds subject to shear- driven Stokes flows. We characterize this system with a theoretical model which accounts for the large-deformation flow response of hair beds. Hair bending results in a drag-reducing nonlinearity because the hair tip lowers toward the base, widening the gap through which fluid flows. When hairs are cantilevered at an angle subnormal to the surface, flow against the grain bends hairs away from the base, narrowing the gap. The flow response of angled hair beds is axially asymmetric and amounts to a rectification nonlinearity. We identify an elastoviscous parameter which controls nonlinear behavior. Our study raises the hypothesis that biological hairy surfaces function to reduce fluid drag. Furthermore, angled hairs may be incorporated in the design of integrated microfluidic components, such as diodes and pumps. J.A. acknowledges support the U. S. Army Research Office under Grant Number W911NF-14-1-0396.

Nonlinearity and Strain-Rate Dependence in the Deformation Response of Polymer Matrix Composites Modeled

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

2000-01-01

There has been no accurate procedure for modeling the high-speed impact of composite materials, but such an analytical capability will be required in designing reliable lightweight engine-containment systems. The majority of the models in use assume a linear elastic material response that does not vary with strain rate. However, for containment systems, polymer matrix composites incorporating ductile polymers are likely to be used. For such a material, the deformation response is likely to be nonlinear and to vary with strain rate. An analytical model has been developed at the NASA Glenn Research Center at Lewis Field that incorporates both of these features. A set of constitutive equations that was originally developed to analyze the viscoplastic deformation of metals (Ramaswamy-Stouffer equations) was modified to simulate the nonlinear, rate-dependent deformation of polymers. Specifically, the effects of hydrostatic stresses on the inelastic response, which can be significant in polymers, were accounted for by a modification of the definition of the effective stress. The constitutive equations were then incorporated into a composite micromechanics model based on the mechanics of materials theory. This theory predicts the deformation response of a composite material from the properties and behavior of the individual constituents. In this manner, the nonlinear, rate-dependent deformation response of a polymer matrix composite can be predicted.

An equivalent frequency approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

NASA Astrophysics Data System (ADS)

Giaccu, Gian Felice

2018-05-01

Pre-tensioned cable braces are widely used as bracing systems in various structural typologies. This technology is fundamentally utilized for stiffening purposes in the case of steel and timber structures. The pre-stressing force imparted to the braces provides to the system a remarkable increment of stiffness. On the other hand, the pre-tensioning force in the braces must be properly calibrated in order to satisfactorily meet both serviceability and ultimate limit states. Dynamic properties of these systems are however affected by non-linear behavior due to potential slackening of the pre-tensioned brace. In the recent years the author has been working on a similar problem regarding the non-linear response of cables in cable-stayed bridges and braced structures. In the present paper a displacement-based approach is used to examine the non-linear behavior of a building system. The methodology operates through linearization and allows obtaining an equivalent linearized frequency to approximately characterize, mode by mode, the dynamic behavior of the system. The equivalent frequency depends on both the mechanical characteristics of the system, the pre-tensioning level assigned to the braces and a characteristic vibration amplitude. The proposed approach can be used as a simplified technique, capable of linearizing the response of structural systems, characterized by non-linearity induced by the slackening of pre-tensioned braces.

Theory of plasmonic effects in nonlinear optics: the case of graphene

NASA Astrophysics Data System (ADS)

Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration

The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

NASA Astrophysics Data System (ADS)

Fang, Fei; Xia, Guanghui; Wang, Jianguo

2018-02-01

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

NASA Astrophysics Data System (ADS)

Fang, Fei; Xia, Guanghui; Wang, Jianguo

2018-06-01

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Nonlinear dynamics near resonances of a rotor-active magnetic bearings system with 16-pole legs and time varying stiffness

NASA Astrophysics Data System (ADS)

Wu, R. Q.; Zhang, W.; Yao, M. H.

2018-02-01

In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing equation of motion for rotor-active magnetic bearings is derived by using the Newton's second law. The resulting dimensionless equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.

Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle.

PubMed

Serebryannikov, E E; Zheltikov, A M

2014-07-25

Ultrafast ionization dynamics within the field half cycle is shown to be the key physical factor that controls the properties of optical nonlinearity as a function of the carrier wavelength and intensity of a driving laser field. The Schrödinger-equation analysis of a generic hydrogen quantum system reveals universal tendencies in the wavelength dependence of optical nonlinearity, shedding light on unusual properties of optical nonlinearities in the midinfrared. For high-intensity low-frequency fields, free-state electrons are shown to dominate over bound electrons in the overall nonlinear response of a quantum system. In this regime, semiclassical models are shown to offer useful insights into the physics behind optical nonlinearity.

Nonlinear transient analysis of multi-mass flexible rotors - theory and applications

NASA Technical Reports Server (NTRS)

Kirk, R. G.; Gunter, E. J.

1973-01-01

The equations of motion necessary to compute the transient response of multi-mass flexible rotors are formulated to include unbalance, rotor acceleration, and flexible damped nonlinear bearing stations. A method of calculating the unbalance response of flexible rotors from a modified Myklestad-Prohl technique is discussed in connection with the method of solution for the transient response. Several special cases of simplified rotor-bearing systems are presented and analyzed for steady-state response, stability, and transient behavior. These simplified rotor models produce extensive design information necessary to insure stable performance to elastic mounted rotor-bearing systems under varying levels and forms of excitation. The nonlinear journal bearing force expressions derived from the short bearing approximation are utilized in the study of the stability and transient response of the floating bush squeeze damper support system. Both rigid and flexible rotor models are studied, and results indicate that the stability of flexible rotors supported by journal bearings can be greatly improved by the use of squeeze damper supports. Results from linearized stability studies of flexible rotors indicate that a tuned support system can greatly improve the performance of the units from the standpoint of unbalanced response and impact loading. Extensive stability and design charts may be readily produced for given rotor specifications by the computer codes presented in this analysis.

A Bayesian approach to identifying structural nonlinearity using free-decay response: Application to damage detection in composites

USGS Publications Warehouse

Nichols, J.M.; Link, W.A.; Murphy, K.D.; Olson, C.C.

2010-01-01

This work discusses a Bayesian approach to approximating the distribution of parameters governing nonlinear structural systems. Specifically, we use a Markov Chain Monte Carlo method for sampling the posterior parameter distributions thus producing both point and interval estimates for parameters. The method is first used to identify both linear and nonlinear parameters in a multiple degree-of-freedom structural systems using free-decay vibrations. The approach is then applied to the problem of identifying the location, size, and depth of delamination in a model composite beam. The influence of additive Gaussian noise on the response data is explored with respect to the quality of the resulting parameter estimates.

Nonlinear identification of the total baroreflex arc.

PubMed

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru; Mukkamala, Ramakrishna

2015-12-15

The total baroreflex arc [the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP)] is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this study was to develop a nonlinear model of the sympathetically mediated total arc without assuming any model form. Normal rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned, the carotid sinus regions were isolated and attached to a servo-controlled piston pump, and the AP and sympathetic nerve activity (SNA) were measured. CSP was perturbed using a Gaussian white noise signal. A second-order Volterra model was developed by applying nonparametric identification to the measurements. The second-order kernel was mainly diagonal, but the diagonal differed in shape from the first-order kernel. Hence, a reduced second-order model was similarly developed comprising a linear dynamic system in parallel with a squaring system in cascade with a slower linear dynamic system. This "Uryson" model predicted AP changes 12% better (P < 0.01) than a linear model in response to new Gaussian white noise CSP. The model also predicted nonlinear behaviors, including thresholding and mean responses to CSP changes about the mean. Models of the neural arc (the system relating CSP to SNA) and peripheral arc (the system relating SNA to AP) were likewise developed and tested. However, these models of subsystems of the total arc showed approximately linear behaviors. In conclusion, the validated nonlinear model of the total arc revealed that the system takes on an Uryson structure. Copyright © 2015 the American Physiological Society.

Nonlinear identification of the total baroreflex arc

PubMed Central

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru

2015-01-01

The total baroreflex arc [the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP)] is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this study was to develop a nonlinear model of the sympathetically mediated total arc without assuming any model form. Normal rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned, the carotid sinus regions were isolated and attached to a servo-controlled piston pump, and the AP and sympathetic nerve activity (SNA) were measured. CSP was perturbed using a Gaussian white noise signal. A second-order Volterra model was developed by applying nonparametric identification to the measurements. The second-order kernel was mainly diagonal, but the diagonal differed in shape from the first-order kernel. Hence, a reduced second-order model was similarly developed comprising a linear dynamic system in parallel with a squaring system in cascade with a slower linear dynamic system. This “Uryson” model predicted AP changes 12% better (P < 0.01) than a linear model in response to new Gaussian white noise CSP. The model also predicted nonlinear behaviors, including thresholding and mean responses to CSP changes about the mean. Models of the neural arc (the system relating CSP to SNA) and peripheral arc (the system relating SNA to AP) were likewise developed and tested. However, these models of subsystems of the total arc showed approximately linear behaviors. In conclusion, the validated nonlinear model of the total arc revealed that the system takes on an Uryson structure. PMID:26354845

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

NASA Technical Reports Server (NTRS)

Rabinowitz, Matthew (Inventor)

2002-01-01

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.

A tensor approach to modeling of nonhomogeneous nonlinear systems

NASA Technical Reports Server (NTRS)

Yurkovich, S.; Sain, M.

1980-01-01

Model following control methodology plays a key role in numerous application areas. Cases in point include flight control systems and gas turbine engine control systems. Typical uses of such a design strategy involve the determination of nonlinear models which generate requested control and response trajectories for various commands. Linear multivariable techniques provide trim about these motions; and protection logic is added to secure the hardware from excursions beyond the specification range. This paper reports upon experience in developing a general class of such nonlinear models based upon the idea of the algebraic tensor product.

FAST Modularization Framework for Wind Turbine Simulation: Full-System Linearization

DOE PAGES

Jonkman, Jason M.; Jonkman, Bonnie J.

2016-10-03

The wind engineering community relies on multiphysics engineering software to run nonlinear time-domain simulations e.g. for design-standards-based loads analysis. Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system response and exploit well-established methods and tools for analyzing linear systems. Here, this paper presents the development and verification of the new linearization functionality of the open-source engineering tool FAST v8 for land-based wind turbines, as well as the concepts and mathematical background needed to understand and apply it correctly.

FAST modularization framework for wind turbine simulation: full-system linearization

NASA Astrophysics Data System (ADS)

Jonkman, J. M.; Jonkman, B. J.

2016-09-01

The wind engineering community relies on multiphysics engineering software to run nonlinear time-domain simulations e.g. for design-standards-based loads analysis. Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system response and exploit well- established methods and tools for analyzing linear systems. This paper presents the development and verification of the new linearization functionality of the open-source engineering tool FAST v8 for land-based wind turbines, as well as the concepts and mathematical background needed to understand and apply it correctly.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter.

PubMed

Song, Xuegang; Zhang, Yuexin; Liang, Dakai

2017-10-10

This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

PubMed

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

Nonlinear Time Series Analysis of Nodulation Factor Induced Calcium Oscillations: Evidence for Deterministic Chaos?

PubMed Central

Hazledine, Saul; Sun, Jongho; Wysham, Derin; Downie, J. Allan; Oldroyd, Giles E. D.; Morris, Richard J.

2009-01-01

Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling. PMID:19675679

Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system

NASA Astrophysics Data System (ADS)

Kurt, Mehmet; Moore, Keegan J.; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

2017-05-01

We consider the application of a new nonlinear model updating strategy to a computational benchmark system. The approach relies on analyzing system response time series in the frequency-energy domain by constructing both Hamiltonian and forced and damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental measured time series. By matching the frequency-energy plots of the benchmark system and its reduced-order model, we show that we are able to retrieve the global strongly nonlinear dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series. We apply the proposed methodology to a benchmark problem, which was posed to the system identification community prior to the IMAC XXXII (2014) and XXXIII (2015) Conferences as a "Round Robin Exercise on Nonlinear System Identification". We show that we are able to identify the parameters of the non-linear element in the problem with a priori knowledge about its position.

Robust decentralized hybrid adaptive output feedback fuzzy control for a class of large-scale MIMO nonlinear systems and its application to AHS.

PubMed

Huang, Yi-Shao; Liu, Wel-Ping; Wu, Min; Wang, Zheng-Wu

2014-09-01

This paper presents a novel observer-based decentralized hybrid adaptive fuzzy control scheme for a class of large-scale continuous-time multiple-input multiple-output (MIMO) uncertain nonlinear systems whose state variables are unmeasurable. The scheme integrates fuzzy logic systems, state observers, and strictly positive real conditions to deal with three issues in the control of a large-scale MIMO uncertain nonlinear system: algorithm design, controller singularity, and transient response. Then, the design of the hybrid adaptive fuzzy controller is extended to address a general large-scale uncertain nonlinear system. It is shown that the resultant closed-loop large-scale system keeps asymptotically stable and the tracking error converges to zero. The better characteristics of our scheme are demonstrated by simulations. Copyright © 2014. Published by Elsevier Ltd.

Characterizing Feedback Control Mechanisms in Nonlinear Microbial Models of Soil Organic Matter Decomposition by Stability Analysis

NASA Astrophysics Data System (ADS)

Georgiou, K.; Tang, J.; Riley, W. J.; Torn, M. S.

2014-12-01

Soil organic matter (SOM) decomposition is regulated by biotic and abiotic processes. Feedback interactions between such processes may act to dampen oscillatory responses to perturbations from equilibrium. Indeed, although biological oscillations have been observed in small-scale laboratory incubations, the overlying behavior at the plot-scale exhibits a relatively stable response to disturbances in input rates and temperature. Recent studies have demonstrated the ability of microbial models to capture nonlinear feedbacks in SOM decomposition that linear Century-type models are unable to reproduce, such as soil priming in response to increased carbon input. However, these microbial models often exhibit strong oscillatory behavior that is deemed unrealistic. The inherently nonlinear dynamics of SOM decomposition have important implications for global climate-carbon and carbon-concentration feedbacks. It is therefore imperative to represent these dynamics in Earth System Models (ESMs) by introducing sub-models that accurately represent microbial and abiotic processes. In the present study we explore, both analytically and numerically, four microbe-enabled model structures of varying levels of complexity. The most complex model combines microbial physiology, a non-linear mineral sorption isotherm, and enzyme dynamics. Based on detailed stability analysis of the nonlinear dynamics, we calculate the system modes as functions of model parameters. This dependence provides insight into the source of state oscillations. We find that feedback mechanisms that emerge from careful representation of enzyme and mineral interactions, with parameter values in a prescribed range, are critical for both maintaining system stability and capturing realistic responses to disturbances. Corroborating and expanding upon the results of recent studies, we explain the emergence of oscillatory responses and discuss the appropriate microbe-enabled model structure for inclusion in ESMs.

A discourse on sensitivity analysis for discretely-modeled structures

NASA Technical Reports Server (NTRS)

Adelman, Howard M.; Haftka, Raphael T.

1991-01-01

A descriptive review is presented of the most recent methods for performing sensitivity analysis of the structural behavior of discretely-modeled systems. The methods are generally but not exclusively aimed at finite element modeled structures. Topics included are: selections of finite difference step sizes; special consideration for finite difference sensitivity of iteratively-solved response problems; first and second derivatives of static structural response; sensitivity of stresses; nonlinear static response sensitivity; eigenvalue and eigenvector sensitivities for both distinct and repeated eigenvalues; and sensitivity of transient response for both linear and nonlinear structural response.

General response formula and application to topological insulator in quantum open system.

PubMed

Shen, H Z; Qin, M; Shao, X Q; Yi, X X

2015-11-01

It is well-known that the quantum linear response theory is based on the first-order perturbation theory for a system in thermal equilibrium. Hence, this theory breaks down when the system is in a steady state far from thermal equilibrium and the response up to higher order in perturbation is not negligible. In this paper, we develop a nonlinear response theory for such quantum open system. We first formulate this theory in terms of general susceptibility, after which we apply it to the derivation of Hall conductance for open system at finite temperature. As an example, the Hall conductance of the two-band model is derived. Then we calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model. The calculations show that the transition points of topological phase are robust against the environment. Our results provide a promising platform for the coherent manipulation of the nonlinear response in quantum open system, which has potential applications for quantum information processing and statistical physics.

Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable. [noting unstable convolution subsystem forward control and time varying nonlinear feedback

NASA Technical Reports Server (NTRS)

Callier, F. M.; Desoer, C. A.

1973-01-01

A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.

Thermospheric dynamics - A system theory approach

NASA Technical Reports Server (NTRS)

Codrescu, M.; Forbes, J. M.; Roble, R. G.

1990-01-01

A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location.

Time-Domain Full-Wave Modeling of Nonlinear Air Breakdown in High-Power Microwave Devices and Systems

DTIC Science & Technology

2017-09-30

AFRL-RD-PS- AFRL-RD-PS- TR-2017-0047 TR-2017-0047 TIME -DOMAIN FULL-WAVE MODELING OF NONLINEAR AIR BREAKDOWN IN HIGH-POWER MICROWAVE...Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions...TITLE AND SUBTITLE Time -Domain Full-Wave Modeling of Nonlinear Air Breakdown in High-Power Microwave Devices and Systems 5a. CONTRACT NUMBER 5b

On-line and real-time diagnosis method for proton membrane fuel cell (PEMFC) stack by the superposition principle

NASA Astrophysics Data System (ADS)

Lee, Young-Hyun; Kim, Jonghyeon; Yoo, Seungyeol

2016-09-01

The critical cell voltage drop in a stack can be followed by stack defect. A method of detecting defective cell is the cell voltage monitoring. The other methods are based on the nonlinear frequency response. In this paper, the superposition principle for the diagnosis of PEMFC stack is introduced. If critical cell voltage drops exist, the stack behaves as a nonlinear system. This nonlinearity can explicitly appear in the ohmic overpotential region of a voltage-current curve. To detect the critical cell voltage drop, a stack is excited by two input direct test-currents which have smaller amplitude than an operating stack current and have an equal distance value from the operating current. If the difference between one voltage excited by a test current and the voltage excited by a load current is not equal to the difference between the other voltage response and the voltage excited by the load current, the stack system acts as a nonlinear system. This means that there is a critical cell voltage drop. The deviation from the value zero of the difference reflects the grade of the system nonlinearity. A simulation model for the stack diagnosis is developed based on the SPP, and experimentally validated.

Nonlinear dynamics of global atmospheric and earth system processes

NASA Technical Reports Server (NTRS)

Zhang, Taiping; Verbitsky, Mikhail; Saltzman, Barry; Mann, Michael E.; Park, Jeffrey; Lall, Upmanu

1995-01-01

During the grant period, the authors continued ongoing studies aimed at enhancing their understanding of the operation of the atmosphere as a complex nonlinear system interacting with the hydrosphere, biosphere, and cryosphere in response to external radiative forcing. Five papers were completed with support from the grant, representing contributions in three main areas of study: (1) theoretical studies of the interactive atmospheric response to changed biospheric boundary conditions measurable from satellites; (2) statistical-observational studies of global-scale temperature variability on interannual to century time scales; and (3) dynamics of long-term earth system changes associated with ice sheet surges.

Nonlinear mechanical response of the extracellular matrix: learning from articular cartilage

NASA Astrophysics Data System (ADS)

Kearns, Sarah; Das, Moumita

2015-03-01

We study the mechanical structure-function relations in the extracellular matrix (ECM) with focus on nonlinear shear and compression response. As a model system, our study focuses on the ECM in articular cartilage tissue which has two major mechanobiological components: a network of the biopolymer collagen that acts as a stiff, reinforcing matrix, and a flexible aggrecan network that facilitates deformability. We model this system as a double network hydrogel made of interpenetrating networks of stiff and flexible biopolymers respectively. We study the linear and nonlinear mechanical response of the model ECM to shear and compression forces using a combination of rigidity percolation theory and energy minimization approaches. Our results may provide useful insights into the design principles of the ECM as well as biomimetic hydrogels that are mechanically robust and can, at the same time, easily adapt to cues in their surroundings.

Dynamic response signatures of a scaled model platform for floating wind turbines in an ocean wave basin

PubMed Central

Jaksic, V.; O'Shea, R.; Cahill, P.; Murphy, J.; Mandic, D. P.; Pakrashi, V.

2015-01-01

Understanding of dynamic behaviour of offshore wind floating substructures is extremely important in relation to design, operation, maintenance and management of floating wind farms. This paper presents assessment of nonlinear signatures of dynamic responses of a scaled tension-leg platform (TLP) in a wave tank exposed to different regular wave conditions and sea states characterized by the Bretschneider, the Pierson–Moskowitz and the JONSWAP spectra. Dynamic responses of the TLP were monitored at different locations using load cells, a camera-based motion recognition system and a laser Doppler vibrometer. The analysis of variability of the TLP responses and statistical quantification of their linearity or nonlinearity, as non-destructive means of structural monitoring from the output-only condition, remains a challenging problem. In this study, the delay vector variance (DVV) method is used to statistically study the degree of nonlinearity of measured response signals from a TLP. DVV is observed to create a marker estimating the degree to which a change in signal nonlinearity reflects real-time behaviour of the structure and also to establish the sensitivity of the instruments employed to these changes. The findings can be helpful in establishing monitoring strategies and control strategies for undesirable levels or types of dynamic response and can help to better estimate changes in system characteristics over the life cycle of the structure. PMID:25583866

State Space Formulation of Nonlinear Vibration Responses Collected from a Dynamic Rotor-Bearing System: An Extension of Bearing Diagnostics to Bearing Prognostics

PubMed Central

Tse, Peter W.; Wang, Dong

2017-01-01

Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions. PMID:28216586

State Space Formulation of Nonlinear Vibration Responses Collected from a Dynamic Rotor-Bearing System: An Extension of Bearing Diagnostics to Bearing Prognostics.

PubMed

Tse, Peter W; Wang, Dong

2017-02-14

Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions.

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

NASA Astrophysics Data System (ADS)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

Stable scalable control of soliton propagation in broadband nonlinear optical waveguides

NASA Astrophysics Data System (ADS)

Peleg, Avner; Nguyen, Quan M.; Huynh, Toan T.

2017-02-01

We develop a method for achieving scalable transmission stabilization and switching of N colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in N-sequence transmission is described by a generalized N-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of M out of N soliton sequences. Numerical simulations for single-waveguide transmission with a system of N coupled nonlinear Schrödinger equations with 2 ≤ N ≤ 4 show excellent agreement with the predator-prey model's predictions and stable propagation over significantly larger distances compared with other broadband nonlinear single-waveguide systems. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated by the simulations. We discuss the reasons for the robustness and scalability of transmission stabilization and switching in waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss, and explain their advantages compared with other broadband nonlinear waveguides.

An analysis of a nonlinear instability in the implementation of a VTOL control system

NASA Technical Reports Server (NTRS)

Weber, J. M.

1982-01-01

The contributions to nonlinear behavior and unstable response of the model following yaw control system of a VTOL aircraft during hover were determined. The system was designed as a state rate feedback implicit model follower that provided yaw rate command/heading hold capability and used combined full authority parallel and limited authority series servo actuators to generate an input to the yaw reaction control system of the aircraft. Both linear and nonlinear system models, as well as describing function linearization techniques were used to determine the influence on the control system instability of input magnitude and bandwidth, series servo authority, and system bandwidth. Results of the analysis describe stability boundaries as a function of these system design characteristics.

Experiments and numerical simulations of nonlinear vibration responses of an assembly with friction joints - Application on a test structure named "Harmony"

NASA Astrophysics Data System (ADS)

Claeys, M.; Sinou, J.-J.; Lambelin, J.-P.; Todeschini, R.

2016-03-01

In presence of friction, the frequency response function of a metallic assembly is strongly dependent on the excitation level. The local stick-slip behavior at the friction interfaces induces energy dissipation and local stiffness softening. These phenomena are studied both experimentally and numerically on a test structure named "Harmony". Concerning the numerical part, a classical complete methodology from the finite element and friction modeling to the prediction of the nonlinear vibrational response is implemented. The well-known Harmonic Balance Method with a specific condensation process on the nonlinear frictional elements is achieved. Also, vibration experiments are performed to validate not only the finite element model of the test structure named "Harmony" at low excitation levels but also to investigate the nonlinear behavior of the system on several excitation levels. A scanning laser vibrometer is used to measure the nonlinear behavior and the local stick-slip movement near the contacts.

Distributed synchronization of networked drive-response systems: A nonlinear fixed-time protocol.

PubMed

Zhao, Wen; Liu, Gang; Ma, Xi; He, Bing; Dong, Yunfeng

2017-11-01

The distributed synchronization of networked drive-response systems is investigated in this paper. A novel nonlinear protocol is proposed to ensure that the tracking errors converge to zeros in a fixed-time. By comparison with previous synchronization methods, the present method considers more practical conditions and the synchronization time is not dependent of arbitrary initial conditions but can be offline pre-assign according to the task assignment. Finally, the feasibility and validity of the presented protocol have been illustrated by a numerical simulation. Copyright © 2017. Published by Elsevier Ltd.

Fast novel nonlinear optical NLC system with local response

NASA Astrophysics Data System (ADS)

Iljin, Andrey; Residori, Stefania; Bortolozzo, Umberto

2017-06-01

Nonlinear optical performance of a novel liquid crystalline (LC) cell has been studied in two-wave mixing experiments revealing high diffraction efficiency within extremely wide intensity range, fast recording times and spatial resolution. Photo-induced modulation of the LC order parameter resulting from trans-cis isomerisation of dye molecules causes consequent changes of refractive indices of the medium (Light-Induced Order Modification, LIOM-mechanism) and is proved to be the main mechanism of optical nonlinearity. The proposed arrangement of the electric-field-stabilised homeotropic alignment hinders the LC director reorientation, prevents appearance of surface effects and ensures the optical cell quality. The LIOM-type nonlinearity, characterised with the substantially local nonlinear optical response, could also be extended for the recording of arbitrary phase profiles as requested in several applications for light-beam manipulation, recording of dynamic volume holograms and photonic lattices.

Incomplete data based parameter identification of nonlinear and time-variant oscillators with fractional derivative elements

NASA Astrophysics Data System (ADS)

Kougioumtzoglou, Ioannis A.; dos Santos, Ketson R. M.; Comerford, Liam

2017-09-01

Various system identification techniques exist in the literature that can handle non-stationary measured time-histories, or cases of incomplete data, or address systems following a fractional calculus modeling. However, there are not many (if any) techniques that can address all three aforementioned challenges simultaneously in a consistent manner. In this paper, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. In this regard, the oscillator is transformed into an equivalent MISO system in the wavelet domain. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Finally, these wavelet coefficients are utilized to determine appropriately defined time- and frequency-dependent wavelet based frequency response functions and related oscillator parameters. Several linear and nonlinear time-variant systems with fractional derivative elements are used as numerical examples to demonstrate the reliability of the technique even in cases of noise corrupted and incomplete data.

Nonlinear engine model for idle speed control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Livshiz, M.; Sanvido, D.J.; Stiles, S.D.

1994-12-31

This paper describes a nonlinear model of an engine used for the design of idle speed control and prediction in a broad range of idle speeds and operational conditions. Idle speed control systems make use of both spark advance and the idle air actuator to control engine speed for improved response relative to variations in the target idle speed due to load disturbances. The control system at idle can be presented by a multiple input multiple output (MIMO) nonlinear model. Information of nonlinearities helps to improve performance of the system over the whole range of engine speeds. A proposed simplemore » nonlinear model of the engine at idle was applied for design of optimal controllers and predictors for improved steady state, load rejection and transition from and to idle. This paper describes vehicle results of engine speed prediction based on the described model.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ganguly, Jayanta; Ghosh, Manas, E-mail: pcmg77@rediffmail.com

We investigate the profiles of diagonal components of frequency-dependent first nonlinear (β{sub xxx} and β{sub yyy}) optical response of repulsive impurity doped quantum dots. We have assumed a Gaussian function to represent the dopant impurity potential. This study primarily addresses the role of noise on the polarizability components. We have invoked Gaussian white noise consisting of additive and multiplicative characteristics (in Stratonovich sense). The doped system has been subjected to an oscillating electric field of given intensity, and the frequency-dependent first nonlinear polarizabilities are computed. The noise characteristics are manifested in an interesting way in the nonlinear polarizability components. Inmore » case of additive noise, the noise strength remains practically ineffective in influencing the optical responses. The situation completely changes with the replacement of additive noise by its multiplicative analog. The replacement enhances the nonlinear optical response dramatically and also causes their maximization at some typical value of noise strength that depends on oscillation frequency.« less

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

PubMed

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

Review of probabilistic analysis of dynamic response of systems with random parameters

NASA Technical Reports Server (NTRS)

Kozin, F.; Klosner, J. M.

1989-01-01

The various methods that have been studied in the past to allow probabilistic analysis of dynamic response for systems with random parameters are reviewed. Dynamic response may have been obtained deterministically if the variations about the nominal values were small; however, for space structures which require precise pointing, the variations about the nominal values of the structural details and of the environmental conditions are too large to be considered as negligible. These uncertainties are accounted for in terms of probability distributions about their nominal values. The quantities of concern for describing the response of the structure includes displacements, velocities, and the distributions of natural frequencies. The exact statistical characterization of the response would yield joint probability distributions for the response variables. Since the random quantities will appear as coefficients, determining the exact distributions will be difficult at best. Thus, certain approximations will have to be made. A number of techniques that are available are discussed, even in the nonlinear case. The methods that are described were: (1) Liouville's equation; (2) perturbation methods; (3) mean square approximate systems; and (4) nonlinear systems with approximation by linear systems.

Neural network L1 adaptive control of MIMO systems with nonlinear uncertainty.

PubMed

Zhen, Hong-tao; Qi, Xiao-hui; Li, Jie; Tian, Qing-min

2014-01-01

An indirect adaptive controller is developed for a class of multiple-input multiple-output (MIMO) nonlinear systems with unknown uncertainties. This control system is comprised of an L 1 adaptive controller and an auxiliary neural network (NN) compensation controller. The L 1 adaptive controller has guaranteed transient response in addition to stable tracking. In this architecture, a low-pass filter is adopted to guarantee fast adaptive rate without generating high-frequency oscillations in control signals. The auxiliary compensation controller is designed to approximate the unknown nonlinear functions by MIMO RBF neural networks to suppress the influence of uncertainties. NN weights are tuned on-line with no prior training and the project operator ensures the weights bounded. The global stability of the closed-system is derived based on the Lyapunov function. Numerical simulations of an MIMO system coupled with nonlinear uncertainties are used to illustrate the practical potential of our theoretical results.

The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid

NASA Technical Reports Server (NTRS)

Peterson, Lee D.; Crawley, Edward F.; Hansman, R. John

1988-01-01

The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.

On the Response of a Nonlinear Structure to High Kurtosis Non-Gaussian Random Loadings

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam; Turner, Travis L.

2011-01-01

This paper is a follow-on to recent work by the authors in which the response and high-cycle fatigue of a nonlinear structure subject to non-Gaussian loadings was found to vary markedly depending on the nature of the loading. There it was found that a non-Gaussian loading having a steady rate of short-duration, high-excursion peaks produced essentially the same response as would have been incurred by a Gaussian loading. In contrast, a non-Gaussian loading having the same kurtosis, but with bursts of high-excursion peaks was found to elicit a much greater response. This work is meant to answer the question of when consideration of a loading probability distribution other than Gaussian is important. The approach entailed nonlinear numerical simulation of a beam structure under Gaussian and non-Gaussian random excitations. Whether the structure responded in a Gaussian or non-Gaussian manner was determined by adherence to, or violations of, the Central Limit Theorem. Over a practical range of damping, it was found that the linear response to a non-Gaussian loading was Gaussian when the period of the system impulse response is much greater than the rate of peaks in the loading. Lower damping reduced the kurtosis, but only when the linear response was non-Gaussian. In the nonlinear regime, the response was found to be non-Gaussian for all loadings. The effect of a spring-hardening type of nonlinearity was found to limit extreme values and thereby lower the kurtosis relative to the linear response regime. In this case, lower damping gave rise to greater nonlinearity, resulting in lower kurtosis than a higher level of damping.

Integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksiy O.

2018-05-01

Developing the idea of increasing the number of structural elements in the unit cell of a quasi-one-dimensional lattice as applied to the semi-discrete integrable systems of nonlinear Schrödinger type, we construct the zero-curvature representation for the general integrable nonlinear system on a lattice with three structural elements in the unit cell. The integrability of the obtained general system permits to find explicitly a number of local conservation laws responsible for the main features of system dynamics and in particular for the so-called natural constraints separating the field variables into the basic and the concomitant ones. Thus, considering the reduction to the semi-discrete integrable system of nonlinear Schrödinger type, we revealed the essentially nontrivial impact of concomitant fields on the Poisson structure and on the whole Hamiltonian formulation of system dynamics caused by the nonzero background values of these fields. On the other hand, the zero-curvature representation of a general nonlinear system serves as an indispensable key to the dressing procedure of system integration based upon the Darboux transformation of the auxiliary linear problem and the implicit Bäcklund transformation of field variables. Due to the symmetries inherent to the six-component semi-discrete integrable nonlinear Schrödinger system with attractive-type nonlinearities, the Darboux-Bäcklund dressing scheme is shown to be simplified considerably, giving rise to the appropriately parameterized multi-component soliton solution consisting of six basic and four concomitant components.

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Topological nature of nonlinear optical effects in solids.

PubMed

Morimoto, Takahiro; Nagaosa, Naoto

2016-05-01

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials.

Topological nature of nonlinear optical effects in solids

PubMed Central

Morimoto, Takahiro; Nagaosa, Naoto

2016-01-01

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials. PMID:27386523

Use of the dynamic stiffness method to interpret experimental data from a nonlinear system

NASA Astrophysics Data System (ADS)

Tang, Bin; Brennan, M. J.; Gatti, G.

2018-05-01

The interpretation of experimental data from nonlinear structures is challenging, primarily because of dependency on types and levels of excitation, and coupling issues with test equipment. In this paper, the use of the dynamic stiffness method, which is commonly used in the analysis of linear systems, is used to interpret the data from a vibration test of a controllable compressed beam structure coupled to a test shaker. For a single mode of the system, this method facilitates the separation of mass, stiffness and damping effects, including nonlinear stiffness effects. It also allows the separation of the dynamics of the shaker from the structure under test. The approach needs to be used with care, and is only suitable if the nonlinear system has a response that is predominantly at the excitation frequency. For the structure under test, the raw experimental data revealed little about the underlying causes of the dynamic behaviour. However, the dynamic stiffness approach allowed the effects due to the nonlinear stiffness to be easily determined.

Strange nonchaotic attractors for computation

NASA Astrophysics Data System (ADS)

Sathish Aravindh, M.; Venkatesan, A.; Lakshmanan, M.

2018-05-01

We investigate the response of quasiperiodically driven nonlinear systems exhibiting strange nonchaotic attractors (SNAs) to deterministic input signals. We show that if one uses two square waves in an aperiodic manner as input to a quasiperiodically driven double-well Duffing oscillator system, the response of the system can produce logical output controlled by such a forcing. Changing the threshold or biasing of the system changes the output to another logic operation and memory latch. The interplay of nonlinearity and quasiperiodic forcing yields logical behavior, and the emergent outcome of such a system is a logic gate. It is further shown that the logical behaviors persist even for an experimental noise floor. Thus the SNA turns out to be an efficient tool for computation.

Generation mechanisms of fundamental rogue wave spatial-temporal structure.

PubMed

Ling, Liming; Zhao, Li-Chen; Yang, Zhan-Ying; Guo, Boling

2017-08-01

We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation. Furthermore, our results show that N-component coupled nonlinear Schrödinger systems may possess N different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.

Using waveform information in nonlinear data assimilation

NASA Astrophysics Data System (ADS)

Rey, Daniel; Eldridge, Michael; Morone, Uriel; Abarbanel, Henry D. I.; Parlitz, Ulrich; Schumann-Bischoff, Jan

2014-12-01

Information in measurements of a nonlinear dynamical system can be transferred to a quantitative model of the observed system to establish its fixed parameters and unobserved state variables. After this learning period is complete, one may predict the model response to new forces and, when successful, these predictions will match additional observations. This adjustment process encounters problems when the model is nonlinear and chaotic because dynamical instability impedes the transfer of information from the data to the model when the number of measurements at each observation time is insufficient. We discuss the use of information in the waveform of the data, realized through a time delayed collection of measurements, to provide additional stability and accuracy to this search procedure. Several examples are explored, including a few familiar nonlinear dynamical systems and small networks of Colpitts oscillators.

The study of micro-inextensible piezoelectric cantilever plate

NASA Astrophysics Data System (ADS)

Chen, L. H.; Xu, J. W.; Zhang, W.

2018-06-01

In this paper, a micro-inextensible piezoelectric cantilever plate is analyzed and its nonlinear dynamic behaviour is studied. The nonlinear oscillation differential equation is established by using Hamilton’s principle with the application of strain gradient theory to consider the size effect, and inextensible theory to consider the large deformation and rotation effect of cantilever plate. Based on MATLAB software, using the Runge-Kuta method, we can obtain the response of the nonlinear oscillation differential equation. The influences of the strain gradient length scale parameter and voltage on the dynamic response of micro piezoelectric cantilever plate are investigated separately. The results confirmed an increase of the stiffness of the system by using the strain gradient theory and the amplitude of the vibration is reduced. The vibration of the system can be controlled by applying an active voltage. The effect of external excitation frequency on nonlinear dynamic behaviour is considered by using Poincare surface of section and diagrams of waveforms, phase and bifurcation.

Reflections on the nature of non-linear responses of the climate to forcing

NASA Astrophysics Data System (ADS)

Ditlevsen, Peter

2017-04-01

On centennial to multi-millennial time scales the paleoclimatic record shows that climate responds in a very non-linear way to the external forcing. Perhaps most puzzling is the change in glacial period duration at the Middle Pleistocene Transition. From a dynamical systems perspective, this could be a change in frequency locking between the orbital forcing and the climatic response or it could be a non-linear resonance phenomenon. In both cases the climate system shows a non-trivial oscillatory behaviour. From the records it seems that this behaviour can be described by an effective dynamics on a low-dimensional slow manifold. These different possible dynamical behaviours will be discussed. References: Arianna Marchionne, Peter Ditlevsen, and Sebastian Wieczorek, "Three types of nonlinear resonances", arXiv:1605.00858 Peter Ashwin and Peter Ditlevsen, "The middle Pleistocene transition as a generic bifurcation on a slow manifold", Climate Dynamics, 45, 2683, 2015. Peter D. Ditlevsen, "The bifurcation structure and noise assisted transitions in the Pleistocene glacial cycles", Paleoceanography, 24, PA3204, 2009

Dynamic response signatures of a scaled model platform for floating wind turbines in an ocean wave basin.

PubMed

Jaksic, V; O'Shea, R; Cahill, P; Murphy, J; Mandic, D P; Pakrashi, V

2015-02-28

Understanding of dynamic behaviour of offshore wind floating substructures is extremely important in relation to design, operation, maintenance and management of floating wind farms. This paper presents assessment of nonlinear signatures of dynamic responses of a scaled tension-leg platform (TLP) in a wave tank exposed to different regular wave conditions and sea states characterized by the Bretschneider, the Pierson-Moskowitz and the JONSWAP spectra. Dynamic responses of the TLP were monitored at different locations using load cells, a camera-based motion recognition system and a laser Doppler vibrometer. The analysis of variability of the TLP responses and statistical quantification of their linearity or nonlinearity, as non-destructive means of structural monitoring from the output-only condition, remains a challenging problem. In this study, the delay vector variance (DVV) method is used to statistically study the degree of nonlinearity of measured response signals from a TLP. DVV is observed to create a marker estimating the degree to which a change in signal nonlinearity reflects real-time behaviour of the structure and also to establish the sensitivity of the instruments employed to these changes. The findings can be helpful in establishing monitoring strategies and control strategies for undesirable levels or types of dynamic response and can help to better estimate changes in system characteristics over the life cycle of the structure. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Non-Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves

NASA Astrophysics Data System (ADS)

Khatri, Devvrath

A chain of granular particles is one of the most studied examples of highly nonlinear systems deriving its response from the nonlinear Hertzian contact interaction between particles. Interest in these systems derives from their tunable dynamic response, encompassing linear, weakly nonlinear, and strongly nonlinear regimes, controlled by varying the static and dynamic load applied. In chains with a very weak (or zero) static precompression, the system supports the formation and propagation of highly nonlinear solitary waves (HNSWs). The dual-nonlinear interaction between particles (i.e., a power-law type contact potential in compression, and zero strength in tension) combined with discreteness of the system, makes the granular system highly tunable. The propagation properties of these waves, such as traveling pulse width, wave speed, number of separated pulses (single or train of pulses), etc., can be controlled by modifying one or many of the parameters, like the particle's dimension, material properties, static and dynamic force amplitude, the type and duration of the initial excitation applied to the system, and/or the periodicity of the chain. The ability to control the wave properties in such chains has been proposed for several different practical engineering applications. The dynamic properties of these granular chains have been conventionally studied using discrete particle models (DPMs) which consider the particles in the chains as point masses connected by nonlinear Hertzian springs with the neighboring particles. Although, this is a good approximation under proper circumstances, it does not capture many features of the three dimensional elastic particles such as the elastic wave propagation within the particles, the local deformation of the particles in the vicinity of the contact point, the corresponding changes in the contact area, and the collective vibrations of the particles among others. This thesis focuses on the development of a finite element model (FEM) using the commercially available software Abaqus, which takes into account many of these characteristic features. The finite element model discretizes particles by considering them as three-dimensional deformable bodies of revolution and describes the nonlinear dynamic response of one-dimensional granular chains composed of particles with various geometries and orientations. We showed that particles' geometries and orientations provide additional design parameters for controlling the dynamic response of the system, compared to chains composed of spherical particles. We also showed that the tunable and compact nature of these waves can be used to tailor the properties of HNSWs for specific application, such as information carriers for actuation and sensing of mechanical properties and boundary effects of adjoining media in Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Using experiments and numerics, we characterized interface dynamics between granular media and adjoining linear elastic media, and found that the coupling produced temporary localization of the incident waves at the boundaries between the two media and their decomposition into reflected waves. We monitored the formation of reflected solitary waves propagating back from the interface and found that their properties are sensitive to the geometric and material properties of the adjoining media. The work done in this research enhances our understanding of the basic physics and tunability of nonlinear granular media, and further establishes a theoretical and numerical foundation in the applications of HNSWs as information carriers.

How linear response shaped models of neural circuits and the quest for alternatives.

PubMed

Herfurth, Tim; Tchumatchenko, Tatjana

2017-10-01

In the past decades, many mathematical approaches to solve complex nonlinear systems in physics have been successfully applied to neuroscience. One of these tools is the concept of linear response functions. However, phenomena observed in the brain emerge from fundamentally nonlinear interactions and feedback loops rather than from a composition of linear filters. Here, we review the successes achieved by applying the linear response formalism to topics, such as rhythm generation and synchrony and by incorporating it into models that combine linear and nonlinear transformations. We also discuss the challenges encountered in the linear response applications and argue that new theoretical concepts are needed to tackle feedback loops and non-equilibrium dynamics which are experimentally observed in neural networks but are outside of the validity regime of the linear response formalism. Copyright © 2017 Elsevier Ltd. All rights reserved.

Nonlinear optical response in narrow graphene nanoribbons

NASA Astrophysics Data System (ADS)

Karimi, Farhad; Knezevic, Irena

We present an iterative method to calculate the nonlinear optical response of armchair graphene nanoribbons (aGNRs) and zigzag graphene nanoribbons (zGNRs) while including the effects of dissipation. In contrast to methods that calculate the nonlinear response in the ballistic (dissipation-free) regime, here we obtain the nonlinear response of an electronic system to an external electromagnetic field while interacting with a dissipative environment (to second order). We use a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations, and we solve the master equation iteratively to obtain the higher-order response functions. We employ the SCF-MMEF to calculate the nonlinear conductance and susceptibility, as well as to calculate the dependence of the plasmon dispersion and plasmon propagation length on the intensity of the electromagnetic field in GNRs. The electron scattering mechanisms included in this work are scattering with intrinsic phonons, ionized impurities, surface optical phonons, and line-edge roughness. Unlike in wide GNRs, where ionized-impurity scattering dominates dissipation, in ultra-narrow nanoribbons on polar substrates optical-phonon scattering and ionized-impurity scattering are equally prominent. Support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0008712.

Transient responses of phosphoric acid fuel cell power plant system. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lu, Cheng-Yi

1983-01-01

An analytical and computerized study of the steady state and transient response of a phosphoric acid fuel cell (PAFC) system was completed. Parametric studies and sensitivity analyses of the PAFC system's operation were accomplished. Four non-linear dynamic models of the fuel cell stack, reformer, shift converters, and heat exchangers were developed based on nonhomogeneous non-linear partial differential equations, which include the material, component, energy balance, and electrochemical kinetic features. Due to a lack of experimental data for the dynamic response of the components only the steady state results were compared with data from other sources, indicating reasonably good agreement. A steady state simulation of the entire system was developed using, nonlinear ordinary differential equations. The finite difference method and trial-and-error procedures were used to obtain a solution. Using the model, a PAFC system, that was developed under NASA Grant, NCC3-17, was improved through the optimization of the heat exchanger network. Three types of cooling configurations for cell plates were evaluated to obtain the best current density and temperature distributions. The steady state solutions were used as the initial conditions in the dynamic model. The transient response of a simplified PAFC system, which included all of the major components, subjected to a load change was obtained. Due to the length of the computation time for the transient response calculations, analysis on a real-time computer was not possible. A simulation of the real-time calculations was developed on a batch type computer. The transient response characteristics are needed for the optimization of the design and control of the whole PAFC system. All of the models, procedures and simulations were programmed in Fortran and run on IBM 370 computers at Cleveland State University and the NASA Lewis Research Center.

Nonlinear analysis for dual-frequency concurrent energy harvesting

NASA Astrophysics Data System (ADS)

Yan, Zhimiao; Lei, Hong; Tan, Ting; Sun, Weipeng; Huang, Wenhu

2018-05-01

The dual-frequency responses of the hybrid energy harvester undergoing the base excitation and galloping were analyzed numerically. In this work, an approximate dual-frequency analytical method is proposed for the nonlinear analysis of such a system. To obtain the approximate analytical solutions of the full coupled distributed-parameter model, the forcing interactions is first neglected. Then, the electromechanical decoupled governing equation is developed using the equivalent structure method. The hybrid mechanical response is finally separated to be the self-excited and forced responses for deriving the analytical solutions, which are confirmed by the numerical simulations of the full coupled model. The forced response has great impacts on the self-excited response. The boundary of Hopf bifurcation is analytically determined by the onset wind speed to galloping, which is linearly increased by the electrical damping. Quenching phenomenon appears when the increasing base excitation suppresses the galloping. The theoretical quenching boundary depends on the forced mode velocity. The quenching region increases with the base acceleration and electrical damping, but decreases with the wind speed. Superior to the base-excitation-alone case, the existence of the aerodynamic force protects the hybrid energy harvester at resonance from damages caused by the excessive large displacement. From the view of the harvested power, the hybrid system surpasses the base-excitation-alone system or the galloping-alone system. This study advances our knowledge on intrinsic nonlinear dynamics of the dual-frequency energy harvesting system by taking advantage of the analytical solutions.

The response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric resonance

NASA Astrophysics Data System (ADS)

Nayfeh, A. H.

1983-09-01

An analysis is presented of the response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric excitation in the presence of an internal resonance of the combination type ω3 ≈ ω2 + ω1, where the ωn are the linear natural frequencies of the systems. In the case of a fundamental resonance of the third mode (i.e., Ω ≈ω 3, where Ω is the frequency of the excitation), one can identify two critical values ζ 1 and ζ 2, where ζ 2 ⩾ ζ 1, of the amplitude F of the excitation. The value F = ζ2 corresponds to the transition from stable to unstable solutions. When F < ζ1, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but the non-linearity limits the motion to a finite amplitude steady state. The amplitude of the third mode, which is directly excited, is independent of F, whereas the amplitudes of the first and second modes, which are indirectly excited through the internal resonance, are functions of F. When ζ1 ⩽ F ⩽ ζ2, the motion decays or achieves a finite amplitude steady state depending on the initial conditions according to the non-linear theory, whereas it decays to zero according to the linear theory. This is an example of subcritical instability. In the case of a fundamental resonance of either the first or second mode, the trivial response is the only possible steady state. When F ⩽ ζ2, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but it is aperiodic according to the non-linear theory. Experiments are being planned to check these theoretical results.

A comparative study of the effects of cone-plate and parallel-plate geometries on rheological properties under oscillatory shear flow

NASA Astrophysics Data System (ADS)

Song, Hyeong Yong; Salehiyan, Reza; Li, Xiaolei; Lee, Seung Hak; Hyun, Kyu

2017-11-01

In this study, the effects of cone-plate (C/P) and parallel-plate (P/P) geometries were investigated on the rheological properties of various complex fluids, e.g. single-phase (polymer melts and solutions) and multiphase systems (polymer blend and nanocomposite, and suspension). Small amplitude oscillatory shear (SAOS) tests were carried out to compare linear rheological responses while nonlinear responses were compared using large amplitude oscillatory shear (LAOS) tests at different frequencies. Moreover, Fourier-transform (FT)-rheology method was used to analyze the nonlinear responses under LAOS flow. Experimental results were compared with predictions obtained by single-point correction and shear rate correction. For all systems, SAOS data measured by C/P and P/P coincide with each other, but results showed discordance between C/P and P/P measurements in the nonlinear regime. For all systems except xanthan gum solutions, first-harmonic moduli were corrected using a single horizontal shift factor, whereas FT rheology-based nonlinear parameters ( I 3/1, I 5/1, Q 3, and Q 5) were corrected using vertical shift factors that are well predicted by single-point correction. Xanthan gum solutions exhibited anomalous corrections. Their first-harmonic Fourier moduli were superposed using a horizontal shift factor predicted by shear rate correction applicable to highly shear thinning fluids. The distinguished corrections were observed for FT rheology-based nonlinear parameters. I 3/1 and I 5/1 were superposed by horizontal shifts, while the other systems displayed vertical shifts of I 3/1 and I 5/1. Q 3 and Q 5 of xanthan gum solutions were corrected using both horizontal and vertical shift factors. In particular, the obtained vertical shift factors for Q 3 and Q 5 were twice as large as predictions made by single-point correction. Such larger values are rationalized by the definitions of Q 3 and Q 5. These results highlight the significance of horizontal shift corrections in nonlinear oscillatory shear data.

Optical response of two coupled optomechanical systems in the presence of nonlinear mediums

NASA Astrophysics Data System (ADS)

Asghari Nejad, A.; Askari, H. R.; Baghshahi, H. R.

2018-01-01

In this paper, we investigate response of a hybrid optomechanical system in different situations. This system is composed of two coupled optomechanical cavities, which one of them is filled with an optical parametric amplifier (OPA) and the other one encompasses a nonlinear Kerr medium. The Hamiltonian of the system is written in a rotating frame. The dynamics of the system is obtained by the quantum Langevin equations of motion in a steady state regime. The results show that the presence of OPA and the Kerr medium in the system can considerably change the behavior of both cavities. For this reason, we show that by choosing different values for the optical parameters of the system, one can switches the behaviors of the cavities between mono-, bi- and tristability. Also, we show that by changing the detunings of the cavities, one can obtain uncommon responses from the system. Furthermore, we show that it is possible to create proper optical multistability regions for both cavities.

Transfer Functions Via Laplace- And Fourier-Borel Transforms

NASA Technical Reports Server (NTRS)

Can, Sumer; Unal, Aynur

1991-01-01

Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.

Narrow band noise response of a Belleville spring resonator.

PubMed

Lyon, Richard H

2013-09-01

This study of nonlinear dynamics includes (i) an identification of quasi-steady states of response using equivalent linearization, (ii) the temporal simulation of the system using Heun's time step procedure on time domain analytic signals, and (iii) a laboratory experiment. An attempt has been made to select material and measurement parameters so that nearly the same systems are used and analyzed for all three parts of the study. This study illustrates important features of nonlinear response to narrow band excitation: (a) states of response that the system can acquire with transitions of the system between those states, (b) the interaction between the noise source and the vibrating load in which the source transmits energy to or draws energy from the load as transitions occur; (c) the lag or lead of the system response relative to the source as transitions occur that causes the average frequencies of source and response to differ; and (d) the determination of the state of response (mass or stiffness controlled) by observation of the instantaneous phase of the influence function. These analyses take advantage of the use of time domain analytic signals that have a complementary role to functions that are analytic in the frequency domain.

Nonlinear ultrasonic stimulated thermography for damage assessment in isotropic fatigued structures

NASA Astrophysics Data System (ADS)

Fierro, Gian Piero Malfense; Calla', Danielle; Ginzburg, Dmitri; Ciampa, Francesco; Meo, Michele

2017-09-01

Traditional non-destructive evaluation (NDE) and structural health monitoring (SHM) systems are used to analyse that a structure is free of any harmful damage. However, these techniques still lack sensitivity to detect the presence of material micro-flaws in the form of fatigue damage and often require time-consuming procedures and expensive equipment. This research work presents a novel "nonlinear ultrasonic stimulated thermography" (NUST) method able to overcome some of the limitations of traditional linear ultrasonic/thermography NDE-SHM systems and to provide a reliable, rapid and cost effective estimation of fatigue damage in isotropic materials. Such a hybrid imaging approach combines the high sensitivity of nonlinear acoustic/ultrasonic techniques to detect micro-damage, with local defect frequency selection and infrared imaging. When exciting structures with an optimised frequency, nonlinear elastic waves are observed and higher frictional work at the fatigue damaged area is generated due to clapping and rubbing of the crack faces. This results in heat at cracked location that can be measured using an infrared camera. A Laser Vibrometer (LV) was used to evaluate the extent that individual frequency components contribute to the heating of the damage region by quantifying the out-of-plane velocity associated with the fundamental and second order harmonic responses. It was experimentally demonstrated the relationship between a nonlinear ultrasound parameter (βratio) of the material nonlinear response to the actual temperature rises near the crack. These results demonstrated that heat generation at damaged regions could be amplified by exciting at frequencies that provide nonlinear responses, thus improving the imaging of material damage and the reliability of NUST in a quick and reproducible manner.

Design of a nonlinear torsional vibration absorber

NASA Astrophysics Data System (ADS)

Tahir, Ammaar Bin

Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is usually tuned for a specific resonant frequency or an operating frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies, or for a system with varying excitation frequency. Vibration dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. In this study, an experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber with geometrically induced cubic stiffness nonlinearity. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, the design optimization of the nonlinear torsional vibration absorber was carried out using an equivalent 2-DOF modal model. The optimality criterion was chosen to be maximization of energy dissipation in the nonlinear absorber attached to the equivalent 2-DOF system. The optimized design parameters of the nonlinear absorber were tested on the original 5-DOF system numerically. A comparison was made between the performance of linear and nonlinear absorbers using the numerical models. The comparison showed the superiority of the nonlinear absorber over its linear counterpart for the given set of primary system parameters as the vibration energy dissipation in the former is larger than that in the latter. A nonlinear absorber design has been proposed comprising of thin beams as elastic elements. The geometric configuration of the proposed design has been shown to provide cubic stiffness nonlinearity in torsion. The values of design variables, namely the strength of nonlinearity alpha and torsional stiffness kalpha, were obtained by optimizing dimensions and material properties of the beams for a maximum vibration energy dissipation in the nonlinear absorber. A parametric study has also been conducted to analyze the effect of the magnitude of excitation provided to the system on the performance of a nonlinear absorber. It has been shown that the nonlinear absorber turns out to be more effective in terms of energy dissipation as compared to a linear absorber with an increase in the excitation level applied to the system.

Modeling and comparative study of linear and nonlinear controllers for rotary inverted pendulum

NASA Astrophysics Data System (ADS)

Lima, Byron; Cajo, Ricardo; Huilcapi, Víctor; Agila, Wilton

2017-01-01

The rotary inverted pendulum (RIP) is a problem difficult to control, several studies have been conducted where different control techniques have been applied. Literature reports that, although problem is nonlinear, classical PID controllers presents appropriate performances when applied to the system. In this paper, a comparative study of the performances of linear and nonlinear PID structures is carried out. The control algorithms are evaluated in the RIP system, using indices of performance and power consumption, which allow the categorization of control strategies according to their performance. This article also presents the modeling system, which has been estimated some of the parameters involved in the RIP system, using computer-aided design tools (CAD) and experimental methods or techniques proposed by several authors attended. The results indicate a better performance of the nonlinear controller with an increase in the robustness and faster response than the linear controller.

Analysis of helicopter flight dynamics through modeling and simulation of primary flight control actuation system

NASA Astrophysics Data System (ADS)

Nelson, Hunter Barton

A simplified second-order transfer function actuator model used in most flight dynamics applications cannot easily capture the effects of different actuator parameters. The present work integrates a nonlinear actuator model into a nonlinear state space rotorcraft model to determine the effect of actuator parameters on key flight dynamics. The completed actuator model was integrated with a swashplate kinematics where step responses were generated over a range of key hydraulic parameters. The actuator-swashplate system was then introduced into a nonlinear state space rotorcraft simulation where flight dynamics quantities such as bandwidth and phase delay analyzed. Frequency sweeps were simulated for unique actuator configurations using the coupled nonlinear actuator-rotorcraft system. The software package CIFER was used for system identification and compared directly to the linearized models. As the actuator became rate saturated, the effects on bandwidth and phase delay were apparent on the predicted handling qualities specifications.

Strong Local-Field Enhancement of the Nonlinear Soft-Mode Response in a Molecular Crystal

NASA Astrophysics Data System (ADS)

Folpini, Giulia; Reimann, Klaus; Woerner, Michael; Elsaesser, Thomas; Hoja, Johannes; Tkatchenko, Alexandre

2017-09-01

The nonlinear response of soft-mode excitations in polycrystalline acetylsalicylic acid (aspirin) is studied with two-dimensional terahertz spectroscopy. We demonstrate that the correlation of CH3 rotational modes with collective oscillations of π electrons drives the system into the nonperturbative regime of light-matter interaction, even for a moderate strength of the THz driving field on the order of 50 kV /cm . Nonlinear absorption around 1.1 THz leads to a blueshifted coherent emission at 1.7 THz, revealing the dynamic breakup of the strong electron-phonon correlations. The observed behavior is reproduced by theoretical calculations including dynamic local-field correlations.

Agent-based modeling of endotoxin-induced acute inflammatory response in human blood leukocytes.

PubMed

Dong, Xu; Foteinou, Panagiota T; Calvano, Steven E; Lowry, Stephen F; Androulakis, Ioannis P

2010-02-18

Inflammation is a highly complex biological response evoked by many stimuli. A persistent challenge in modeling this dynamic process has been the (nonlinear) nature of the response that precludes the single-variable assumption. Systems-based approaches offer a promising possibility for understanding inflammation in its homeostatic context. In order to study the underlying complexity of the acute inflammatory response, an agent-based framework is developed that models the emerging host response as the outcome of orchestrated interactions associated with intricate signaling cascades and intercellular immune system interactions. An agent-based modeling (ABM) framework is proposed to study the nonlinear dynamics of acute human inflammation. The model is implemented using NetLogo software. Interacting agents involve either inflammation-specific molecules or cells essential for the propagation of the inflammatory reaction across the system. Spatial orientation of molecule interactions involved in signaling cascades coupled with the cellular heterogeneity are further taken into account. The proposed in silico model is evaluated through its ability to successfully reproduce a self-limited inflammatory response as well as a series of scenarios indicative of the nonlinear dynamics of the response. Such scenarios involve either a persistent (non)infectious response or innate immune tolerance and potentiation effects followed by perturbations in intracellular signaling molecules and cascades. The ABM framework developed in this study provides insight on the stochastic interactions of the mediators involved in the propagation of endotoxin signaling at the cellular response level. The simulation results are in accordance with our prior research effort associated with the development of deterministic human inflammation models that include transcriptional dynamics, signaling, and physiological components. The hypothetical scenarios explored in this study would potentially improve our understanding of how manipulating the behavior of the molecular species could manifest into emergent behavior of the overall system.

Damage detection in sandwich composite materials using laser vibrometry in conjunction with nonlinear system identification

NASA Astrophysics Data System (ADS)

Underwood, Sara; Koester, David; Adams, Douglas E.

2009-03-01

Fiberglass sandwich panels are tested to study a vibration-based method for locating damage in composite materials. This method does not rely on a direct comparison of the natural frequencies, mode shapes, or residues in the forced vibration response data. Specifically, a nonlinear system identification based method for damage detection is sought that reduces the sensitivity of damage detection results to changes in vibration measurements due to variations in boundary conditions, environmental conditions, and material properties of the panel. Damage mechanisms considered include a disbond between the core and face sheet and a crack within the core. A panel is excited by a skewed piezoelectric actuator over a broad frequency range while a three-dimensional scanning laser vibrometer measures the surface velocity of the panel along three orthogonal axes. The forced frequency response data measured using the scanning laser vibrometer at multiple excitation amplitudes is processed to identify areas of the panel that exhibit significant nonlinear response characteristics. It is demonstrated that these localized nonlinearities in the panel coincide with the damaged areas of the composite material. Because changes in the measured frequency response functions due to nonlinear distortions associated with the damage can be identified without comparing the vibration data to a reference (baseline) signature of the undamaged material, this vibration technique for damage detection in composite materials exhibits less sensitivity to variations in the underlying linear characteristics than traditional methods. It is also demonstrated that the damage at a given location can be classified as either due to a disbond or core crack because these two types of damage produce difference signatures when comparing the multi-amplitude frequency response functions.

On the geometrically nonlinear elastic response of class θ = 1 tensegrity prisms

NASA Astrophysics Data System (ADS)

Mascolo, Ida; Amendola, Ada; Zuccaro, Giulio; Feo, Luciano; Fraternali, Fernando

2018-03-01

The present work studies the geometrically nonlinear response of class ϑ=1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables) or compression (bars), under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either 'standard' or 'expanded' configurations. An experimental validation of the predicted constitutive response is conducted with reference to a 'thick' and a 'slender' model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.

Nonlinear Time Delayed Feedback Control of Aeroelastic Systems: A Functional Approach

NASA Technical Reports Server (NTRS)

Marzocca, Piergiovanni; Librescu, Liviu; Silva, Walter A.

2003-01-01

In addition to its intrinsic practical importance, nonlinear time delayed feedback control applied to lifting surfaces can result in interesting aeroelastic behaviors. In this paper, nonlinear aeroelastic response to external time-dependent loads and stability boundary for actively controlled lifting surfaces, in an incompressible flow field, are considered. The structural model and the unsteady aerodynamics are considered linear. The implications of the presence of time delays in the linear/nonlinear feedback control and of geometrical parameters on the aeroelasticity of lifting surfaces are analyzed and conclusions on their implications are highlighted.

A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2003-01-01

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.

Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equations

NASA Technical Reports Server (NTRS)

Mitchell, L. D.; David, J. W.

1983-01-01

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

A simple approach to nonlinear estimation of physical systems

USGS Publications Warehouse

Christakos, G.

1988-01-01

Recursive algorithms for estimating the states of nonlinear physical systems are developed. This requires some key hypotheses regarding the structure of the underlying processes. Members of this class of random processes have several desirable properties for the nonlinear estimation of random signals. An assumption is made about the form of the estimator, which may then take account of a wide range of applications. Under the above assumption, the estimation algorithm is mathematically suboptimal but effective and computationally attractive. It may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. To link theory with practice, some numerical results for a simulated system are presented, in which the responses from the proposed and the extended Kalman algorithms are compared. ?? 1988.

Nonlinear adaptive control system design with asymptotically stable parameter estimation error

NASA Astrophysics Data System (ADS)

Mishkov, Rumen; Darmonski, Stanislav

2018-01-01

The paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error. The advantages of the approach include asymptotic unknown parameter estimation without persistent excitation and capability to directly control the estimates transient response time. The method proposed modifies the basic parameter estimation dynamics designed via a known nonlinear adaptive control approach. The modification is based on the generalised prediction error, a priori constraints with a hierarchical parameter projection algorithm, and the stable data accumulation concepts. The data accumulation principle is the main tool for achieving asymptotic unknown parameter estimation. It relies on the parametric identifiability system property introduced. Necessary and sufficient conditions for exponential stability of the data accumulation dynamics are derived. The approach is applied in a nonlinear adaptive speed tracking vector control of a three-phase induction motor.

The Shock and Vibration Digest. Volume 15. Number 1

DTIC Science & Technology

1983-01-01

acoustics The books are arranged to engineer is statistical energy analysis (SEA). This show the wealth of information that exists and the concept is...is also used for vibrating systems in pie nonlinear elements. However, for systems with a which statistical energy analysis and power flow continuous... statistical energy analysis to analyze the random nonlinear algebraic equations can be difficult. response of two identical subsystems coupled at an end

Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

NASA Astrophysics Data System (ADS)

Chiang, C. K.; Xue, David Y.; Mei, Chuh

1993-04-01

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

NASA Technical Reports Server (NTRS)

Chiang, C. K.; Xue, David Y.; Mei, Chuh

1993-01-01

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

Nonlinear Whirl Response of a High-Speed Seal Test Rotor With Marginal and Extended Squeeze-Film Dampers

NASA Technical Reports Server (NTRS)

Proctor, Margaret P.; Gunter, Edgar J.

2005-01-01

Synchronous and nonsynchronous whirl response analysis of a double overhung, high-speed seal test rotor with ball bearings supported in 5.84- and 12.7-mm-long, un-centered squeeze-film oil dampers is presented. Test performance with the original damper of length 5.84 mm was marginal, with nonsynchronous whirling at the overhung seal test disk and high amplitude synchronous response above 32,000 rpm near the drive spline section occurring. A system critical speed analysis of the drive system and the high-speed seal test rotor indicated that the first two critical speeds are associated with the seal test rotor. Nonlinear synchronous unbalance and time transient whirl studies were conducted on the seal test rotor with the original and extended damper lengths. With the original damper design, the nonlinear synchronous response showed that unbalance could cause damper lockup at 33,000 rpm. Alford cross-coupling forces were also included at the overhung seal test disk for the whirl analysis. Sub-synchronous whirling at the seal test disk was observed in the nonlinear time transient analysis. With the extended damper length of 12.7 mm, the sub-synchronous motion was eliminated and the rotor unbalance response was acceptable to 45,000 rpm with moderate rotor unbalance. However, with high rotor unbalance, damper lockup could still occur at 33,000 rpm, even with the extended squeeze-film dampers. Therefore, the test rotor must be reasonably balanced in order for the un-centered dampers to be effective.

A design pathfinder with material correlation points for inflatable systems

NASA Astrophysics Data System (ADS)

Fulcher, Jared Terrell

The incorporation of inflatable structures into aerospace systems can produce significant advantages in stowed volume to mechanical effectiveness and overall weight. Many applications of these ultra-lightweight systems are designed to precisely control internal or external surfaces, or both, to achieve desired performance. The modeling of these structures becomes complex due to the material nonlinearities inherent to the majority of construction materials used in inflatable structures. Furthermore, accurately modeling the response and behavior of the interfacing boundaries that are common to many inflatable systems will lead to better understanding of the entire class of structures. The research presented involved using nonlinear finite element simulations correlated with photogrammetry testing to develop a procedure for defining material properties for commercially available polyurethane-coated woven nylon fabric, which is representative of coated materials that have been proven materials for use in many inflatable systems. Further, the new material model was used to design and develop an inflatable pathfinder system which employs only internal pressure to control an assembly of internal membranes. This canonical inflatable system will be used for exploration and development of general understanding of efficient design methodology and analysis of future systems. Canonical structures are incorporated into the design of the phased pathfinder system to allow for more universal insight. Nonlinear finite element simulations were performed to evaluate the effect of various boundary conditions, loading configurations, and material orientations on the geometric precision of geometries representing typical internal/external surfaces commonly incorporated into inflatable pathfinder system. The response of the inflatable system to possible damage was also studied using nonlinear finite element simulations. Development of a correlated material model for analysis of the inflatable pathfinder system has improved the efficiency of design and analysis techniques of future inflatable structures. KEYWORDS: Nonlinear Finite Element, Inflatable Structures, Gossamer Space Systems, Photogrammetry Measurements, Coated Woven Fabric.

A distributed lag approach to fitting non-linear dose-response models in particulate matter air pollution time series investigations.

PubMed

Roberts, Steven; Martin, Michael A

2007-06-01

The majority of studies that have investigated the relationship between particulate matter (PM) air pollution and mortality have assumed a linear dose-response relationship and have used either a single-day's PM or a 2- or 3-day moving average of PM as the measure of PM exposure. Both of these modeling choices have come under scrutiny in the literature, the linear assumption because it does not allow for non-linearities in the dose-response relationship, and the use of the single- or multi-day moving average PM measure because it does not allow for differential PM-mortality effects spread over time. These two problems have been dealt with on a piecemeal basis with non-linear dose-response models used in some studies and distributed lag models (DLMs) used in others. In this paper, we propose a method for investigating the shape of the PM-mortality dose-response relationship that combines a non-linear dose-response model with a DLM. This combined model will be shown to produce satisfactory estimates of the PM-mortality dose-response relationship in situations where non-linear dose response models and DLMs alone do not; that is, the combined model did not systemically underestimate or overestimate the effect of PM on mortality. The combined model is applied to ten cities in the US and a pooled dose-response model formed. When fitted with a change-point value of 60 microg/m(3), the pooled model provides evidence for a positive association between PM and mortality. The combined model produced larger estimates for the effect of PM on mortality than when using a non-linear dose-response model or a DLM in isolation. For the combined model, the estimated percentage increase in mortality for PM concentrations of 25 and 75 microg/m(3) were 3.3% and 5.4%, respectively. In contrast, the corresponding values from a DLM used in isolation were 1.2% and 3.5%, respectively.

The coupled nonlinear dynamics of a lift system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk

2014-12-10

Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This papermore » presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.« less

Triggering of longitudinal combustion instabilities in solid rocket motors: Nonlinear combustion response

NASA Technical Reports Server (NTRS)

Wicker, J. M.; Greene, W. D.; Kim, S. I.; Yang, V.

1995-01-01

Pulsed oscillations in solid rocket motors are investigated with emphasis on nonlinear combustion response. The study employs a wave equation governing the unsteady motions in a two-phase flow, and a solution technique based on spatial- and time-averaging. A wide class of combustion response functions is studied to second-order in fluctuation amplitude to determine if, when, and how triggered instabilities arise. Conditions for triggering are derived from analysis of limit cycles, and regions of triggering are found in parametric space. Based on the behavior of model dynamical systems, introduction of linear cross-coupling and quadratic self-coupling among the acoustic modes appears to be the manner in which the nonlinear combustion response produces triggering to a stable limit cycle. Regions of initial conditions corresponding to stable pulses were found, suggesting that stability depends on initial phase angle and harmonic content, as well as the composite amplitude, of the pulse.

A semi-active H∞ control strategy with application to the vibration suppression of nonlinear high-rise building under earthquake excitations.

PubMed

Yan, Guiyun; Chen, Fuquan; Wu, Yingxiong

2016-01-01

Different from previous researches which mostly focused on linear response control of seismically excited high-rise buildings, this study aims to control nonlinear seismic response of high-rise buildings. To this end, a semi-active control strategy, in which H∞ control algorithm is used and magneto-rheological dampers are employed for an actuator, is presented to suppress the nonlinear vibration. In this strategy, a modified Kalman-Bucy observer which is suitable for the proposed semi-active strategy is developed to obtain the state vector from the measured semi-active control force and acceleration feedback, taking into account of the effects of nonlinearity, disturbance and uncertainty of controlled system parameters by the observed nonlinear accelerations. Then, the proposed semi-active H∞ control strategy is applied to the ASCE 20-story benchmark building when subjected to earthquake excitation and compared with the other control approaches by some control criteria. It is indicated that the proposed semi-active H∞ control strategy provides much better control performances by comparison with the semi-active MPC and Clipped-LQG control approaches, and can reduce nonlinear seismic response and minimize the damage in the buildings. Besides, it enhances the reliability of the control performance when compared with the active control strategy. Thus, the proposed semi-active H∞ control strategy is suitable for suppressing the nonlinear vibration of high-rise buildings.

Cross-Diffusion Driven Instability for a Lotka-Volterra Competitive Reaction-Diffusion System

NASA Astrophysics Data System (ADS)

Gambino, G.; Lombardo, M. C.; Sammartino, M.

2008-04-01

In this work we investigate the possibility of the pattern formation for a reaction-diffusion system with nonlinear diffusion terms. Through a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-diffusion effects are responsible for the initiation of spatial patterns. Finally, we find a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.

Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system

NASA Astrophysics Data System (ADS)

Yang, J. H.; Sanjuán, Miguel A. F.; Liu, H. G.; Litak, G.; Li, X.

2016-12-01

We investigate the stochastic response of a noisy bistable fractional-order system when the fractional-order lies in the interval (0, 2]. We focus mainly on the stochastic P-bifurcation and the phenomenon of the stochastic resonance. We compare the generalized Euler algorithm and the predictor-corrector approach which are commonly used for numerical calculations of fractional-order nonlinear equations. Based on the predictor-corrector approach, the stochastic P-bifurcation and the stochastic resonance are investigated. Both the fractional-order value and the noise intensity can induce an stochastic P-bifurcation. The fractional-order may lead the stationary probability density function to turn from a single-peak mode to a double-peak mode. However, the noise intensity may transform the stationary probability density function from a double-peak mode to a single-peak mode. The stochastic resonance is investigated thoroughly, according to the linear and the nonlinear response theory. In the linear response theory, the optimal stochastic resonance may occur when the value of the fractional-order is larger than one. In previous works, the fractional-order is usually limited to the interval (0, 1]. Moreover, the stochastic resonance at the subharmonic frequency and the superharmonic frequency are investigated respectively, by using the nonlinear response theory. When it occurs at the subharmonic frequency, the resonance may be strong and cannot be ignored. When it occurs at the superharmonic frequency, the resonance is weak. We believe that the results in this paper might be useful for the signal processing of nonlinear systems.

Linear and nonlinear dynamics of isospectral granular chains

NASA Astrophysics Data System (ADS)

Chaunsali, R.; Xu, H.; Yang, J.; Kevrekidis, P. G.

2017-04-01

We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the similarities in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains, both ordered and disordered. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.

Step-response of a torsional device with multiple discontinuous non-linearities: Formulation of a vibratory experiment

NASA Astrophysics Data System (ADS)

Krak, Michael D.; Dreyer, Jason T.; Singh, Rajendra

2016-03-01

A vehicle clutch damper is intentionally designed to contain multiple discontinuous non-linearities, such as multi-staged springs, clearances, pre-loads, and multi-staged friction elements. The main purpose of this practical torsional device is to transmit a wide range of torque while isolating torsional vibration between an engine and transmission. Improved understanding of the dynamic behavior of the device could be facilitated by laboratory measurement, and thus a refined vibratory experiment is proposed. The experiment is conceptually described as a single degree of freedom non-linear torsional system that is excited by an external step torque. The single torsional inertia (consisting of a shaft and torsion arm) is coupled to ground through parallel production clutch dampers, which are characterized by quasi-static measurements provided by the manufacturer. Other experimental objectives address physical dimensions, system actuation, flexural modes, instrumentation, and signal processing issues. Typical measurements show that the step response of the device is characterized by three distinct non-linear regimes (double-sided impact, single-sided impact, and no-impact). Each regime is directly related to the non-linear features of the device and can be described by peak angular acceleration values. Predictions of a simplified single degree of freedom non-linear model verify that the experiment performs well and as designed. Accordingly, the benchmark measurements could be utilized to validate non-linear models and simulation codes, as well as characterize dynamic parameters of the device including its dissipative properties.

Active muscle response using feedback control of a finite element human arm model.

PubMed

Östh, Jonas; Brolin, Karin; Happee, Riender

2012-01-01

Mathematical human body models (HBMs) are important research tools that are used to study the human response in car crash situations. Development of automotive safety systems requires the implementation of active muscle response in HBM, as novel safety systems also interact with vehicle occupants in the pre-crash phase. In this study, active muscle response was implemented using feedback control of a nonlinear muscle model in the right upper extremity of a finite element (FE) HBM. Hill-type line muscle elements were added, and the active and passive properties were assessed. Volunteer tests with low impact loading resulting in elbow flexion motions were performed. Simulations of posture maintenance in a gravity field and the volunteer tests were successfully conducted. It was concluded that feedback control of a nonlinear musculoskeletal model can be used to obtain posture maintenance and human-like reflexive responses in an FE HBM.

Nonlinear Processing of Auditory Brainstem Response

DTIC Science & Technology

2001-10-25

Kraków, Poland Abstract: - Auditory brainstem response potentials (ABR) are signals calculated from the EEG signals registered as responses to an...acoustic activation of the auditory system. The ABR signals provide an objective, diagnostic method, widely applied in examinations of hearing organs

Model based design of electronic throttle control

NASA Astrophysics Data System (ADS)

Cherian, Fenin; Ranjan, Ashish; Bhowmick, Pathikrit; Rammohan, A.

2017-11-01

With the advent of torque based Engine Management Systems, the precise control and robust performance of the throttle body becomes a key factor in the overall performance of the vehicle. Electronic Throttle Control provides benefits such as improved air-fuel ratio for improving the vehicle performance and lower exhausts emissions to meet the stringent emission norms. Modern vehicles facilitate various features such as Cruise Control, Traction Control, Electronic Stability Program and Pre-crash systems. These systems require control over engine power without driver intervention, which is not possible with conventional mechanical throttle system. Thus these systems are integrated to function with the electronic throttle control. However, due to inherent non-linearities in the throttle body, the control becomes a difficult task. In order to eliminate the influence of this hysteresis at the initial operation of the butterfly valve, a control to compensate the shortage must be added to the duty required for starting throttle operation when the initial operation is detected. Therefore, a lot of work is being done in this field to incorporate the various nonlinearities to achieve robust control. In our present work, the ETB was tested to verify the working of the system. Calibration of the TPS sensors was carried out in order to acquire accurate throttle opening angle. The response of the calibrated system was then plotted against a step input signal. A linear model of the ETB was prepared using Simulink and its response was compared with the experimental data to find out the initial deviation of the model from the actual system. To reduce this deviation, non-linearities from existing literature were introduced to the system and a response analysis was performed to check the deviation from the actual system. Based on this investigation, an introduction of a new nonlinearity parameter can be used in future to reduce the deviation further making the control of the ETB more precise and accurate.

Analysis of tristable energy harvesting system having fractional order viscoelastic material

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oumbé Tékam, G. T.; Woafo, P.; Kitio Kwuimy, C. A.

2015-01-15

A particular attention is devoted to analyze the dynamics of a strongly nonlinear energy harvester having fractional order viscoelastic flexible material. The strong nonlinearity is obtained from the magnetic interaction between the end free of the flexible material and three equally spaced magnets. Periodic responses are computed using the KrylovBogoliubov averaging method, and the effects of fractional order damping on the output electric energy are analyzed. It is obtained that the harvested energy is enhanced for small order of the fractional derivative. Considering the order and strength of the fractional viscoelastic property as control parameter, the complexity of the systemmore » response is investigated through the Melnikov criteria for horseshoes chaos, which allows us to derive the mathematical expression of the boundary between intra-well motion and bifurcations appearance domain. We observe that the order and strength of the fractional viscoelastic property can be effectively used to control chaos in the system. The results are confirmed by the smooth and fractal shape of the basin of attraction as the order of derivative decreases. The bifurcation diagrams and the corresponding Lyapunov exponents are plotted to get insight into the nonlinear response of the system.« less

Computational Studies on Optoelectronic and Nonlinear Properties of Octaphyrin Derivatives

PubMed Central

Islam, Nasarul; Lone, Irfan H.

2017-01-01

The electronic and nonlinear optical (NLO) properties of octaphyrin derivatives were studied by employing the DFT/TDFT at CAM-B3LYP/6-311++G (2d, 2p) level of the theory. Thiophene, phenyl, methyl and cyano moieties were substituted on the molecular framework of octaphyrin core, in order to observe the change in optoelectronic and nonlinear response of these systems. The frontier molecular orbital studies and values of electron affinity reveals that the studied compounds are stable against the oxygen and moisture present in air. The calculated ionization energies, adiabatic electron affinity and reorganization energy values indicate that octaphyrin derivatives can be employed as effective n-type material for Organic Light Emitting Diodes (OLEDs). This character shows an enhancement with the introduction of an electron withdrawing group in the octaphyrin framework. The polarizability and hyperpolarizability values of octaphyrin derivatives demonstrate that they are good candidates for NLO devices. The nonlinear response of these systems shows enhancement on the introduction of electron donating groups on octaphyrin moiety. However, these claims needs further experimental verification. PMID:28321394

Study of the use of a nonlinear, rate limited, filter on pilot control signals

NASA Technical Reports Server (NTRS)

Adams, J. J.

1977-01-01

The use of a filter on the pilot's control output could improve the performance of the pilot-aircraft system. What is needed is a filter with a sharp high frequency cut-off, no resonance peak, and a minimum of lag at low frequencies. The present investigation studies the usefulness of a nonlinear, rate limited, filter in performing the needed function. The nonlinear filter is compared with a linear, first order filter, and no filter. An analytical study using pilot models and a simulation study using experienced test pilots was performed. The results showed that the nonlinear filter does promote quick, steady maneuvering. It is shown that the nonlinear filter attenuates the high frequency remnant and adds less phase lag to the low frequency signal than does the linear filter. It is also shown that the rate limit in the nonlinear filter can be set to be too restrictive, causing an unstable pilot-aircraft system response.

Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks

PubMed Central

Mangussi, Franco

2016-01-01

In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined. PMID:27648829

The Design of Feedback Control Systems Containing a Saturation Type Nonlinearity

NASA Technical Reports Server (NTRS)

Schmidt, Stanley F.; Harper, Eleanor V.

1960-01-01

A derivation of the optimum response for a step input for plant transfer functions which have an unstable pole and further data on plants with a single zero in the left half of the s plane. The calculated data are presented tabulated in normalized form. Optimum control systems are considered. The optimum system is defined as one which keeps the error as small as possible regardless of the input, under the constraint that the input to the plant (or controlled system) is limited. Intuitive arguments show that in the case where only the error can be sensed directly, the optimum system is obtained from the optimum relay or on-off solution. References to known solutions are presented. For the case when the system is of the sampled-data type, arguments are presented which indicate the optimum sampled-data system may be extremely difficult if not impossible to realize practically except for very simple plant transfer functions. Two examples of aircraft attitude autopilots are presented, one for a statically stable and the other for a statically unstable airframe. The rate of change of elevator motion is assumed limited for these examples. It is shown that by use of nonlinear design techniques described in NASA TN D-20 one can obtain near optimum response for step inputs and reason- able response to sine wave inputs for either case. Also, the nonlinear design prevents inputs from driving the system unstable for either case.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Nonlinear cavity optomechanics with nanomechanical thermal fluctuations

PubMed Central

Leijssen, Rick; La Gala, Giada R.; Freisem, Lars; Muhonen, Juha T.; Verhagen, Ewold

2017-01-01

Although the interaction between light and motion in cavity optomechanical systems is inherently nonlinear, experimental demonstrations to date have allowed a linearized description in all except highly driven cases. Here, we demonstrate a nanoscale optomechanical system in which the interaction between light and motion is so large (single-photon cooperativity C0≈103) that thermal motion induces optical frequency fluctuations larger than the intrinsic optical linewidth. The system thereby operates in a fully nonlinear regime, which pronouncedly impacts the optical response, displacement measurement and radiation pressure backaction. Specifically, we measure an apparent optical linewidth that is dominated by thermo-mechanically induced frequency fluctuations over a wide temperature range, and show that in this regime thermal displacement measurements cannot be described by conventional analytical models. We perform a proof-of-concept demonstration of exploiting the nonlinearity to conduct sensitive quadratic readout of nanomechanical displacement. Finally, we explore how backaction in this regime affects the mechanical fluctuation spectra. PMID:28685755

Development of a multi-body nonlinear model for a seat-occupant system

NASA Astrophysics Data System (ADS)

Azizi, Yousof

A car seat is an important component of today's cars, which directly affects ride comfort experienced by occupants. Currently, the process of ride comfort evaluation is subjective. Alternatively, the ride comfort can be evaluated by a series of objective metrics in the dynamic response of the occupant. From previous studies it is well known that the dynamic behavior of a seat-occupant system is greatly affected by soft nonlinear viscoelastic materials used in the seat cushion. Therefore, in this research, especial attention was given to efficiently modeling the behavior of seat cushion. In the first part of this research, a phenomenological nonlinear viscoelastic foam model was proposed and its ability to capture uniaxial behavior of foam was investigated. The model is based on the assumption that the total stress can be decomposed into the sum of a nonlinear elastic component, modeled by a higher order polynomial of strain, and a nonlinear hereditary type viscoelastic component. System identification procedures were developed to estimate the model parameters using uniaxial cyclic compression data from experiments conducted at different rates on two types of low density polyurethane foams and three types of high density CONFOR foams. The performance of the proposed model was compared to that of other traditional continuum models. For each foam type, it was observed that lower order models are sufficient to describe the uniaxial behavior of the foam compressed at different rates. Although, the estimated model parameters were functions of the input strain rate. Alternatively, higher order comprehensive models, with strain independent parameters, were estimated as well. The estimated comprehensive model predicts foam responses under different compression rates. Also, a methodology was proposed to predict the stress-response of a layered foam system using the estimated models of each foam in the layers. Next, the estimated foam model was incorporated into a single-degree of freedom foam-mass model which is also the simplest model of seat-occupant systems. The steady-state response of the system when it is subjected to harmonic base excitation was studied using the incremental harmonic balance method. The incremental harmonic balance method was used to reduce the time required to generate the steady-state response of the system. The incremental harmonic balance method was used to reduce the time required to generate the steady-state response of the system. Experiments are conducted on a single-degree of freedom foam-mass system subjected to harmonic base excitation. Initially, the simulated response predictions were found to deviate from the experimental results. The foam-mass model was then modified to incorporate rate dependency of foam parameters resulting in response predictions that were in good agreement with experimental results. In the second part of this research, the dynamic response of a seat-occupant system was examined through a more realistic planar multi-body seat-occupant model. A constraint Lagrangian formulation was used to derive the governing equations for the seat-occupant model. First, the governing equations were solved numerically to obtain the occupant transient response, the occupant's H-Point location and the interfacial pressure distribution. Variations in the H-Point location and the seat-occupant pressure distribution with changes in the seat-occupant parameters, including the seat geometry and the occupant's characteristics, were studied. The estimated pressure was also investigated experimentally and was found to match with the results obtained using the seat-occupant model. Next, the incremental harmonic balance method was modified and used to obtain the occupant's steady-state response when the seat-occupant system was subjected to harmonic base excitation at different frequencies. The system frequency response and mode shapes at different frequencies were also obtained and compared to the previously measured experimental frequency responses. Finally, variations in the estimated frequency response with changes in the seat-occupant parameters, including the seat geometry and the occupant characteristics, were studied.

Rotor systems research aircraft risk-reduction shake test

NASA Technical Reports Server (NTRS)

Wellman, J. Brent

1990-01-01

A shake test and an extensive analysis of results were performed to evaluate the possibility of and the method for dynamically calibrating the Rotor Systems Research Aircraft (RSRA). The RSRA airframe was subjected to known vibratory loads in several degrees of freedom and the responses of many aircraft transducers were recorded. Analysis of the transducer responses using the technique of dynamic force determination showed that the RSRA, when used as a dynamic measurement system, could predict, a posteriori, an excitation force in a single axis to an accuracy of about 5 percent and sometimes better. As the analysis was broadened to include multiple degrees of freedom for the excitation force, the predictive ability of the measurement system degraded to about 20 percent, with the error occasionally reaching 100 percent. The poor performance of the measurement system is explained by the nonlinear response of the RSRA to vibratory forces and the inadequacy of the particular method used in accounting for this nonlinearity.

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

NASA Astrophysics Data System (ADS)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

Nonlinear structural joint model updating based on instantaneous characteristics of dynamic responses

NASA Astrophysics Data System (ADS)

Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin

2016-08-01

This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.

L1 adaptive control of uncertain gear transmission servo systems with deadzone nonlinearity.

PubMed

Zuo, Zongyu; Li, Xiao; Shi, Zhiguang

2015-09-01

This paper deals with the adaptive control problem of Gear Transmission Servo (GTS) systems in the presence of unknown deadzone nonlinearity and viscous friction. A global differential homeomorphism based on a novel differentiable deadzone model is proposed first. Since there exist both matched and unmatched state-dependent unknown nonlinearities, a full-state feedback L1 adaptive controller is constructed to achieve uniformly bounded transient response in addition to steady-state performance. Finally, simulation results are included to show the elimination of limit cycles, in addition to demonstrating the main results in this paper. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

A recurrence network approach for the analysis of skin blood flow dynamics in response to loading pressure.

PubMed

Liao, Fuyuan; Jan, Yih-Kuen

2012-06-01

This paper presents a recurrence network approach for the analysis of skin blood flow dynamics in response to loading pressure. Recurrence is a fundamental property of many dynamical systems, which can be explored in phase spaces constructed from observational time series. A visualization tool of recurrence analysis called recurrence plot (RP) has been proved to be highly effective to detect transitions in the dynamics of the system. However, it was found that delay embedding can produce spurious structures in RPs. Network-based concepts have been applied for the analysis of nonlinear time series recently. We demonstrate that time series with different types of dynamics exhibit distinct global clustering coefficients and distributions of local clustering coefficients and that the global clustering coefficient is robust to the embedding parameters. We applied the approach to study skin blood flow oscillations (BFO) response to loading pressure. The results showed that global clustering coefficients of BFO significantly decreased in response to loading pressure (p<0.01). Moreover, surrogate tests indicated that such a decrease was associated with a loss of nonlinearity of BFO. Our results suggest that the recurrence network approach can practically quantify the nonlinear dynamics of BFO.

A competitive binding model predicts the response of mammalian olfactory receptors to mixtures

NASA Astrophysics Data System (ADS)

Singh, Vijay; Murphy, Nicolle; Mainland, Joel; Balasubramanian, Vijay

Most natural odors are complex mixtures of many odorants, but due to the large number of possible mixtures only a small fraction can be studied experimentally. To get a realistic understanding of the olfactory system we need methods to predict responses to complex mixtures from single odorant responses. Focusing on mammalian olfactory receptors (ORs in mouse and human), we propose a simple biophysical model for odor-receptor interactions where only one odor molecule can bind to a receptor at a time. The resulting competition for occupancy of the receptor accounts for the experimentally observed nonlinear mixture responses. We first fit a dose-response relationship to individual odor responses and then use those parameters in a competitive binding model to predict mixture responses. With no additional parameters, the model predicts responses of 15 (of 18 tested) receptors to within 10 - 30 % of the observed values, for mixtures with 2, 3 and 12 odorants chosen from a panel of 30. Extensions of our basic model with odorant interactions lead to additional nonlinearities observed in mixture response like suppression, cooperativity, and overshadowing. Our model provides a systematic framework for characterizing and parameterizing such mixing nonlinearities from mixture response data.

The Life-Changing Magic of Nonlinearity in Network Control

NASA Astrophysics Data System (ADS)

Cornelius, Sean

The proper functioning and reliability of many man-made and natural systems is fundamentally tied to our ability to control them. Indeed, applications as diverse as ecosystem management, emergency response and cell reprogramming all, at their heart, require us to drive a system to--or keep it in--a desired state. This process is complicated by the nonlinear dynamics inherent to most real systems, which has traditionally been viewed as the principle obstacle to their control. In this talk, I will discuss two ways in which nonlinearity turns this view on its head, in fact representing an asset to the control of complex systems. First, I will show how nonlinearity in the form of multistability allows one to systematically design control interventions that can deliberately induce ``reverse cascading failures'', in which a network spontaneously evolves to a desirable (rather than a failed) state. Second, I will show that nonlinearity in the form of time-varying dynamics unexpectedly makes temporal networks easier to control than their static counterparts, with the former enjoying dramatic and simultaneous reductions in all costs of control. This is true despite the fact that temporality tends to fragment a network's structure, disrupting the paths that allow the directly-controlled or ``driver'' nodes to communicate with the rest of the network. Taken together, these studies shed new light on the crucial role of nonlinearity in network control, and provide support to the idea we can control nonlinearity, rather than letting nonlinearity control us.

LDV measurement of small nonlinearities in flat and curved membranes. A model for eardrum nonlinear acoustic behaviour

NASA Astrophysics Data System (ADS)

Kilian, Gladiné; Pieter, Muyshondt; Joris, Dirckx

2016-06-01

Laser Doppler Vibrometry is an intrinsic highly linear measurement technique which makes it a great tool to measure extremely small nonlinearities in the vibration response of a system. Although the measurement technique is highly linear, other components in the experimental setup may introduce nonlinearities. An important source of artificially introduced nonlinearities is the speaker, which generates the stimulus. In this work, two correction methods to remove the effects of stimulus nonlinearity are investigated. Both correction methods were found to give similar results but have different pros and cons. The aim of this work is to investigate the importance of the conical shape of the eardrum as a source of nonlinearity in hearing. We present measurements on flat and indented membranes. The data shows that the curved membrane exhibit slightly higher levels of nonlinearity compared to the flat membrane.

A new analytical method for characterizing nonlinear visual processes with stimuli of arbitrary distribution: Theory and applications.

PubMed

Hayashi, Ryusuke; Watanabe, Osamu; Yokoyama, Hiroki; Nishida, Shin'ya

2017-06-01

Characterization of the functional relationship between sensory inputs and neuronal or observers' perceptual responses is one of the fundamental goals of systems neuroscience and psychophysics. Conventional methods, such as reverse correlation and spike-triggered data analyses are limited in their ability to resolve complex and inherently nonlinear neuronal/perceptual processes because these methods require input stimuli to be Gaussian with a zero mean. Recent studies have shown that analyses based on a generalized linear model (GLM) do not require such specific input characteristics and have advantages over conventional methods. GLM, however, relies on iterative optimization algorithms and its calculation costs become very expensive when estimating the nonlinear parameters of a large-scale system using large volumes of data. In this paper, we introduce a new analytical method for identifying a nonlinear system without relying on iterative calculations and yet also not requiring any specific stimulus distribution. We demonstrate the results of numerical simulations, showing that our noniterative method is as accurate as GLM in estimating nonlinear parameters in many cases and outperforms conventional, spike-triggered data analyses. As an example of the application of our method to actual psychophysical data, we investigated how different spatiotemporal frequency channels interact in assessments of motion direction. The nonlinear interaction estimated by our method was consistent with findings from previous vision studies and supports the validity of our method for nonlinear system identification.

Ontology of Earth's nonlinear dynamic complex systems

NASA Astrophysics Data System (ADS)

Babaie, Hassan; Davarpanah, Armita

2017-04-01

As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.

Nonlinear Dynamics of a Multistage Gear Transmission System with Multi-Clearance

NASA Astrophysics Data System (ADS)

Xiang, Ling; Zhang, Yue; Gao, Nan; Hu, Aijun; Xing, Jingtang

The nonlinear torsional model of a multistage gear transmission system which consists of a planetary gear and two parallel gear stages is established with time-varying meshing stiffness, comprehensive gear error and multi-clearance. The nonlinear dynamic responses are analyzed by applying the reference of backlash bifurcation parameters. The motions of the system on the change of backlash are identified through global bifurcation diagram, largest Lyapunov exponent (LLE), FFT spectra, Poincaré maps, the phase diagrams and time series. The numerical results demonstrate that the system exhibits rich features of nonlinear dynamics such as the periodic motion, nonperiodic states and chaotic states. It is found that the sun-planet backlash has more complex effect on the system than the ring-planet backlash. The motions of the system with backlash of parallel gear are diverse including some different multi-periodic motions. Furthermore, the state of the system can change from chaos into quasi-periodic behavior, which means that the dynamic behavior of the system is composed of more stable components with the increase of the backlash. Correspondingly, the parameters of the system should be designed properly and controlled timely for better operation and enhancing the life of the system.

Data-based fault-tolerant control of high-speed trains with traction/braking notch nonlinearities and actuator failures.

PubMed

Song, Qi; Song, Yong-Duan

2011-12-01

This paper investigates the position and velocity tracking control problem of high-speed trains with multiple vehicles connected through couplers. A dynamic model reflecting nonlinear and elastic impacts between adjacent vehicles as well as traction/braking nonlinearities and actuation faults is derived. Neuroadaptive fault-tolerant control algorithms are developed to account for various factors such as input nonlinearities, actuator failures, and uncertain impacts of in-train forces in the system simultaneously. The resultant control scheme is essentially independent of system model and is primarily data-driven because with the appropriate input-output data, the proposed control algorithms are capable of automatically generating the intermediate control parameters, neuro-weights, and the compensation signals, literally producing the traction/braking force based upon input and response data only--the whole process does not require precise information on system model or system parameter, nor human intervention. The effectiveness of the proposed approach is also confirmed through numerical simulations.

Internal resonance and low frequency vibration energy harvesting

NASA Astrophysics Data System (ADS)

Yang, Wei; Towfighian, Shahrzad

2017-09-01

A nonlinear vibration energy harvester with internal resonance is presented. The proposed harvester consists of two cantilevers, each with a permanent magnet on its tip. One cantilever has a piezoelectric layer at its base. When magnetic force is applied this two degrees-of-freedom nonlinear vibration system shows the internal resonance phenomenon that broadens the frequency bandwidth compared to a linear system. Three coupled partial differential equations are obtained to predict the dynamic behavior of the nonlinear energy harvester. The perturbation method of multiple scales is used to solve equations. Results from experiments done at different vibration levels with varying distances between the magnets validate the mathematical model. Experiments and simulations show the design outperforms the linear system by doubling the frequency bandwidth. Output voltage for frequency response is studied for different system parameters. The optimal load resistance is obtained for the maximum power in the internal resonance case. The results demonstrate that a design combining internal resonance and magnetic nonlinearity improves the efficiency of energy harvesting.

Vibrational dynamics of vocal folds using nonlinear normal modes.

PubMed

Pinheiro, Alan P; Kerschen, Gaëtan

2013-08-01

Many previous works involving physical models, excised and in vivo larynges have pointed out nonlinear vibration in vocal folds during voice production. Moreover, theoretical studies involving mechanical modeling of these folds have tried to gain a profound understanding of the observed nonlinear phenomena. In this context, the present work uses the nonlinear normal mode theory to investigate the nonlinear modal behavior of 16 subjects using a two-mass mechanical modeling of the vocal folds. The free response of the conservative system at different energy levels is considered to assess the impact of the structural nonlinearity of the vocal fold tissues. The results show very interesting and complex nonlinear phenomena including frequency-energy dependence, subharmonic regimes and, in some cases, modal interactions, entrainment and bifurcations. Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

High-frequency vibration energy harvesting from impulsive excitation utilizing intentional dynamic instability caused by strong nonlinearity

NASA Astrophysics Data System (ADS)

Remick, Kevin; Dane Quinn, D.; Michael McFarland, D.; Bergman, Lawrence; Vakakis, Alexander

2016-05-01

The authors investigate a vibration-based energy harvesting system utilizing essential (nonlinearizable) nonlinearities and electromagnetic coupling elements. The system consists of a grounded, weakly damped linear oscillator (primary system) subjected to a single impulsive load. This primary system is coupled to a lightweight, damped oscillating attachment (denoted as nonlinear energy sink, NES) via a neodymium magnet and an inductance coil, and a piano wire, which generates an essential geometric cubic stiffness nonlinearity. Under impulsive input, the transient damped dynamics of this system exhibit transient resonance captures (TRCs) causing intentional large-amplitude and high-frequency instabilities in the response of the NES. These TRCs result in strong energy transfer from the directly excited primary system to the light-weight attachment. The energy is harvested by the electromagnetic elements in the coupling and, in the present case, dissipated in a resistive element in the electrical circuit. The primary goal of this work is to numerically, analytically, and experimentally demonstrate the efficacy of employing this type of intentional high-frequency dynamic instability to achieve enhanced vibration energy harvesting under impulsive excitation.

Nonlinear system identification of smart structures under high impact loads

NASA Astrophysics Data System (ADS)

Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

2013-05-01

The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure-MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure-MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes.

Efficient sparse matrix-matrix multiplication for computing periodic responses by shooting method on Intel Xeon Phi

NASA Astrophysics Data System (ADS)

Stoykov, S.; Atanassov, E.; Margenov, S.

2016-10-01

Many of the scientific applications involve sparse or dense matrix operations, such as solving linear systems, matrix-matrix products, eigensolvers, etc. In what concerns structural nonlinear dynamics, the computations of periodic responses and the determination of stability of the solution are of primary interest. Shooting method iswidely used for obtaining periodic responses of nonlinear systems. The method involves simultaneously operations with sparse and dense matrices. One of the computationally expensive operations in the method is multiplication of sparse by dense matrices. In the current work, a new algorithm for sparse matrix by dense matrix products is presented. The algorithm takes into account the structure of the sparse matrix, which is obtained by space discretization of the nonlinear Mindlin's plate equation of motion by the finite element method. The algorithm is developed to use the vector engine of Intel Xeon Phi coprocessors. It is compared with the standard sparse matrix by dense matrix algorithm and the one developed by Intel MKL and it is shown that by considering the properties of the sparse matrix better algorithms can be developed.

Active Control by Conservation of Energy Concept

NASA Technical Reports Server (NTRS)

Maestrello, Lucio

2000-01-01

Three unrelated experiments are discussed; each was extremely sensitive to initial conditions. The initial conditions are the beginnings of the origins of the information that nonlinearity displays. Initial conditions make the phenomenon unstable and unpredictable. With the knowledge of the initial conditions, active control requires far less power than that present in the system response. The first experiment is on the control of shocks from an axisymmetric supersonic jet; the second, control of a nonlinear panel response forced by turbulent boundary layer and sound; the third, control of subharmonic and harmonics of a panel forced by sound. In all three experiments, control is achieved by redistribution of periodic energy response such that the energy is nearly preserved from a previous uncontrolled state. This type of active control improves the performance of the system being controlled.

Nonequilibrium response of an electron-mediated charge density wave ordered material to a large dc electric field

NASA Astrophysics Data System (ADS)

Matveev, O. P.; Shvaika, A. M.; Devereaux, T. P.; Freericks, J. K.

2016-01-01

Using the Kadanoff-Baym-Keldysh formalism, we employ nonequilibrium dynamical mean-field theory to exactly solve for the nonlinear response of an electron-mediated charge-density-wave-ordered material. We examine both the dc current and the order parameter of the conduction electrons as the ordered system is driven by the electric field. Although the formalism we develop applies to all models, for concreteness, we examine the charge-density-wave phase of the Falicov-Kimball model, which displays a number of anomalous behaviors including the appearance of subgap density of states as the temperature increases. These subgap states should have a significant impact on transport properties, particularly the nonlinear response of the system to a large dc electric field.

Nonlinear feedback drives homeostatic plasticity in H2O2 stress response

PubMed Central

Goulev, Youlian; Morlot, Sandrine; Matifas, Audrey; Huang, Bo; Molin, Mikael; Toledano, Michel B; Charvin, Gilles

2017-01-01

Homeostatic systems that rely on genetic regulatory networks are intrinsically limited by the transcriptional response time, which may restrict a cell’s ability to adapt to unanticipated environmental challenges. To bypass this limitation, cells have evolved mechanisms whereby exposure to mild stress increases their resistance to subsequent threats. However, the mechanisms responsible for such adaptive homeostasis remain largely unknown. Here, we used live-cell imaging and microfluidics to investigate the adaptive response of budding yeast to temporally controlled H2O2 stress patterns. We demonstrate that acquisition of tolerance is a systems-level property resulting from nonlinearity of H2O2 scavenging by peroxiredoxins and our study reveals that this regulatory scheme induces a striking hormetic effect of extracellular H2O2 stress on replicative longevity. Our study thus provides a novel quantitative framework bridging the molecular architecture of a cellular homeostatic system to the emergence of nonintuitive adaptive properties. DOI: http://dx.doi.org/10.7554/eLife.23971.001 PMID:28418333

Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures

NASA Astrophysics Data System (ADS)

Sun, Limin; Chen, Lin

2017-10-01

Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.

Rail vehicle dynamic response to a nonlinear physical 'in-service' model of its secondary suspension hydraulic dampers

NASA Astrophysics Data System (ADS)

Wang, W. L.; Zhou, Z. R.; Yu, D. S.; Qin, Q. H.; Iwnicki, S.

2017-10-01

A full nonlinear physical 'in-service' model was built for a rail vehicle secondary suspension hydraulic damper with shim-pack-type valves. In the modelling process, a shim pack deflection theory with an equivalent-pressure correction factor was proposed, and a Finite Element Analysis (FEA) approach was applied. Bench test results validated the damper model over its full velocity range and thus also proved that the proposed shim pack deflection theory and the FEA-based parameter identification approach are effective. The validated full damper model was subsequently incorporated into a detailed vehicle dynamics simulation to study how its key in-service parameter variations influence the secondary-suspension-related vehicle system dynamics. The obtained nonlinear physical in-service damper model and the vehicle dynamic response characteristics in this study could be used in the product design optimization and nonlinear optimal specifications of high-speed rail hydraulic dampers.

Accounting For Nonlinearity In A Microwave Radiometer

NASA Technical Reports Server (NTRS)

Stelzried, Charles T.

1991-01-01

Simple mathematical technique found to account adequately for nonlinear component of response of microwave radiometer. Five prescribed temperatures measured to obtain quadratic calibration curve. Temperature assumed to vary quadratically with reading. Concept not limited to radiometric application; applicable to other measuring systems in which relationships between quantities to be determined and readings of instruments differ slightly from linearity.

Nonlinear optical response in graphene nanoribbons: The critical role of electron scattering

NASA Astrophysics Data System (ADS)

Karimi, F.; Davoody, A. H.; Knezevic, I.

2018-06-01

Nonlinear nanophotonics has many potential applications, such as in mode locking, frequency-comb generation, and all-optical switching. The development of materials with large nonlinear susceptibility is key to realizing nonlinear nanophotonics. Nanostructured graphene systems, such as graphene nanoribbons and nanoislands, have been predicted to have a strong plasmon-enhanced nonlinear optical behavior in the nonretarded regime. Plasmons concentrate the light field down to subwavelength scales and can enhance the nonlinear optical effects; however, plasmon resonances are narrowband and sensitive to the nanostructure geometry. Here we show that graphene nanoribbons, particularly armchair graphene nanoribbons, have a remarkably strong nonlinear optical response in the long-wavelength regime and over a broad frequency range, from terahertz to the near infrared. We use a quantum-mechanical master equation with a detailed treatment of scattering and show that, in the retarded regime, electron scattering has a critical effect on the optical nonlinearity of graphene nanoribbons, which cannot be captured via the commonly used relaxation-time approximation. At terahertz frequencies, where intraband optical transitions dominate, the strong nonlinearity (in particular, third-order Kerr nonlinearity) stems from the jagged shape of the electron energy distribution, caused by the interband electron scattering mechanisms along with the intraband inelastic scattering mechanisms. We show that the relaxation-time approximation fails to capture this quantum-mechanical phenomenon and results in a significant underestimation of the intraband nonlinearity. At the midinfrared to near infrared frequencies, where interband optical transitions dominate, the Kerr nonlinearity is significantly overestimated within the relaxation-time approximation. These findings unveil the critical effect of electron scattering on the optical nonlinearity of nanostructured graphene, and also underscore the capability of this class of materials for nonlinear nanophotonic applications.

Transient response of an active nonlinear sandwich piezolaminated plate

NASA Astrophysics Data System (ADS)

Oveisi, Atta; Nestorović, Tamara

2017-04-01

In this paper, the dynamic modelling and active vibration control of a piezolaminated plate with geometrical nonlinearities are investigated using a semi-analytical approach. For active vibration control purposes, the core orthotropic elastic layer is assumed to be perfectly bonded with two piezo-layers on its top and bottom surfaces which act as sensor and actuator, respectively. In the modelling procedure, the piezo-layers are assumed to be connected via a proportional derivative (PD) feedback control law. Hamilton's principle is employed to acquire the strong form of the dynamic equation in terms of additional higher order strain expressions by means of von Karman strain-displacement correlation. The obtained nonlinear partial differential equation (NPDE) is converted to a system of nonlinear ordinary differential equations (NODEs) by engaging Galerkin method and using the orthogonality of shape functions for the simply supported boundary conditions. Then, the resulting system of NODEs is solved numerically by employing the built-in Mathematica function, "NDSolve". Next, the vibration attenuation performance is evaluated and sensitivity of the closed-loop system is investigated for several control parameters and the external disturbance parameters. The proposed solution in open loop configuration is validated by finite element (FE) package ABAQUS both in the spatial domain and for the time-/frequency-dependent response.

Hydroelastic response of a floating runway to cnoidal waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ertekin, R. C., E-mail: ertekin@hawaii.edu; Xia, Dingwu

2014-02-15

The hydroelastic response of mat-type Very Large Floating Structures (VLFSs) to severe sea conditions, such as tsunamis and hurricanes, must be assessed for safety and survivability. An efficient and robust nonlinear hydroelastic model is required to predict accurately the motion of and the dynamic loads on a VLFS due to such large waves. We develop a nonlinear theory to predict the hydroelastic response of a VLFS in the presence of cnoidal waves and compare the predictions with the linear theory that is also developed here. This hydroelastic problem is formulated by directly coupling the structure with the fluid, by usemore » of the Level I Green-Naghdi theory for the fluid motion and the Kirchhoff thin plate theory for the runway. The coupled fluid structure system, together with the appropriate jump conditions are solved in two-dimensions by the finite-difference method. The numerical model is used to study the nonlinear response of a VLFS to storm waves which are modeled by use of the cnoidal-wave theory. Parametric studies show that the nonlinearity of the waves is very important in accurately predicting the dynamic bending moment and wave run-up on a VLFS in high seas.« less

Nonlinear Color–Metallicity Relations of Globular Clusters. VII. Nonlinear Absorption-line Index versus Metallicity Relations and Bimodal Index Distributions of NGC 5128 Globular Clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Sooyoung; Yoon, Suk-Jin, E-mail: sjyoon0691@yonsei.ac.kr

Spectroscopy on the globular cluster (GC) system of NGC 5128 revealed bimodality in absorption-line index distributions of its old GCs. GC division is a widely observed and studied phenomenon whose interpretation has depicted host galaxy formation and evolution such that it harbors two distinct metallicity groups. Such a conventional view of GC bimodality has mainly been based on photometry. The recent GC photometric data, however, presented an alternative perspective in which the nonlinear metallicity-to-color transformation is responsible for color bimodality of GC systems. Here we apply the same line of analysis to the spectral indices and examine the absorption-line indexmore » versus metallicity relations for the NGC 5128 GC system. NGC 5128 GCs display nonlinearity in the metallicity-index planes, most prominently for the Balmer lines and by a non-negligible degree for the metallicity-sensitive magnesium line. We demonstrate that the observed spectroscopic division of NGC 5128 GCs can be caused by the nonlinear nature of the metallicity-to-index conversions and thus one does not need to resort to two separate GC subgroups. Our analysis incorporating this nonlinearity provides a new perspective on the structure of NGC 5128's GC system, and a further piece to the global picture of the formation of GC systems and their host galaxies.« less

A theoretical investigation of soliton induced supercontinuum generation in liquid core photonic crystal fiber and dual core optical fiber

NASA Astrophysics Data System (ADS)

Porsezian, K.; Nithyanandan, K.; Vasantha Jayakantha Raja, R.; Ganapathy, R.

2013-07-01

The supercontinuum generation (SCG) in liquid core photonic crystal fiber (LCPCF) with versatile nonlinear response and the spectral broadening in dual core optical fiber is presented. The analysis is presented in two phase, phase I deals with the SCG in LCPCF with the effect of saturable nonlinearity and re-orientational nonlinearity. We identify and discuss the generic nature of the saturable nonlinearity and reorientational nonlinearity in the SCG, using suitable model. For the physical explanation, modulational instability and soliton fission techniques is implemented to investigate the impact of saturable nonlinear response and slow nonlinear response, respectively. It is observed that the saturable nonlinearity inevitably suppresses the MI and the subsequent SCG. On the other hand, the re-orientational nonlinearity contributes to the slow nonlinear response in addition to the conventional fast response due to the electronic contribution. The phase II features the exclusive investigation of the spectral broadening in the dual core optical fiber.

Nonlinear characterization of a bolted, industrial structure using a modal framework

NASA Astrophysics Data System (ADS)

Roettgen, Daniel R.; Allen, Matthew S.

2017-02-01

This article presents measurements from a sub assembly of an off-the-shelf automotive exhaust system containing a bolted-flange connection and uses a recently proposed modal framework to develop a nonlinear dynamic model for the structure. The nonlinear identification and characterization methods used are reviewed to highlight the strengths of the current approach and the areas where further development is needed. This marks the first use of these new testing and nonlinear identification tools, and the associated modal framework, on production hardware with a realistic joint and realistic torque levels. To screen the measurements for nonlinearities, we make use of a time frequency analysis routine designed for transient responses called the zeroed early-time fast Fourier transform (ZEFFT). This tool typically reveals the small frequency shifts and distortions that tend to occur near each mode that is affected by the nonlinearity. The damping in this structure is found to be significantly nonlinear and a Hilbert transform is used to characterize the damping versus amplitude behavior. A model is presented that captures these effects for each mode individually (e.g. assuming negligible nonlinear coupling between modes), treating each mode as a single degree-of-freedom oscillator with a spring and viscous damping element in parallel with a four parameter Iwan model. The parameters of this model are identified for each of the structure's modes that exhibited nonlinearity and the resulting nonlinear model is shown to capture the stiffness and damping accurately over a large range of response amplitudes.

Nonlinear viscoelasticity and generalized failure criterion for biopolymer gels

NASA Astrophysics Data System (ADS)

Divoux, Thibaut; Keshavarz, Bavand; Manneville, Sébastien; McKinley, Gareth

2016-11-01

Biopolymer gels display a multiscale microstructure that is responsible for their solid-like properties. Upon external deformation, these soft viscoelastic solids exhibit a generic nonlinear mechanical response characterized by pronounced stress- or strain-stiffening prior to irreversible damage and failure, most often through macroscopic fractures. Here we show on a model acid-induced protein gel that the nonlinear viscoelastic properties of the gel can be described in terms of a 'damping function' which predicts the gel mechanical response quantitatively up to the onset of macroscopic failure. Using a nonlinear integral constitutive equation built upon the experimentally-measured damping function in conjunction with power-law linear viscoelastic response, we derive the form of the stress growth in the gel following the start up of steady shear. We also couple the shear stress response with Bailey's durability criteria for brittle solids in order to predict the critical values of the stress σc and strain γc for failure of the gel, and how they scale with the applied shear rate. This provides a generalized failure criterion for biopolymer gels in a range of different deformation histories. This work was funded by the MIT-France seed fund and by the CNRS PICS-USA scheme (#36939). BK acknowledges financial support from Axalta Coating Systems.

Investigation of the dynamics of a nonlinear optical response in glassy chalcogenide semiconductors by the pump–probe method

NASA Astrophysics Data System (ADS)

Romanova, E. A.; Kuzyutkina, Yu S.; Shiryaev, V. S.; Guizard, S.

2018-03-01

An analysis of the results of measurements by using the pump–probe method with a femtosecond resolution in time and computer simulation of the charge carrier kinetics have revealed two types of a nonlinear optical response in samples of chalcogenide glasses belonging to the As – S – Se system, irradiated by 50-fs laser pulses with a wavelength of 0.79 μm. The difference in the nonlinear dynamics is due to the difference in the photoexcitation character, because laser radiation can be absorbed either through bound states in the band gap or without their participation, depending on the ratio of the pump photon energy to the bandgap energy.

Differential behavior of amino-imino constitutional isomers in nonlinear optical processes.

PubMed

Latorre, Sonia; Moreira, Ibério de P R; Villacampa, Belén; Julià, Lluís; Velasco, Dolores; Bofill, Josep Maria; López-Calahorra, Francisco

2010-03-15

A detailed study of the "blocked" amino-imino tautomers derived from N-acridine-substituted 2-aminobenzothiazole--and their effect on the nonlinear optical response--is presented. The synthesis, characterization, and nonlinear optical properties of these frozen tautomers, namely, N-methyl-N-(2-nitroacridin-6-yl)-2-aminobenzothia-zole and 3-methyl-N-(7-nitroacridin-3-yl)-2-iminobenzothiazole, are reported. A theoretical model based on valence-bond theory is also proposed and used to analyze the effects of the nuclear configuration corresponding to each frozen tautomer structure. In the present case, the aromatic form and the allylic-anion-like system of the -N-C-N- group inherent to each isomer are crucial for understanding and analyzing the different responses of each "blocked" tautomer.

Fluctuation Reduction in a Si Micromechanical Resonator Tuned to Nonlinear Internal Resonance

NASA Astrophysics Data System (ADS)

Strachan, B. Scott; Czaplewski, David; Chen, Changyao; Dykman, Mark; Lopez, Daniel; Shaw, Steven

2015-03-01

We describe experimental and theoretical results on an unusual behavior of fluctuations when the system exhibits internal resonance. We study the fundamental flexural mode (FFM) of a Si microbeam. The FFM is electrically actuated and detected. It is resonantly nonlinearly coupled to another mode, which is not directly accessible and has a frequency nearly three times the FFM frequency. Both the FFM and the passive mode have long lifetimes. We find that the passive mode can be a ``sink'' for fluctuations of the FFM. This explains the recently observed dramatic decrease of these fluctuations at nonlinear resonance. The re-distribution of the vibration amplitudes and the fluctuations is reminiscent of what happens at level anti-crossing in quantum mechanics. However, here it is different because of interplay of the dependence of the vibration frequency of the FFM on its amplitude due to internal nonlinearity and the nonlinear resonance with the passive mode. We study both the response of the system to external resonant driving and also the behavior of the system in the presence of a feedback loop. The experimental and theoretical results are in good agreement.

Response of jammed packings to thermal fluctuations

NASA Astrophysics Data System (ADS)

Wu, Qikai; Bertrand, Thibault; Shattuck, Mark D.; O'Hern, Corey S.

2017-12-01

We focus on the response of mechanically stable (MS) packings of frictionless, bidisperse disks to thermal fluctuations, with the aim of quantifying how nonlinearities affect system properties at finite temperature. In contrast, numerous prior studies characterized the structural and mechanical properties of MS packings of frictionless spherical particles at zero temperature. Packings of disks with purely repulsive contact interactions possess two main types of nonlinearities, one from the form of the interaction potential (e.g., either linear or Hertzian spring interactions) and one from the breaking (or forming) of interparticle contacts. To identify the temperature regime at which the contact-breaking nonlinearities begin to contribute, we first calculated the minimum temperatures Tc b required to break a single contact in the MS packing for both single- and multiple-eigenmode perturbations of the T =0 MS packing. We find that the temperature required to break a single contact for equal velocity-amplitude perturbations involving all eigenmodes approaches the minimum value obtained for a perturbation in the direction connecting disk pairs with the smallest overlap. We then studied deviations in the constant volume specific heat C¯V and deviations of the average disk positions Δ r from their T =0 values in the temperature regime TC ¯V100 for linear spring interactions is independent of system size. This result emphasizes that contact-breaking nonlinearities are dominant over form nonlinearities in the low-temperature range Tc b

Study of the effect of static/dynamic Coulomb friction variation at the tape-head interface of a spacecraft tape recorder by non-linear time response simulation

NASA Technical Reports Server (NTRS)

Mukhopadhyay, A. K.

1978-01-01

A description is presented of six simulation cases investigating the effect of the variation of static-dynamic Coulomb friction on servo system stability/performance. The upper and lower levels of dynamic Coulomb friction which allowed operation within requirements were determined roughly to be three times and 50% respectively of nominal values considered in a table. A useful application for the nonlinear time response simulation is the sensitivity analysis of final hardware design with respect to such system parameters as cannot be varied realistically or easily in the actual hardware. Parameters of the static/dynamic Coulomb friction fall in this category.

Studying Climate Response to Forcing by the Nonlinear Dynamical Mode Decomposition

NASA Astrophysics Data System (ADS)

Mukhin, Dmitry; Gavrilov, Andrey; Loskutov, Evgeny; Feigin, Alexander

2017-04-01

An analysis of global climate response to external forcing, both anthropogenic (mainly, CO2 and aerosol) and natural (solar and volcanic), is needed for adequate predictions of global climate change. Being complex dynamical system, the climate reacts to external perturbations exciting feedbacks (both positive and negative) making the response non-trivial and poorly predictable. Thus an extraction of internal modes of climate system, investigation of their interaction with external forcings and further modeling and forecast of their dynamics, are all the problems providing the success of climate modeling. In the report the new method for principal mode extraction from climate data is presented. The method is based on the Nonlinear Dynamical Mode (NDM) expansion [1,2], but takes into account a number of external forcings applied to the system. Each NDM is represented by hidden time series governing the observed variability, which, together with external forcing time series, are mapped onto data space. While forcing time series are considered to be known, the hidden unknown signals underlying the internal climate dynamics are extracted from observed data by the suggested method. In particular, it gives us an opportunity to study the evolution of principal system's mode structure in changing external conditions and separate the internal climate variability from trends forced by external perturbations. Furthermore, the modes so obtained can be extrapolated beyond the observational time series, and long-term prognosis of modes' structure including characteristics of interconnections and responses to external perturbations, can be carried out. In this work the method is used for reconstructing and studying the principal modes of climate variability on inter-annual and decadal time scales accounting the external forcings such as anthropogenic emissions, variations of the solar activity and volcanic activity. The structure of the obtained modes as well as their response to external factors, e.g. forecast their change in 21 century under different CO2 emission scenarios, are discussed. [1] Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510 [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J. (2016). Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. http://doi.org/10.1063/1.4968852

Vibrational resonance in an inhomogeneous medium with periodic dissipation

NASA Astrophysics Data System (ADS)

Roy-Layinde, T. O.; Laoye, J. A.; Popoola, O. O.; Vincent, U. E.; McClintock, P. V. E.

2017-09-01

The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.

Request for Information Response for the Flight Validation of Adaptive Control to Prevent Loss-of-Control Events. Overview of RFI Responses

NASA Technical Reports Server (NTRS)

Bosworth, John T.

2009-01-01

Adaptive control should be integrated with a baseline controller and only used when necessary (5 responses). Implementation as an emergency system. Immediately re-stabilize and return to controlled flight. Forced perturbation (excitation) for fine-tuning system a) Check margins; b) Develop requirements for amplitude of excitation. Adaptive system can improve performance by eating into margin constraints imposed on the non-adaptive system. Nonlinear effects due to multi-string voting.

Seismic response evaluation of base-isolated reinforced concrete buildings under bidirectional excitation

NASA Astrophysics Data System (ADS)

Bhagat, Satish; Wijeyewickrema, Anil C.

2017-04-01

This paper reports on an investigation of the seismic response of base-isolated reinforced concrete buildings, which considers various isolation system parameters under bidirectional near-fault and far-fault motions. Three-dimensional models of 4-, 8-, and 12-story base-isolated buildings with nonlinear effects in the isolation system and the superstructure are investigated, and nonlinear response history analysis is carried out. The bounding values of isolation system properties that incorporate the aging effect of isolators are also taken into account, as is the current state of practice in the design and analysis of base-isolated buildings. The response indicators of the buildings are studied for near-fault and far-fault motions weight-scaled to represent the design earthquake (DE) level and the risk-targeted maximum considered earthquake (MCER) level. Results of the nonlinear response history analyses indicate no structural damage under DE-level motions for near-fault and far-fault motions and for MCER-level far-fault motions, whereas minor structural damage is observed under MCER-level near-fault motions. Results of the base-isolated buildings are compared with their fixed-base counterparts. Significant reduction of the superstructure response of the 12-story base-isolated building compared to the fixed-base condition indicates that base isolation can be effectively used in taller buildings to enhance performance. Additionally, the applicability of a rigid superstructure to predict the isolator displacement demand is also investigated. It is found that the isolator displacements can be estimated accurately using a rigid body model for the superstructure for the buildings considered.

Optical response in a laser-driven quantum pseudodot system

NASA Astrophysics Data System (ADS)

Kilic, D. Gul; Sakiroglu, S.; Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sokmen, I.

2017-03-01

We investigate theoretically the intense laser-induced optical absorption coefficients and refractive index changes in a two-dimensional quantum pseudodot system under an uniform magnetic field. The effects of non-resonant, monochromatic intense laser field upon the system are treated within the framework of high-frequency Floquet approach in which the system is supposed to be governed by a laser-dressed potential. Linear and nonlinear absorption coefficients and relative changes in the refractive index are obtained by means of the compact-density matrix approach and iterative method. The results of numerical calculations for a typical GaAs quantum dot reveal that the optical response depends strongly on the magnitude of external magnetic field and characteristic parameters of the confinement potential. Moreover, we have demonstrated that the intense laser field modifies the confinement and thereby causes remarkable changes in the linear and nonlinear optical properties of the system.

A nonlinear energy sink with an energy harvester: Harmonically forced responses

NASA Astrophysics Data System (ADS)

Kremer, Daniel; Liu, Kefu

2017-12-01

This study intends to achieve simultaneous vibration suppression and energy harvesting using a variant form of nonlinear energy sink (NES). The proposed apparatus is not a true NES as its spring is not essentially nonlinear. In a previous study [22] (Journal of Sound and Vibration, 333 (20) (2014)), it has been shown that the apparatus demonstrates the transient behaviors similar to those of the NES. As a sequel, the present paper focuses on harmonically forced responses of the system. First, the approximate solutions of steady state responses are derived. Using the approximate solutions, the steady state behaviors are investigated by using the numerical continuation method. This is followed by an experimental study. The study has shown that under harmonic excitation, the proposed apparatus functions similarly to the NES with the typical behaviors such as strongly modulated responses, amplitude jumping, excitation level dependence, etc. Overall, the apparatus meets the design objectives: the vibration suppression and energy harvesting in a broadband manner.

Linearizing an intermodulation radar transmitter by filtering switched tones

NASA Astrophysics Data System (ADS)

Mazzaro, Gregory J.; Sherbondy, Andrew J.; Ranney, Kenneth I.; Sherbondy, Kelly D.; Martone, Anthony F.

2017-05-01

For nonlinear radar, the transmit power required to measure a detectable response from a target is relatively high, and generating that high power is achieved at the cost of linearity. This paper applies the distortion mitigation technique Linearization by Time-Multiplexed Spectrum (LITMUS) to intermodulation radar, a type of nonlinear radar which receives spectral content produced by the mixing of multiple frequencies at a nonlinear target. By implementing LITMUS, an experimental detection system for an intermodulation radar achieves a signal-to-noise ratio up to 20 dB for a total transmit power of approximately 80 mW and nonlinear targets placed at a standoff distance of 2 meters.

Generalised Transfer Functions of Neural Networks

NASA Astrophysics Data System (ADS)

Fung, C. F.; Billings, S. A.; Zhang, H.

1997-11-01

When artificial neural networks are used to model non-linear dynamical systems, the system structure which can be extremely useful for analysis and design, is buried within the network architecture. In this paper, explicit expressions for the frequency response or generalised transfer functions of both feedforward and recurrent neural networks are derived in terms of the network weights. The derivation of the algorithm is established on the basis of the Taylor series expansion of the activation functions used in a particular neural network. This leads to a representation which is equivalent to the non-linear recursive polynomial model and enables the derivation of the transfer functions to be based on the harmonic expansion method. By mapping the neural network into the frequency domain information about the structure of the underlying non-linear system can be recovered. Numerical examples are included to demonstrate the application of the new algorithm. These examples show that the frequency response functions appear to be highly sensitive to the network topology and training, and that the time domain properties fail to reveal deficiencies in the trained network structure.

Investigation of the Flutter Suppression by Fuzzy Logic Control for Hypersonic Wing

NASA Astrophysics Data System (ADS)

Li, Dongxu; Luo, Qing; Xu, Rui

This paper presents a fundamental study of flutter characteristics and control performance of an aeroelastic system based on a two-dimensional double wedge wing in the hypersonic regime. Dynamic equations were established based on the modified third order nonlinear piston theory and some nonlinear structural effects are also included. A set of important parameters are observed. And then aeroelastic control law is designed to suppress the amplitude of the LCOs for the system in the sub/supercritical speed range by applying fuzzy logic control on the input of the deflection of the flap. The overall effects of the parameters on the aeroelastic system were outlined. Nonlinear aeroelastic responses in the open- and closed-loop system are obtained through numerical methods. The simulations show fuzzy logic control methods are effective in suppressing flutter and provide a smart approach for this complicated system.

GA-optimized feedforward-PID tracking control for a rugged electrohydraulic system design.

PubMed

Sarkar, B K; Mandal, P; Saha, R; Mookherjee, S; Sanyal, D

2013-11-01

Rugged electrohydraulic systems are preferred for remote and harsh applications. Despite the low bandwidth, large deadband and flow nonlinearities in proportional valves valve and highly nonlinear friction in industry-grade cylinders that comprise rugged systems, their maintenance are much easier than very sophisticated and delicate servocontrol and servocylinder systems. With the target of making the easily maintainable system to perform comparably to a servosystem, a feedforward control has been designed here for compensating the nonlinearities. A PID feedback of the piston displacement has been employed in tandem for absorbing the unmodeled effects. All the controller parameters have been optimized by a real-coded genetic algorithm. The agreement between the achieved real-time responses for step and sinusoidal demands with those achieved by modern servosystems clearly establishes the acceptability of the controller design. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Modeling nonlinearities in MEMS oscillators.

PubMed

Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

2013-08-01

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

Development of a nonlinear model for the prediction of response times of glucose affinity sensors using concanavalin A and dextran and the development of a differential osmotic glucose affinity sensor

NASA Astrophysics Data System (ADS)

Reis, Louis G.

With the increasing prevalence of diabetes in the United States and worldwide, blood glucose monitoring must be accurate and reliable. Current enzymatic sensors have numerous disadvantages that make them unreliable and unfavorable among patients. Recent research in glucose affinity sensors correct some of the problems that enzymatic sensors experience. Dextran and concanavalin A are two of the more common components used in glucose affinity sensors. When these sensors were first explored, a model was derived to predict the response time of a glucose affinity sensor using concanavalin A and dextran. However, the model assumed the system was linear and fell short of calculating times representative of the response times determined through experimental tests with the sensors. In this work, a new model that uses the Stokes-Einstein Equation to demonstrate the nonlinear behavior of the glucose affinity assay was developed to predict the response times of similar glucose affinity sensors. In addition to the device tested by the original linear model, additional devices were identified and tested with the proposed model. The nonlinear model was designed to accommodate the many different variations between systems. The proposed model was able to accurately calculate response times for sensors using the concanavalin A-dextran affinity assay with respect to the experimentally reported times by the independent research groups. Parameter studies using the nonlinear model were able to identify possible setbacks that could compromise the response of thesystem. Specifically, the model showed that the improper use of asymmetrical membranes could increase the response time by as little as 20% or more as the device is miniaturized. The model also demonstrated that systems using the concanavalin Adextran assay would experience higher response times in the hypoglycemic range. This work attempted to replicate and improve an osmotic glucose affinity sensor. The system was designed to negate additional effects that could cause artifacts or irregular readings such as external osmotic differences and external pressure differences. However, the experimental setup and execution faced numerous setbacks that highlighted the additional difficulty that sensors using asymmetrical ceramic membranes and the concanavalin A-dextran affinity assay may experience.

Handling times and saturating transmission functions in a snail-worm symbiosis.

PubMed

Hopkins, Skylar R; McGregor, Cari M; Belden, Lisa K; Wojdak, Jeremy M

2018-06-16

All dynamic species interaction models contain an assumption that describes how contact rates scale with population density. Choosing an appropriate contact-density function is important, because different functions have different implications for population dynamics and stability. However, this choice can be challenging, because there are many possible functions, and most are phenomenological and thus difficult to relate to underlying ecological processes. Using one such phenomenological function, we described a nonlinear relationship between field transmission rates and host density in a common snail-oligochaete symbiosis. We then used a well-known contact function from predator-prey models, the Holling Type II functional response, to describe and predict host snail contact rates in the laboratory. The Holling Type II functional response accurately described both the nonlinear contact-density relationship and the average contact duration that we observed. Therefore, we suggest that contact rates saturate with host density in this system because each snail contact requires a non-instantaneous handling time, and additional possible contacts do not occur during that handling time. Handling times and nonlinear contact rates might also explain the nonlinear relationship between symbiont transmission and snail density that we observed in the field, which could be confirmed by future work that controls for other potential sources of seasonal variation in transmission rates. Because most animal contacts are not instantaneous, the Holling Type II functional response might be broadly relevant to diverse host-symbiont systems.

Boundedness and global stability of the two-predator and one-prey models with nonlinear prey-taxis

NASA Astrophysics Data System (ADS)

Wang, Jianping; Wang, Mingxin

2018-06-01

This paper concerns the reaction-diffusion systems modeling the population dynamics of two predators and one prey with nonlinear prey-taxis. We first investigate the global existence and boundedness of the unique classical solution for the general model. Then, we study the global stabilities of nonnegative spatially homogeneous equilibria for an explicit system with type I functional responses and density-dependent death rates for the predators and logistic growth for the prey. Moreover, the convergence rates are also established.

Modeling transonic aerodynamic response using nonlinear systems theory for use with modern control theory

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1993-01-01

The presentation begins with a brief description of the motivation and approach that has been taken for this research. This will be followed by a description of the Volterra Theory of Nonlinear Systems and the CAP-TSD code which is an aeroelastic, transonic CFD (Computational Fluid Dynamics) code. The application of the Volterra theory to a CFD model and, more specifically, to a CAP-TSD model of a rectangular wing with a NACA 0012 airfoil section will be presented.

Microstructural Origins of Nonlinear Response in Associating Polymers under Oscillatory Shear

DOE PAGES

Wilson, Mark A.; Baljon, Arlette R. C.

2017-10-26

The response of associating polymers with oscillatory shear is studied through large-scale simulations. A hybrid molecular dynamics (MD), Monte Carlo (MC) algorithm is employed. Polymer chains are modeled as a coarse-grained bead-spring system. Functionalized end groups, at both ends of the polymer chains, can form reversible bonds according to MC rules. Stress-strain curves show nonlinearities indicated by a non-ellipsoidal shape. We consider two types of nonlinearities. Type I occurs at a strain amplitude much larger than one, type II at a frequency at which the elastic storage modulus dominates the viscous loss modulus. In this last case, the network topologymore » resembles that of the system at rest. The reversible bonds are broken and chains stretch when the system moves away from the zero-strain position. For type I, the chains relax and the number of reversible bonds peaks when the system is near an extreme of the motion. During the movement to the other extreme of the cycle, first a stress overshoot occurs, then a yield accompanied by shear-banding. Lastly, the network restructures. Interestingly, the system periodically restores bonds between the same associating groups. Even though major restructuring occurs, the system remembers previous network topologies.« less

Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

NASA Astrophysics Data System (ADS)

Mikhlin, Yu V.; Perepelkin, N. V.; Klimenko, A. A.; Harutyunyan, E.

2012-08-01

Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

Nonlinear degradation of a visible-light communication link: A Volterra-series approach

NASA Astrophysics Data System (ADS)

Kamalakis, Thomas; Dede, Georgia

2018-06-01

Visible light communications can be used to provide illumination and data communication at the same time. In this paper, a reverse-engineering approach is presented for assessing the impact of nonlinear signal distortion in visible light communication links. The approach is based on the Volterra series expansion and has the advantage of accurately accounting for memory effects in contrast to the static nonlinear models that are popular in the literature. Volterra kernels describe the end-to-end system response and can be inferred from measurements. Consequently, this approach does not rely on any particular physical models and assumptions regarding the individual link components. We provide the necessary framework for estimating the nonlinear distortion on the symbol estimates of a discrete multitone modulated link. Various design aspects such as waveform clipping and predistortion are also incorporated in the analysis. Using this framework, the nonlinear signal-to-interference is calculated for the system at hand. It is shown that at high signal amplitudes, the nonlinear signal-to-interference can be less than 25 dB.

Nonlinear Dynamics and Bifurcation Analysis of a Boost Converter for Battery Charging in Photovoltaic Applications

NASA Astrophysics Data System (ADS)

Al-Hindawi, Mohammed M.; Abusorrah, Abdullah; Al-Turki, Yusuf; Giaouris, Damian; Mandal, Kuntal; Banerjee, Soumitro

Photovoltaic (PV) systems with a battery back-up form an integral part of distributed generation systems and therefore have recently attracted a lot of interest. In this paper, we consider a system of charging a battery from a PV panel through a current mode controlled boost dc-dc converter. We analyze its complete nonlinear/nonsmooth dynamics, using a piecewise model of the converter and realistic nonlinear v-i characteristics of the PV panel. Through this study, it is revealed that system design without taking into account the nonsmooth dynamics of the converter combined with the nonlinear v-i characteristics of the PV panel can lead to unpredictable responses of the overall system with high current ripple and other undesirable phenomena. This analysis can lead to better designed converters that can operate under a wide variation of the solar irradiation and the battery's state of charge. We show that the v-i characteristics of the PV panel combined with the battery's output voltage variation can increase or decrease the converter's robustness, both under peak current mode control and average current mode control. We justify the observation in terms of the change in the discrete-time map caused by the nonlinear v-i characteristics of the PV panel. The theoretical results are validated experimentally.

Nonlinear dynamic macromodeling techniques for audio systems

NASA Astrophysics Data System (ADS)

Ogrodzki, Jan; Bieńkowski, Piotr

2015-09-01

This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.

Nonlinear adaptive control of grid-connected three-phase inverters for renewable energy applications

NASA Astrophysics Data System (ADS)

Mahdian-Dehkordi, N.; Namvar, M.; Karimi, H.; Piya, P.; Karimi-Ghartemani, M.

2017-01-01

Distributed generation (DG) units are often interfaced to the main grid using power electronic converters including voltage-source converters (VSCs). A VSC offers dc/ac power conversion, high controllability, and fast dynamic response. Because of nonlinearities, uncertainties, and system parameters' changes involved in the nature of a grid-connected renewable DG system, conventional linear control methods cannot completely and efficiently address all control objectives. In this paper, a nonlinear adaptive control scheme based on adaptive backstepping strategy is presented to control the operation of a grid-connected renewable DG unit. As compared to the popular vector control technique, the proposed controller offers smoother transient responses, and lower level of current distortions. The Lyapunov approach is used to establish global asymptotic stability of the proposed control system. Linearisation technique is employed to develop guidelines for parameters tuning of the controller. Extensive time-domain digital simulations are performed and presented to verify the performance of the proposed controller when employed in a VSC to control the operation of a two-stage DG unit and also that of a single-stage solar photovoltaic system. Desirable and superior performance of the proposed controller is observed.

Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation

NASA Astrophysics Data System (ADS)

Peter, Simon; Leine, Remco I.

2017-11-01

Phase resonance testing is one method for the experimental extraction of nonlinear normal modes. This paper proposes a novel method for nonlinear phase resonance testing. Firstly, the issue of appropriate excitation is approached on the basis of excitation power considerations. Therefore, power quantities known from nonlinear systems theory in electrical engineering are transferred to nonlinear structural dynamics applications. A new power-based nonlinear mode indicator function is derived, which is generally applicable, reliable and easy to implement in experiments. Secondly, the tuning of the excitation phase is automated by the use of a Phase-Locked-Loop controller. This method provides a very user-friendly and fast way for obtaining the backbone curve. Furthermore, the method allows to exploit specific advantages of phase control such as the robustness for lightly damped systems and the stabilization of unstable branches of the frequency response. The reduced tuning time for the excitation makes the commonly used free-decay measurements for the extraction of backbone curves unnecessary. Instead, steady-state measurements for every point of the curve are obtained. In conjunction with the new mode indicator function, the correlation of every measured point with the associated nonlinear normal mode of the underlying conservative system can be evaluated. Moreover, it is shown that the analysis of the excitation power helps to locate sources of inaccuracies in the force appropriation process. The method is illustrated by a numerical example and its functionality in experiments is demonstrated on a benchmark beam structure.

Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

A new nonlinear model for pitch perception

NASA Astrophysics Data System (ADS)

Cartwright, Julyan H. E.; González, Diego L.; Piro, Oreste

The ability of the auditory system to perceive the fundamental frequency of a sound even when this frequency is removed from the stimulus is an interesting phenomenon related to the pitch of complex sounds. This capability is known as residue or virtual pitch perception and was first reported last century in the pioneering work of Seebeck. It is residue perception that allows one to listen to music with small transistor radios, which in general have a very poor and sometimes negligible response to low frequencies. The first attempt, due to von Helmholtz, to explain the residue as a nonlinear effect in the ear considered it to originate from difference combination tones. But later experiments showed that the residue does not coincide with a difference combination tone, and nonlinear theories were abandoned. However, in this paper we use recent results from the theory of nonlinear dynamical systems to show that physical frequencies produced by generic nonlinear oscillators acted upon by two independent periodic excitations can reproduce with great precision most of the experimental data about the residue.

Nonlinear dielectric effects in liquids: a guided tour

NASA Astrophysics Data System (ADS)

Richert, Ranko

2017-09-01

Dielectric relaxation measurements probe how the polarization of a material responds to the application of an external electric field, providing information on structure and dynamics of the sample. In the limit of small fields and thus linear response, such experiments reveal the properties of the material in the same thermodynamic state it would have in the absence of the external field. At sufficiently high fields, reversible changes in enthalpy and entropy of the system occur even at constant temperature, and these will in turn alter the polarization responses. The resulting nonlinear dielectric effects feature field induced suppressions (saturation) and enhancements (chemical effect) of the amplitudes, as well as time constant shifts towards faster (energy absorption) and slower (entropy reduction) dynamics. This review focuses on the effects of high electric fields that are reversible and observed at constant temperature for single component glass-forming liquids. The experimental challenges involved in nonlinear dielectric experiments, the approaches to separating and identifying the different sources of nonlinear behavior, and the current understanding of how high electric fields affect dielectric materials will be discussed. Covering studies from Debye’s initial approach to the present state-of-the-art, it will be emphasized what insight can be gained from the nonlinear responses that are not available from dielectric relaxation results obtained in the linear regime.

Nonlinear Magnus-induced dynamics and Shapiro spikes for ac and dc driven skyrmions on periodic quasi-one-dimensional substrates

NASA Astrophysics Data System (ADS)

Reichhardt, Charles; Reichhardt, Cynthia J. Olson

We numerically examine skyrmions interacting with a periodic quasi-one-dimensional substrate. When we drive the skyrmions perpendicular to the substrate periodicity direction, a rich variety of nonlinear Magnus-induced effects arise, in contrast to an overdamped system that shows only a linear velocity-force curve for this geometry. The skyrmion velocity-force curve is strongly nonlinear and we observe a Magnus-induced speed-up effect when the pinning causes the Magnus velocity response to align with the dissipative response. At higher applied drives these components decouple, resulting in strong negative differential conductivity. For skyrmions under combined ac and dc driving, we find a new class of phase locking phenomena in which the velocity-force curves contain a series of what we call Shapiro spikes, distinct from the Shapiro steps observed in overdamped systems. There are also regimes in which the skyrmion moves in the direction opposite to the applied dc drive to give negative mobility.

Non-linear interactions between CO_2 radiative and physiological effects on Amazonian evapotranspiration in an Earth system model

NASA Astrophysics Data System (ADS)

Halladay, Kate; Good, Peter

2017-10-01

We present a detailed analysis of mechanisms underlying the evapotranspiration response to increased CO_2 in HadGEM2-ES, focussed on western Amazonia. We use three simulations from CMIP5 in which atmospheric CO_2 increases at 1% per year reaching approximately four times pre-industrial levels after 140 years. Using 3-hourly data, we found that evapotranspiration (ET) change was dominated by decreased stomatal conductance (g_s), and to a lesser extent by decreased canopy water and increased moisture gradient (specific humidity difference between surface and near-surface). There were large, non-linear decreases in ET in the simulation in which radiative and physiological forcings could interact. This non-linearity arises from non-linearity in the conductance term (includes aerodynamic and stomatal resistance and partitioning between the two, which is determined by canopy water availability), the moisture gradient, and negative correlation between these two terms. The conductance term is non-linear because GPP responds non-linearly to temperature and GPP is the dominant control on g_s in HadGEM2-ES. In addition, canopy water declines, mainly due to increases in potential evaporation, which further decrease the conductance term. The moisture gradient responds non-linearly owing to the non-linear response of temperature to CO_2 increases, which increases the Bowen ratio. Moisture gradient increases resulting from ET decline increase ET and thus constitute a negative feedback. This analysis highlights the importance of the g_s parametrisation in determining the ET response and the potential differences between offline and online simulations owing to feedbacks on ET via the atmosphere, some of which would not occur in an offline simulation.

Nonlinear analysis of NPP safety against the aircraft attack

DOE Office of Scientific and Technical Information (OSTI.GOV)

Králik, Juraj, E-mail: juraj.kralik@stuba.sk; Králik, Juraj, E-mail: kralik@fa.stuba.sk

The paper presents the nonlinear probabilistic analysis of the reinforced concrete buildings of nuclear power plant under the aircraft attack. The dynamic load is defined in time on base of the airplane impact simulations considering the real stiffness, masses, direction and velocity of the flight. The dynamic response is calculated in the system ANSYS using the transient nonlinear analysis solution method. The damage of the concrete wall is evaluated in accordance with the standard NDRC considering the spalling, scabbing and perforation effects. The simple and detailed calculations of the wall damage are compared.

Observer-Based Adaptive Fault-Tolerant Tracking Control of Nonlinear Nonstrict-Feedback Systems.

PubMed

Wu, Chengwei; Liu, Jianxing; Xiong, Yongyang; Wu, Ligang

2017-06-28

This paper studies an output-based adaptive fault-tolerant control problem for nonlinear systems with nonstrict-feedback form. Neural networks are utilized to identify the unknown nonlinear characteristics in the system. An observer and a general fault model are constructed to estimate the unavailable states and describe the fault, respectively. Adaptive parameters are constructed to overcome the difficulties in the design process for nonstrict-feedback systems. Meanwhile, dynamic surface control technique is introduced to avoid the problem of ''explosion of complexity''. Furthermore, based on adaptive backstepping control method, an output-based adaptive neural tracking control strategy is developed for the considered system against actuator fault, which can ensure that all the signals in the resulting closed-loop system are bounded, and the system output signal can be regulated to follow the response of the given reference signal with a small error. Finally, the simulation results are provided to validate the effectiveness of the control strategy proposed in this paper.

Extrapolation to Nonequilibrium from Coarse-Grained Response Theory

NASA Astrophysics Data System (ADS)

Basu, Urna; Helden, Laurent; Krüger, Matthias

2018-05-01

Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems. It is illustrated in a four-state model and in the near critical Ising model.

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

NASA Astrophysics Data System (ADS)

Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

2016-09-01

The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

A Computational Procedure for Identifying Bilinear Representations of Nonlinear Systems Using Volterra Kernels

NASA Technical Reports Server (NTRS)

Kvaternik, Raymond G.; Silva, Walter A.

2008-01-01

A computational procedure for identifying the state-space matrices corresponding to discrete bilinear representations of nonlinear systems is presented. A key feature of the method is the use of first- and second-order Volterra kernels (first- and second-order pulse responses) to characterize the system. The present method is based on an extension of a continuous-time bilinear system identification procedure given in a 1971 paper by Bruni, di Pillo, and Koch. The analytical and computational considerations that underlie the original procedure and its extension to the title problem are presented and described, pertinent numerical considerations associated with the process are discussed, and results obtained from the application of the method to a variety of nonlinear problems from the literature are presented. The results of these exploratory numerical studies are decidedly promising and provide sufficient credibility for further examination of the applicability of the method.

Influence of laminate sequence and fabric type on the inherent acoustic nonlinearity in carbon fiber reinforced composites.

PubMed

Chakrapani, Sunil Kishore; Barnard, Daniel J; Dayal, Vinay

2016-05-01

This paper presents the study of influence of laminate sequence and fabric type on the baseline acoustic nonlinearity of fiber-reinforced composites. Nonlinear elastic wave techniques are increasingly becoming popular in detecting damage in composite materials. It was earlier observed by the authors that the non-classical nonlinear response of fiber-reinforced composite is influenced by the fiber orientation [Chakrapani, Barnard, and Dayal, J. Acoust. Soc. Am. 137(2), 617-624 (2015)]. The current study expands this effort to investigate the effect of laminate sequence and fabric type on the non-classical nonlinear response. Two hypotheses were developed using the previous results, and the theory of interlaminar stresses to investigate the influence of laminate sequence and fabric type. Each hypothesis was tested by capturing the nonlinear response by performing nonlinear resonance spectroscopy and measuring frequency shifts, loss factors, and higher harmonics. It was observed that the laminate sequence can either increase or decrease the nonlinear response based on the stacking sequence. Similarly, tests were performed to compare unidirectional fabric and woven fabric and it was observed that woven fabric exhibited a lower nonlinear response compared to the unidirectional fabric. Conjectures based on the matrix properties and interlaminar stresses were used in an attempt to explain the observed nonlinear responses for different configurations.

Stochastic Resonance and Safe Basin of Single-Walled Carbon Nanotubes with Strongly Nonlinear Stiffness under Random Magnetic Field.

PubMed

Xu, Jia; Li, Chao; Li, Yiran; Lim, Chee Wah; Zhu, Zhiwen

2018-05-04

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of the microstructure is considered based on Eringen’s differential constitutive model. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.

Substrate clamping effects on irreversible domain wall dynamics in lead zirconate titanate thin films.

PubMed

Griggio, F; Jesse, S; Kumar, A; Ovchinnikov, O; Kim, H; Jackson, T N; Damjanovic, D; Kalinin, S V; Trolier-McKinstry, S

2012-04-13

The role of long-range strain interactions on domain wall dynamics is explored through macroscopic and local measurements of nonlinear behavior in mechanically clamped and released polycrystalline lead zirconate-titanate (PZT) films. Released films show a dramatic change in the global dielectric nonlinearity and its frequency dependence as a function of mechanical clamping. Furthermore, we observe a transition from strong clustering of the nonlinear response for the clamped case to almost uniform nonlinearity for the released film. This behavior is ascribed to increased mobility of domain walls. These results suggest the dominant role of collective strain interactions mediated by the local and global mechanical boundary conditions on the domain wall dynamics. The work presented in this Letter demonstrates that measurements on clamped films may considerably underestimate the piezoelectric coefficients and coupling constants of released structures used in microelectromechanical systems, energy harvesting systems, and microrobots.

Nonlinear Dynamical Model of a Soft Viscoelastic Dielectric Elastomer

NASA Astrophysics Data System (ADS)

Zhang, Junshi; Chen, Hualing; Li, Dichen

2017-12-01

Actuated by alternating stimulation, dielectric elastomers (DEs) show a behavior of complicated nonlinear vibration, implying a potential application as dynamic electromechanical actuators. As is well known, for a vibrational system, including the DE system, the dynamic properties are significantly affected by the geometrical sizes. In this article, a nonlinear dynamical model is deduced to investigate the geometrical effects on dynamic properties of viscoelastic DEs. The DEs with square and arbitrary rectangular geometries are considered, respectively. Besides, the effects of tensile forces on dynamic performances of rectangular DEs with comparably small and large geometrical sizes are explored. Phase paths and Poincaré maps are utilized to detect the periodicity of the nonlinear vibrations of DEs. The resonance characteristics of DEs incorporating geometrical effects are also investigated. The results indicate that the dynamic properties of DEs, including deformation response, vibrational periodicity, and resonance, are tuned when the geometrical sizes vary.

Toward Control of Universal Scaling in Critical Dynamics

DTIC Science & Technology

2016-01-27

program that aims to synergistically combine two powerful and very successful theories for non-linear stochastic dynamics of cooperative multi...RESPONSIBLE PERSON 19b. TELEPHONE NUMBER Uwe Tauber Uwe C. T? uber , Michel Pleimling, Daniel J. Stilwell 611102 c. THIS PAGE The public reporting burden...to synergistically combine two powerful and very successful theories for non-linear stochastic dynamics of cooperative multi-component systems, namely

Nonlinear Structured Illumination Using a Fluorescent Protein Activating at the Readout Wavelength

PubMed Central

Hou, Wenya; Kielhorn, Martin; Arai, Yoshiyuki; Nagai, Takeharu; Kessels, Michael M.; Qualmann, Britta; Heintzmann, Rainer

2016-01-01

Structured illumination microscopy (SIM) is a wide-field technique in fluorescence microscopy that provides fast data acquisition and two-fold resolution improvement beyond the Abbe limit. We observed a further resolution improvement using the nonlinear emission response of a fluorescent protein. We demonstrated a two-beam nonlinear structured illumination microscope by introducing only a minor change into the system used for linear SIM (LSIM). To achieve the required nonlinear dependence in nonlinear SIM (NL-SIM) we exploited the photoswitching of the recently introduced fluorophore Kohinoor. It is particularly suitable due to its positive contrast photoswitching characteristics. Contrary to other reversibly photoswitchable fluorescent proteins which only have high photostability in living cells, Kohinoor additionally showed little degradation in fixed cells over many switching cycles. PMID:27783656

Piezoelectric monolayers as nonlinear energy harvesters.

PubMed

López-Suárez, Miquel; Pruneda, Miguel; Abadal, Gabriel; Rurali, Riccardo

2014-05-02

We study the dynamics of h-BN monolayers by first performing ab-initio calculations of the deformation potential energy and then solving numerically a Langevine-type equation to explore their use in nonlinear vibration energy harvesting devices. An applied compressive strain is used to drive the system into a nonlinear bistable regime, where quasi-harmonic vibrations are combined with low-frequency swings between the minima of a double-well potential. Due to its intrinsic piezoelectric response, the nonlinear mechanical harvester naturally provides an electrical power that is readily available or can be stored by simply contacting the monolayer at its ends. Engineering the induced nonlinearity, a 20 nm2 device is predicted to harvest an electrical power of up to 0.18 pW for a noisy vibration of 5 pN.

Nonlinear response of summer temperature to Holocene insolation forcing in Alaska.

PubMed

Clegg, Benjamin F; Kelly, Ryan; Clarke, Gina H; Walker, Ian R; Hu, Feng Sheng

2011-11-29

Regional climate responses to large-scale forcings, such as precessional changes in solar irradiation and increases in anthropogenic greenhouse gases, may be nonlinear as a result of complex interactions among earth system components. Such nonlinear behaviors constitute a major source of climate "surprises" with important socioeconomic and ecological implications. Paleorecords are key for elucidating patterns and mechanisms of nonlinear responses to radiative forcing, but their utility has been greatly limited by the paucity of quantitative temperature reconstructions. Here we present Holocene July temperature reconstructions on the basis of midge analysis of sediment cores from three Alaskan lakes. Results show that summer temperatures during 10,000-5,500 calibrated years (cal) B.P. were generally lower than modern and that peak summer temperatures around 5,000 were followed by a decreasing trend toward the present. These patterns stand in stark contrast with the trend of precessional insolation, which decreased by ∼10% from 10,000 y ago to the present. Cool summers before 5,500 cal B.P. coincided with extensive summer ice cover in the western Arctic Ocean, persistence of a positive phase of the Arctic Oscillation, predominantly La Niña-like conditions, and variation in the position of the Alaskan treeline. These results illustrate nonlinear responses of summer temperatures to Holocene insolation radiative forcing in the Alaskan sub-Arctic, possibly because of state changes in the Arctic Oscillation and El Niño-Southern Oscillation and associated land-atmosphere-ocean feedbacks.

Nonlinear response of summer temperature to Holocene insolation forcing in Alaska

PubMed Central

Clegg, Benjamin F.; Kelly, Ryan; Clarke, Gina H.; Walker, Ian R.; Hu, Feng Sheng

2011-01-01

Regional climate responses to large-scale forcings, such as precessional changes in solar irradiation and increases in anthropogenic greenhouse gases, may be nonlinear as a result of complex interactions among earth system components. Such nonlinear behaviors constitute a major source of climate “surprises” with important socioeconomic and ecological implications. Paleorecords are key for elucidating patterns and mechanisms of nonlinear responses to radiative forcing, but their utility has been greatly limited by the paucity of quantitative temperature reconstructions. Here we present Holocene July temperature reconstructions on the basis of midge analysis of sediment cores from three Alaskan lakes. Results show that summer temperatures during 10,000–5,500 calibrated years (cal) B.P. were generally lower than modern and that peak summer temperatures around 5,000 were followed by a decreasing trend toward the present. These patterns stand in stark contrast with the trend of precessional insolation, which decreased by ∼10% from 10,000 y ago to the present. Cool summers before 5,500 cal B.P. coincided with extensive summer ice cover in the western Arctic Ocean, persistence of a positive phase of the Arctic Oscillation, predominantly La Niña-like conditions, and variation in the position of the Alaskan treeline. These results illustrate nonlinear responses of summer temperatures to Holocene insolation radiative forcing in the Alaskan sub-Arctic, possibly because of state changes in the Arctic Oscillation and El Niño-Southern Oscillation and associated land–atmosphere–ocean feedbacks. PMID:22084085

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quon, Eliot; Platt, Andrew; Yu, Yi-Hsiang

Extreme loads are often a key cost driver for wave energy converters (WECs). As an alternative to exhaustive Monte Carlo or long-term simulations, the most likely extreme response (MLER) method allows mid- and high-fidelity simulations to be used more efficiently in evaluating WEC response to events at the edges of the design envelope, and is therefore applicable to system design analysis. The study discussed in this paper applies the MLER method to investigate the maximum heave, pitch, and surge force of a point absorber WEC. Most likely extreme waves were obtained from a set of wave statistics data based onmore » spectral analysis and the response amplitude operators (RAOs) of the floating body; the RAOs were computed from a simple radiation-and-diffraction-theory-based numerical model. A weakly nonlinear numerical method and a computational fluid dynamics (CFD) method were then applied to compute the short-term response to the MLER wave. Effects of nonlinear wave and floating body interaction on the WEC under the anticipated 100-year waves were examined by comparing the results from the linearly superimposed RAOs, the weakly nonlinear model, and CFD simulations. Overall, the MLER method was successfully applied. In particular, when coupled to a high-fidelity CFD analysis, the nonlinear fluid dynamics can be readily captured.« less

A novel method to produce nonlinear empirical physical formulas for experimental nonlinear electro-optical responses of doped nematic liquid crystals: Feedforward neural network approach

NASA Astrophysics Data System (ADS)

Yildiz, Nihat; San, Sait Eren; Okutan, Mustafa; Kaya, Hüseyin

2010-04-01

Among other significant obstacles, inherent nonlinearity in experimental physical response data poses severe difficulty in empirical physical formula (EPF) construction. In this paper, we applied a novel method (namely layered feedforward neural network (LFNN) approach) to produce explicit nonlinear EPFs for experimental nonlinear electro-optical responses of doped nematic liquid crystals (NLCs). Our motivation was that, as we showed in a previous theoretical work, an appropriate LFNN, due to its exceptional nonlinear function approximation capabilities, is highly relevant to EPF construction. Therefore, in this paper, we obtained excellently produced LFNN approximation functions as our desired EPFs for above-mentioned highly nonlinear response data of NLCs. In other words, by using suitable LFNNs, we successfully fitted the experimentally measured response and predicted the new (yet-to-be measured) response data. The experimental data (response versus input) were diffraction and dielectric properties versus bias voltage; and they were all taken from our previous experimental work. We conclude that in general, LFNN can be applied to construct various types of EPFs for the corresponding various nonlinear physical perturbation (thermal, electronic, molecular, electric, optical, etc.) data of doped NLCs.

The temporal representation of speech in a nonlinear model of the guinea pig cochlea

NASA Astrophysics Data System (ADS)

Holmes, Stephen D.; Sumner, Christian J.; O'Mard, Lowel P.; Meddis, Ray

2004-12-01

The temporal representation of speechlike stimuli in the auditory-nerve output of a guinea pig cochlea model is described. The model consists of a bank of dual resonance nonlinear filters that simulate the vibratory response of the basilar membrane followed by a model of the inner hair cell/auditory nerve complex. The model is evaluated by comparing its output with published physiological auditory nerve data in response to single and double vowels. The evaluation includes analyses of individual fibers, as well as ensemble responses over a wide range of best frequencies. In all cases the model response closely follows the patterns in the physiological data, particularly the tendency for the temporal firing pattern of each fiber to represent the frequency of a nearby formant of the speech sound. In the model this behavior is largely a consequence of filter shapes; nonlinear filtering has only a small contribution at low frequencies. The guinea pig cochlear model produces a useful simulation of the measured physiological response to simple speech sounds and is therefore suitable for use in more advanced applications including attempts to generalize these principles to the response of human auditory system, both normal and impaired. .

Structural Dynamics of Electronic Systems

NASA Astrophysics Data System (ADS)

Suhir, E.

2013-03-01

The published work on analytical ("mathematical") and computer-aided, primarily finite-element-analysis (FEA) based, predictive modeling of the dynamic response of electronic systems to shocks and vibrations is reviewed. While understanding the physics of and the ability to predict the response of an electronic structure to dynamic loading has been always of significant importance in military, avionic, aeronautic, automotive and maritime electronics, during the last decade this problem has become especially important also in commercial, and, particularly, in portable electronics in connection with accelerated testing of various surface mount technology (SMT) systems on the board level. The emphasis of the review is on the nonlinear shock-excited vibrations of flexible printed circuit boards (PCBs) experiencing shock loading applied to their support contours during drop tests. At the end of the review we provide, as a suitable and useful illustration, the exact solution to a highly nonlinear problem of the dynamic response of a "flexible-and-heavy" PCB to an impact load applied to its support contour during drop testing.

Closed-Loop Estimation of Retinal Network Sensitivity by Local Empirical Linearization

PubMed Central

2018-01-01

Abstract Understanding how sensory systems process information depends crucially on identifying which features of the stimulus drive the response of sensory neurons, and which ones leave their response invariant. This task is made difficult by the many nonlinearities that shape sensory processing. Here, we present a novel perturbative approach to understand information processing by sensory neurons, where we linearize their collective response locally in stimulus space. We added small perturbations to reference stimuli and tested if they triggered visible changes in the responses, adapting their amplitude according to the previous responses with closed-loop experiments. We developed a local linear model that accurately predicts the sensitivity of the neural responses to these perturbations. Applying this approach to the rat retina, we estimated the optimal performance of a neural decoder and showed that the nonlinear sensitivity of the retina is consistent with an efficient encoding of stimulus information. Our approach can be used to characterize experimentally the sensitivity of neural systems to external stimuli locally, quantify experimentally the capacity of neural networks to encode sensory information, and relate their activity to behavior. PMID:29379871

An alternative approach to characterize nonlinear site effects

USGS Publications Warehouse

Zhang, R.R.; Hartzell, S.; Liang, J.; Hu, Y.

2005-01-01

This paper examines the rationale of a method of nonstationary processing and analysis, referred to as the Hilbert-Huang transform (HHT), for its application to a recording-based approach in quantifying influences of soil nonlinearity in site response. In particular, this paper first summarizes symptoms of soil nonlinearity shown in earthquake recordings, reviews the Fourier-based approach to characterizing nonlinearity, and offers justifications for the HHT in addressing nonlinearity issues. This study then uses the HHT method to analyze synthetic data and recordings from the 1964 Niigata and 2001 Nisqually earthquakes. In doing so, the HHT-based site response is defined as the ratio of marginal Hilbert amplitude spectra, alternative to the Fourier-based response that is the ratio of Fourier amplitude spectra. With the Fourier-based approach in studies of site response as a reference, this study shows that the alternative HHT-based approach is effective in characterizing soil nonlinearity and nonlinear site response.

Blind identification of nonlinear models with non-Gaussian inputs

NASA Astrophysics Data System (ADS)

Prakriya, Shankar; Pasupathy, Subbarayan; Hatzinakos, Dimitrios

1995-12-01

Some methods are proposed for the blind identification of finite-order discrete-time nonlinear models with non-Gaussian circular inputs. The nonlinear models consist of two finite memory linear time invariant (LTI) filters separated by a zero-memory nonlinearity (ZMNL) of the polynomial type (the LTI-ZMNL-LTI models). The linear subsystems are allowed to be of non-minimum phase (NMP). The methods base their estimates of the impulse responses on slices of the N plus 1th order polyspectra of the output sequence. It is shown that the identification of LTI-ZMNL systems requires only a 1-D moment or polyspectral slice. The coefficients of the ZMNL are not estimated, and need not be known. The order of the nonlinearity can, in theory, be estimated from the received signal. These methods possess several noise and interference suppression characteristics, and have applications in modeling nonlinearly amplified QAM/QPSK signals in digital satellite and microwave communications.

Superposition rheology.

PubMed

Dhont, J K; Wagner, N J

2001-02-01

The interpretation of superposition rheology data is still a matter of debate due to lack of understanding of viscoelastic superposition response on a microscopic level. So far, only phenomenological approaches have been described, which do not capture the shear induced microstructural deformation, which is responsible for the viscoelastic behavior to the superimposed flow. Experimentally there are indications that there is a fundamental difference between the viscoelastic response to an orthogonally and a parallel superimposed shear flow. We present theoretical predictions, based on microscopic considerations, for both orthogonal and parallel viscoelastic response functions for a colloidal system of attractive particles near their gas-liquid critical point. These predictions extend to values of the stationary shear rate where the system is nonlinearly perturbed, and are based on considerations on the colloidal particle level. The difference in response to orthogonal and parallel superimposed shear flow can be understood entirely in terms of microstructural distortion, where the anisotropy of the microstructure under shear flow conditions is essential. In accordance with experimental observations we find pronounced negative values for response functions in case of parallel superposition for an intermediate range of frequencies, provided that microstructure is nonlinearly perturbed by the stationary shear component. For the critical colloidal systems considered here, the Kramers-Kronig relations for the superimposed response functions are found to be valid. It is argued, however, that the Kramers-Kronig relations may be violated for systems where the stationary shear flow induces a considerable amount of new microstructure.

Sensitivity analysis of primary resonances and bifurcations of a controlled piecewise-smooth system with negative stiffness

NASA Astrophysics Data System (ADS)

Huang, Dongmei; Xu, Wei

2017-11-01

In this paper, the combination of the cubic nonlinearity and time delay is proposed to improve the performance of a piecewise-smooth (PWS) system with negative stiffness. Dynamical properties, feedback control performance and symmetry-breaking bifurcation are mainly considered for a PWS system with negative stiffness under nonlinear position and velocity feedback control. For the free vibration system, the homoclinic-like orbits are firstly derived. Then, the amplitude-frequency response of the controlled system is obtained analytically in aspect of the Lindstedt-Poincaré method and the method of multiple scales, which is also verified through the numerical results. In this regard, a softening-type behavior, which directly leads to the multi-valued responses, is illustrated over the negative position feedback. Especially, the five-valued responses in which three branches of them are stable are found. And complex multi-valued characteristics are also observed in the force-amplitude responses. Furthermore, for explaining the effectiveness of feedback control, the equivalent damping and stiffness are also introduced. Sensitivity of the system response to the feedback gain and time delay is comprehensively considered and interesting dynamical properties are found. Relatively, from the perspective of suppressing the maximum amplitude and controlling the resonance stability, the selection of the feedback parameters is discussed. Finally, the symmetry-breaking bifurcation and chaotic motion are considered.

Nonlinear multimodal model for TLD of irregular tank geometry and small fluid depth

NASA Astrophysics Data System (ADS)

Love, J. S.; Tait, M. J.

2013-11-01

Tuned liquid dampers (TLDs) utilize sloshing fluid to absorb and dissipate structural vibrational energy. TLDs of irregular or complex tank geometry may be required in practice to avoid tank interference with fixed structural or mechanical components. The literature offers few analytical models to predict the response of this type of TLD, particularly when the fluid depth is small. In this paper, a multimodal model is developed utilizing a Boussinesq-type modal theory which is valid for small TLD fluid depths. The Bateman-Luke variational principle is employed to develop a system of coupled nonlinear ordinary differential equations which describe the fluid response when the tank is subjected to base excitation. Energy dissipation is incorporated into the model from the inclusion of damping screens. The fluid model is used to describe the response of a 2D structure-TLD system when the structure is subjected to external loading and the TLD tank geometry is irregular.

Plasmon-induced nonlinear response of silver atomic chains.

PubMed

Yan, Lei; Guan, Mengxue; Meng, Sheng

2018-05-10

Nonlinear response of a linear silver atomic chain upon ultrafast laser excitation has been studied in real time using the time-dependent density functional theory. We observe the presence of nonlinear responses up to the fifth order in tunneling current, which is ascribed to the excitation of high-energy electrons generated by Landau damping of plasmons. The nonlinear effect is enhanced after adsorption of polar molecules such as water due to the enhanced damping rates during plasmon decay. Increasing the length of atomic chains also increases the nonlinear response, favoring higher-order plasmon excitation. These findings offer new insights towards a complete understanding and ultimate control of plasmon-induced nonlinear phenomena to atomic precision.

Recent advances on glass-forming systems driven far from equilibrium. Special issue marking the completion of the Research Unit FOR 1394 `Nonlinear response to probe vitrification'

NASA Astrophysics Data System (ADS)

Fuchs, Matthias

2017-08-01

The nature of the glass transition is one of the frontier questions in Statistical Physics and Materials Science. Highly cooperative structural processes develop in glass-forming melts exhibiting relaxational dynamics which is spread out over many decades in time. While considerable progress has been made in recent decades towards understanding dynamical slowing-down in quiescent systems, the interplay of glassy dynamics with external fields reveals a wealth of novel phenomena yet to be explored. This special issue focuses on recent results obtained by the Research Unit FOR 1394 `Nonlinear response to probe vitrification' which was funded by the German Science Foundation (DFG). In the projects of the research unit, strong external fields were used in order to gain insights into the complex structural and transport phenomena at the glass transition under far-from-equilibrium conditions. This aimed inter alia to test theories of the glass transition developed for quiescent systems by pushing them beyond their original regime. Combining experimental, simulational, and theoretical efforts, the eight projects within the FOR 1394 measured and determined aspects of the nonlinear response of supercooled metallic, polymeric, and silica melts, of colloidal dispersions, and of ionic liquids. Applied fields included electric and mechanic fields, and forced active probing (`micro-rheology'), where a single probe is forced through the glass-forming host. Nonlinear stress-strain and force-velocity relations as well as nonlinear dielectric susceptibilities and conductivities were observed. While the physical manipulation of melts and glasses is interesting in its own right, especially technologically, the investigations performed by the FOR 1394 suggest to use the response to strong homogeneous and inhomogeneous fields as technique to explore on the microscopic level the cooperative mechanisms in dense melts of strongly interacting constituents. Questions considered concern the (de-)coupling of different dynamical degrees of freedom in an external field, and the ensuing state diagrams. What forces are required to detach a localized probe particle from its initial environment in a supercooled liquid, in a glassy or granular system? Do metallic and colloidal glasses yield homogeneously or by strain localization under differently applied stresses? Which mechanisms determine field-dependent susceptibilities in dielectric and ionically conducting glass formers?

Laser pulse self-compression in an active fibre with a finite gain bandwidth under conditions of a nonstationary nonlinear response

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Litvak, A. G.; Mironov, V. A.; Skobelev, S. A.

2018-04-01

We study the influence of a nonstationary nonlinear response of a medium on self-compression of soliton-like laser pulses in active fibres with a finite gain bandwidth. Based on the variational approach, we qualitatively analyse the self-action of the wave packet in the system under consideration in order to classify the main evolution regimes and to determine the minimum achievable laser pulse duration during self-compression. The existence of stable soliton-type structures is shown in the framework of the parabolic approximation of the gain profile (in the approximation of the Gnizburg – Landau equation). An analysis of the self-action of laser pulses in the framework of the nonlinear Schrödinger equation with a sign-constant gain profile demonstrate a qualitative change in the dynamics of the wave field in the case of a nonsta­tionary nonlinear response that shifts the laser pulse spectrum from the amplification region and stops the pulse compression. Expressions for a minimum duration of a soliton-like laser pulse are obtained as a function of the problem parameters, which are in good agreement with the results of numerical simulation.

Controlling nonlinear optical response in an open four-level molecular system using quantum control of spin-orbit interaction

NASA Astrophysics Data System (ADS)

Jamshidi-Ghaleh, Kazem; Ebrahimi-hamed, Zahra; Sahrai, Mostafa

2017-10-01

This paper investigates the behavior of linear and nonlinear optical susceptibility of an open four-level molecular system, under two-step excitation based on electromagnetically induced transparency (EIT). The system was irradiated with a weak probe field and strong coupling field. It is shown that the use of a strong coupling field in the triplet states of an alkali-metal dimer can change the spin-orbit interaction (SOI). The optical response of the system can then be modified in a controllable way. The electromagnetically induced transparency transforms into electromagnetically induced absorption (EIA) in the presence of a coupling field. Changing the sign of the dispersion, this region is associated with switching subluminal and superluminal propagation. Furthermore, for the proper value of the coupling field, the controllable parameters, enhanced Kerr nonlinearity with reduced linear absorption, can be obtained under a weak probe field. With this approach, SOI can be controlled by changing only one of the controllable parameters, using triplet-triplet strong coupling with different spin state. Therefore, the desired region of the spectra can be obtained, in contrast to the other four-level system, in which at least two strong fields are used to change optical properties. This mechanism can be suitable in molecular systems or semiconductors to be used in optical bistability and fast all-optical switching devices.

Neuromechanical tuning of nonlinear postural control dynamics

NASA Astrophysics Data System (ADS)

Ting, Lena H.; van Antwerp, Keith W.; Scrivens, Jevin E.; McKay, J. Lucas; Welch, Torrence D. J.; Bingham, Jeffrey T.; DeWeerth, Stephen P.

2009-06-01

Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.

Time domain nonlinear SMA damper force identification approach and its numerical validation

NASA Astrophysics Data System (ADS)

Xin, Lulu; Xu, Bin; He, Jia

2012-04-01

Most of the currently available vibration-based identification approaches for structural damage detection are based on eigenvalues and/or eigenvectors extracted from vibration measurements and, strictly speaking, are only suitable for linear system. However, the initiation and development of damage in engineering structures under severe dynamic loadings are typical nonlinear procedure. Studies on the identification of restoring force which is a direct indicator of the extent of the nonlinearity have received increasing attention in recent years. In this study, a date-based time domain identification approach for general nonlinear system was developed. The applied excitation and the corresponding response time series of the structure were used for identification by means of standard least-square techniques and a power series polynomial model (PSPM) which was utilized to model the nonlinear restoring force (NRF). The feasibility and robustness of the proposed approach was verified by a 2 degree-of-freedoms (DOFs) lumped mass numerical model equipped with a shape memory ally (SMA) damper mimicking nonlinear behavior. The results show that the proposed data-based time domain method is capable of identifying the NRF in engineering structures without any assumptions on the mass distribution and the topology of the structure, and provides a promising way for damage detection in the presence of structural nonlinearities.

Applications of Non-linearities in RF MEMS Switches and Resonators

NASA Astrophysics Data System (ADS)

Vummidi Murali, Krishna Prasad

The 21st century is emerging into an era of wireless ubiquity. To support this trend, the RF (Radio Frequency) front end must be capable of processing a range of wireless signals (cellular phone, data connectivity, broadcast TV, GPS positioning, etc.) spanning a total bandwidth of nearly 6 GHz. This warrants the need for multi-band/multi-mode radio architectures. For such architectures to satisfy the constraints on size, battery life, functionality and cost, the radio front-end must be made reconfigurable. RF-MEMS (RF Micro-Electro-Mechanical Systems) are seen as an enabling technology for such reconfigurable radios. RF-MEMS mainly include micromechanical switches (used in phase shifters, switched capacitor banks, impedance tuners etc.) and micromechanical resonators (used in tunable filters, oscillators, reference clocks etc.). MEMS technology also has the potential to be directly integrated into CMOS (Complementary metal-oxide semiconductor) ICs (Integrated Circuits) leading to further potential reductions of cost and size. However, RF-MEMS face challenges that must be addressed before they can gain widespread commercial acceptance. Relatively low switching speed, power handling, and high-voltage drive are some of the key issues in MEMS switches. Phase noise influenced by non-linearities, need for temperature compensation (especially Si based resonators), large start-up times, and aging are the key issues in Si MEMS Resonators. In this work potential solutions are proposed to address some of these key issues, specifically the reduction of high voltage drives in switches and the reduction of phase noise in MEMS resonators for timing applications. MEMS devices that are electrostatically actuated exhibit significant non-linearities. The origins of the non-linearities are both electrical (electrostatic actuation) and mechanical (dimensions and material properties). The influence of spring non-linearities (cubic and quadratic) on the performance of switches and resonators are studied. Gold electroplated fixed-fixed beams were fabricated to test the phenomenon of dynamic (or resonant) pull-in in shunt switches. The dynamic pull-in phenomenon was also tested on commercially fabricated lateral switches. It is shown that the resonant pull-in technique reduces the overall voltage required to actuate the switch. There is an additional reduction of total actuation voltage possible via applying an AC actuation signal at the correct non-linear resonant frequency. The demonstrated best case savings from operating at the non-linear resonance is 50% (for the lateral switch) and 60% (for the vertical switch) as compared to 25% and 40% respectively using a fixed frequency approach. However, the timing response for resonant pull-in has been experimentally shown to be slower than the static actuation. To reduce the switching time, a shifted-frequency method is proposed where the excitation frequency is shifted up or down by a discrete amount deltaO after a brief hold time. It was theoretically shown that the shifted-frequency method enables a minimum realizable switching time comparable to the static switching time for a given set of actuation frequencies. The influence of VDC on the effective non-linearities of a fixed-fixed beam is also studied. Based on the dimensions of the resonator and the type of resonance there is a certain VDC,Lin where the response is near linear (S ≈ 0). In the near-linear domain, the dynamic pull-in is the only upper bound to the amplitude of vibrations, and hence the amplitude of output current, thereby maximizing the power handling capacity of the resonator. Apart from maximizing the output current, it is essential to reduce the amplitude and phase variations of the displacement response which are due to noise mixing into frequency of interest, and are eventually manifested as output phase noise due to capacitive current nonlinearity. Two major aliasing schemes were analyzed and it was shown that the capacitive force non-linearity is the major source of mixing that causes the up-conversion of 1/f frequency into signal sidebands. The resonator's periodic response (displacement) is defined by a set of two first-order nonlinear ordinary differential equations that describe the modulation of amplitude and phase of the response. Frequency response curves of amplitude and frequency are determined from these modulation equations. The zero slope point on the amplitude resonance curve is the peak of the resonance curve where the phase (gammadc) of the response is +/-pi/2. For a strongly non-linear system, the resonance curves are skewed based on the amount of total non-linearity S. For systems that are strongly non-linear, the best region to operate the resonator is the fixed point that correspond to infinite slope (gammadc = +/-2pi/3) in the frequency response of the system. The best case phase noise response was analytically developed for such a fixed point. Theoretically at this fixed point, phase noise will have contributions only from 1/ fnoise and not from 1/f2 and 1/ f3. The resonators phase can be set by controlling the rest of the phase in the loop such that the total phase around the loop is zero or 2pi. In addition, this work has also developed an analytical model for a lateral MEMS switch fabricated in a commercial foundry that has the potential to be processed as MEMS on CMOS. This model accounts for trapezoidal cross sections of the electrodes and springs and also models electrostatic fringing as a function of the moving gap. The analytical model matches closely with the Finite Element (FEA) model.

Stochastic modular analysis for gene circuits: interplay among retroactivity, nonlinearity, and stochasticity.

PubMed

Kim, Kyung Hyuk; Sauro, Herbert M

2015-01-01

This chapter introduces a computational analysis method for analyzing gene circuit dynamics in terms of modules while taking into account stochasticity, system nonlinearity, and retroactivity. (1) ANALOG ELECTRICAL CIRCUIT REPRESENTATION FOR GENE CIRCUITS: A connection between two gene circuit components is often mediated by a transcription factor (TF) and the connection signal is described by the TF concentration. The TF is sequestered to its specific binding site (promoter region) and regulates downstream transcription. This sequestration has been known to affect the dynamics of the TF by increasing its response time. The downstream effect-retroactivity-has been shown to be explicitly described in an electrical circuit representation, as an input capacitance increase. We provide a brief review on this topic. (2) MODULAR DESCRIPTION OF NOISE PROPAGATION: Gene circuit signals are noisy due to the random nature of biological reactions. The noisy fluctuations in TF concentrations affect downstream regulation. Thus, noise can propagate throughout the connected system components. This can cause different circuit components to behave in a statistically dependent manner, hampering a modular analysis. Here, we show that the modular analysis is still possible at the linear noise approximation level. (3) NOISE EFFECT ON MODULE INPUT-OUTPUT RESPONSE: We investigate how to deal with a module input-output response and its noise dependency. Noise-induced phenotypes are described as an interplay between system nonlinearity and signal noise. Lastly, we provide the comprehensive approach incorporating the above three analysis methods, which we call "stochastic modular analysis." This method can provide an analysis framework for gene circuit dynamics when the nontrivial effects of retroactivity, stochasticity, and nonlinearity need to be taken into account.

Linear and nonlinear winter atmospheric responses to extreme phases of low frequency Pacific sea surface temperature variability

NASA Astrophysics Data System (ADS)

Cao, Dandan; Wu, Qigang; Hu, Aixue; Yao, Yonghong; Liu, Shizuo; Schroeder, Steven R.; Yang, Fucheng

2018-02-01

This study examines Northern Hemisphere winter (DJFM) atmospheric responses to opposite strong phases of interdecadal (low frequency, LF) Pacific sea surface temperature (SST) forcing, which resembles El Niño-Southern Oscillation (ENSO) on a longer time scale, in observations and GFDL and CAM4 model simulations. Over the Pacific-North America (PNA) sector, linear observed responses of 500-hPa height (Z500) anomalies resemble the PNA teleconnection pattern, but show a PNA-like nonlinear response because of a westward Z500 shift in the negative (LF-) relative to the positive LF (LF+) phase. Significant extratropical linear responses include a North Atlantic Oscillation (NAO)-like Z500 anomaly, a dipole-like Z500 anomaly over northern Eurasia associated with warming over mid-high latitude Eurasia, and a Southern Annular anomaly pattern associated with warming in southern land areas. Significant nonlinear Z500 responses also include a NAO-like anomaly pattern. Models forced by LF+ and LF- SST anomalies reproduce many aspects of observed linear and nonlinear responses over the Pacific-North America sector, and linear responses over southern land, but not in the North Atlantic-European sector and Eurasia. Both models simulate PNA-like linear responses in the North Pacific-North America region similar to observed, but show larger PNA-like LF+ responses, resulting in a PNA nonlinear response. The nonlinear PNA responses result from both nonlinear western tropical Pacific rainfall changes and extratropical transient eddy feedbacks. With LF tropical Pacific forcing only (LFTP+ and LFTP-, climatological SST elsewhere), CAM4 simulates a significant NAO response to LFTP-, including a linear negative and nonlinear positive NAO response.

Nonlinear decoding of a complex movie from the mammalian retina

PubMed Central

Deny, Stéphane; Martius, Georg

2018-01-01

Retina is a paradigmatic system for studying sensory encoding: the transformation of light into spiking activity of ganglion cells. The inverse problem, where stimulus is reconstructed from spikes, has received less attention, especially for complex stimuli that should be reconstructed “pixel-by-pixel”. We recorded around a hundred neurons from a dense patch in a rat retina and decoded movies of multiple small randomly-moving discs. We constructed nonlinear (kernelized and neural network) decoders that improved significantly over linear results. An important contribution to this was the ability of nonlinear decoders to reliably separate between neural responses driven by locally fluctuating light signals, and responses at locally constant light driven by spontaneous-like activity. This improvement crucially depended on the precise, non-Poisson temporal structure of individual spike trains, which originated in the spike-history dependence of neural responses. We propose a general principle by which downstream circuitry could discriminate between spontaneous and stimulus-driven activity based solely on higher-order statistical structure in the incoming spike trains. PMID:29746463

Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs

PubMed Central

McFarland, James M.; Cui, Yuwei; Butts, Daniel A.

2013-01-01

The computation represented by a sensory neuron's response to stimuli is constructed from an array of physiological processes both belonging to that neuron and inherited from its inputs. Although many of these physiological processes are known to be nonlinear, linear approximations are commonly used to describe the stimulus selectivity of sensory neurons (i.e., linear receptive fields). Here we present an approach for modeling sensory processing, termed the Nonlinear Input Model (NIM), which is based on the hypothesis that the dominant nonlinearities imposed by physiological mechanisms arise from rectification of a neuron's inputs. Incorporating such ‘upstream nonlinearities’ within the standard linear-nonlinear (LN) cascade modeling structure implicitly allows for the identification of multiple stimulus features driving a neuron's response, which become directly interpretable as either excitatory or inhibitory. Because its form is analogous to an integrate-and-fire neuron receiving excitatory and inhibitory inputs, model fitting can be guided by prior knowledge about the inputs to a given neuron, and elements of the resulting model can often result in specific physiological predictions. Furthermore, by providing an explicit probabilistic model with a relatively simple nonlinear structure, its parameters can be efficiently optimized and appropriately regularized. Parameter estimation is robust and efficient even with large numbers of model components and in the context of high-dimensional stimuli with complex statistical structure (e.g. natural stimuli). We describe detailed methods for estimating the model parameters, and illustrate the advantages of the NIM using a range of example sensory neurons in the visual and auditory systems. We thus present a modeling framework that can capture a broad range of nonlinear response functions while providing physiologically interpretable descriptions of neural computation. PMID:23874185

Integration of system identification and finite element modelling of nonlinear vibrating structures

NASA Astrophysics Data System (ADS)

Cooper, Samson B.; DiMaio, Dario; Ewins, David J.

2018-03-01

The Finite Element Method (FEM), Experimental modal analysis (EMA) and other linear analysis techniques have been established as reliable tools for the dynamic analysis of engineering structures. They are often used to provide solutions to small and large structures and other variety of cases in structural dynamics, even those exhibiting a certain degree of nonlinearity. Unfortunately, when the nonlinear effects are substantial or the accuracy of the predicted response is of vital importance, a linear finite element model will generally prove to be unsatisfactory. As a result, the validated linear FE model requires further enhancement so that it can represent and predict the nonlinear behaviour exhibited by the structure. In this paper, a pragmatic approach to integrating test-based system identification and FE modelling of a nonlinear structure is presented. This integration is based on three different phases: the first phase involves the derivation of an Underlying Linear Model (ULM) of the structure, the second phase includes experiment-based nonlinear identification using measured time series and the third phase covers augmenting the linear FE model and experimental validation of the nonlinear FE model. The proposed case study is demonstrated on a twin cantilever beam assembly coupled with a flexible arch shaped beam. In this case, polynomial-type nonlinearities are identified and validated with force-controlled stepped-sine test data at several excitation levels.

SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-09-01

This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

A FORTRAN program for calculating nonlinear seismic ground response

USGS Publications Warehouse

Joyner, William B.

1977-01-01

The program described here was designed for calculating the nonlinear seismic response of a system of horizontal soil layers underlain by a semi-infinite elastic medium representing bedrock. Excitation is a vertically incident shear wave in the underlying medium. The nonlinear hysteretic behavior of the soil is represented by a model consisting of simple linear springs and Coulomb friction elements arranged as shown. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. A brief program description is provided here with instructions for preparing the input and a source listing. A more detailed discussion of the method is presented elsewhere as is the description of a different program employing implicit integration.

Quenching chatter instability in turning process with a vibro-impact nonlinear energy sink

NASA Astrophysics Data System (ADS)

Gourc, E.; Seguy, S.; Michon, G.; Berlioz, A.; Mann, B. P.

2015-10-01

This paper investigates the passive control of chatter instability in turning processes using a vibro-impact nonlinear energy sink (NES). The workpiece is assumed to be rigid and the tool is flexible. A dynamical model including a nonlinear cutting law is presented and the stability lobes diagram is obtained. The behavior of the system with the vibro-impact NES is investigated using an asymptotic analysis. A control mechanism by successive beating is revealed, similarly to the strongly modulated response in the case of NES with cubic stiffness. It is shown that such a response regime may be beneficial for chatter mitigation. An original experimental procedure is proposed to verify the sizing of the vibro-impact NES. An experimental setup is developed with a vibro-impact NES embedded on the lathe tool and the results are analyzed and validated.

NONLINEAR COLOR-METALLICITY RELATIONS OF GLOBULAR CLUSTERS. V. NONLINEAR ABSORPTION-LINE INDEX VERSUS METALLICITY RELATIONS AND BIMODAL INDEX DISTRIBUTIONS OF M31 GLOBULAR CLUSTERS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Sooyoung; Yoon, Suk-Jin; Chung, Chul

2013-05-10

Recent spectroscopy on the globular cluster (GC) system of M31 with unprecedented precision witnessed a clear bimodality in absorption-line index distributions of old GCs. Such division of extragalactic GCs, so far asserted mainly by photometric color bimodality, has been viewed as the presence of merely two distinct metallicity subgroups within individual galaxies and forms a critical backbone of various galaxy formation theories. Given that spectroscopy is a more detailed probe into stellar population than photometry, the discovery of index bimodality may point to the very existence of dual GC populations. However, here we show that the observed spectroscopic dichotomy ofmore » M31 GCs emerges due to the nonlinear nature of metallicity-to-index conversion and thus one does not necessarily have to invoke two separate GC subsystems. We take this as a close analogy to the recent view that metallicity-color nonlinearity is primarily responsible for observed GC color bimodality. We also demonstrate that the metallicity-sensitive magnesium line displays non-negligible metallicity-index nonlinearity and Balmer lines show rather strong nonlinearity. This gives rise to bimodal index distributions, which are routinely interpreted as bimodal metallicity distributions, not considering metallicity-index nonlinearity. Our findings give a new insight into the constitution of M31's GC system, which could change much of the current thought on the formation of GC systems and their host galaxies.« less

A robust approach to measuring the detective quantum efficiency of radiographic detectors in a clinical setting

NASA Astrophysics Data System (ADS)

McDonald, Michael C.; Kim, H. K.; Henry, J. R.; Cunningham, I. A.

2012-03-01

The detective quantum efficiency (DQE) is widely accepted as a primary measure of x-ray detector performance in the scientific community. A standard method for measuring the DQE, based on IEC 62220-1, requires the system to have a linear response meaning that the detector output signals are proportional to the incident x-ray exposure. However, many systems have a non-linear response due to characteristics of the detector, or post processing of the detector signals, that cannot be disabled and may involve unknown algorithms considered proprietary by the manufacturer. For these reasons, the DQE has not been considered as a practical candidate for routine quality assurance testing in a clinical setting. In this article we described a method that can be used to measure the DQE of both linear and non-linear systems that employ only linear image processing algorithms. The method was validated on a Cesium Iodide based flat panel system that simultaneously stores a raw (linear) and processed (non-linear) image for each exposure. It was found that the resulting DQE was equivalent to a conventional standards-compliant DQE with measurement precision, and the gray-scale inversion and linear edge enhancement did not affect the DQE result. While not IEC 62220-1 compliant, it may be adequate for QA programs.

Predicting the nonlinear optical response in the resonant region from the linear characterization: a self-consistent theory for the first-, second-, and third-order (non)linear optical response

NASA Astrophysics Data System (ADS)

Pérez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.

2010-08-01

We introduce a self-consistent theory for the description of the optical linear and nonlinear response of molecules that is based strictly on the results of the experimental characterization. We show how the Thomas-Kuhn sum-rules can be used to eliminate the dependence of the nonlinear response on parameters that are not directly measurable. Our approach leads to the successful modeling of the dispersion of the nonlinear response of complex molecular structures with different geometries (dipolar and octupolar), and can be used as a guide towards the modeling in terms of fundamental physical parameters.

Numerical study of surface plasmon enhanced nonlinear absorption and refraction.

PubMed

Kohlgraf-Owens, Dana C; Kik, Pieter G

2008-07-07

Maxwell Garnett effective medium theory is used to study the influence of silver nanoparticle induced field enhancement on the nonlinear response of a Kerr-type nonlinear host. We show that the composite nonlinear absorption coefficient, beta(c), can be enhanced relative to the host nonlinear absorption coefficient near the surface plasmon resonance of silver nanoparticles. This enhancement is not due to a resonant enhancement of the host nonlinear absorption, but rather due to a phase shifted enhancement of the host nonlinear refractive response. The enhancement occurs at the expense of introducing linear absorption, alpha(c), which leads to an overall reduced figure of merit beta(c)/alpha(c) for nonlinear absorption. For thin (< 1 microm) composites, the use of surface plasmons is found to result in an increased nonlinear absorption response compared to that of the host material.

White noise analysis of Phycomyces light growth response system. I. Normal intensity range.

PubMed Central

Lipson, E D

1975-01-01

The Wiener-Lee-Schetzen method for the identification of a nonlinear system through white gaussian noise stimulation was applied to the transient light growth response of the sporangiophore of Phycomyces. In order to cover a moderate dynamic range of light intensity I, the imput variable was defined to be log I. The experiments were performed in the normal range of light intensity, centered about I0 = 10(-6) W/cm2. The kernels of the Wierner functionals were computed up to second order. Within the range of a few decades the system is reasonably linear with log I. The main nonlinear feature of the second-order kernel corresponds to the property of rectification. Power spectral analysis reveals that the slow dynamics of the system are of at least fifth order. The system can be represented approximately by a linear transfer function, including a first-order high-pass (adaptation) filter with a 4 min time constant and an underdamped fourth-order low-pass filter. Accordingly a linear electronic circuit was constructed to simulate the small scale response characteristics. In terms of the adaptation model of Delbrück and Reichardt (1956, in Cellular Mechanisms in Differentiation and Growth, Princeton University Press), kernels were deduced for the dynamic dependence of the growth velocity (output) on the "subjective intensity", a presumed internal variable. Finally the linear electronic simulator above was generalized to accommodate the large scale nonlinearity of the adaptation model and to serve as a tool for deeper test of the model. PMID:1203444

Nonlinear dynamic failure process of tunnel-fault system in response to strong seismic event

NASA Astrophysics Data System (ADS)

Yang, Zhihua; Lan, Hengxing; Zhang, Yongshuang; Gao, Xing; Li, Langping

2013-03-01

Strong earthquakes and faults have significant effect on the stability capability of underground tunnel structures. This study used a 3-Dimensional Discrete Element model and the real records of ground motion in the Wenchuan earthquake to investigate the dynamic response of tunnel-fault system. The typical tunnel-fault system was composed of one planned railway tunnel and one seismically active fault. The discrete numerical model was prudentially calibrated by means of the comparison between the field survey and numerical results of ground motion. It was then used to examine the detailed quantitative information on the dynamic response characteristics of tunnel-fault system, including stress distribution, strain, vibration velocity and tunnel failure process. The intensive tunnel-fault interaction during seismic loading induces the dramatic stress redistribution and stress concentration in the intersection of tunnel and fault. The tunnel-fault system behavior is characterized by the complicated nonlinear dynamic failure process in response to a real strong seismic event. It can be qualitatively divided into 5 main stages in terms of its stress, strain and rupturing behaviors: (1) strain localization, (2) rupture initiation, (3) rupture acceleration, (4) spontaneous rupture growth and (5) stabilization. This study provides the insight into the further stability estimation of underground tunnel structures under the combined effect of strong earthquakes and faults.

Nonlinear responses of coastal salt marshes to nutrient additions and sea level rise

EPA Science Inventory

Increasing nutrients and accelerated sea level rise (SLR) can cause marsh loss in some coastal systems. Responses to nutrients and SLR are complex and vary with soil matrix, marsh elevation, sediment inputs, and hydroperiod. We describe field and greenhouse studies examining sing...

Nonlinear dynamics of electromagnetic turbulence in a nonuniform magnetized plasma

NASA Astrophysics Data System (ADS)

Shukla, P. K.; Mirza, Arshad M.; Faria, R. T.

1998-03-01

By using the hydrodynamic electron response with fixed (kinetic) ions along with Poisson's equation as well as Ampère's law, a system of nonlinear equations for low-frequency (in comparison with the electron gyrofrequency) long-(short-) wavelength electromagnetic waves in a nonuniform resistive magnetoplasma has been derived. The plasma contains equilibrium density gradient and sheared equilibrium plasma flows. In the linear limit, local dispersion relations are obtained and analyzed. It is found that sheared equilibrium flows can cause instability of Alfvén-like electromagnetic waves even in the absence of a density gradient. Furthermore, it is shown that possible stationary solutions of the nonlinear equations without dissipation can be represented in the form of various types of vortices. On the other hand, the temporal behavior of our nonlinear dissipative systems without the equilibrium density inhomogeneity can be described by the generalized Lorenz equations which admit chaotic trajectories. The density inhomogeneity may lead to even qualitative changes in the chaotic dynamics. The results of our investigation should be useful in understanding the linear and nonlinear properties of nonthermal electromagnetic waves in space and laboratory plasmas.

Dependence of upper atmosphere photochemistry on the shape of the diurnal cycle of the photolysis rates

NASA Astrophysics Data System (ADS)

Montecinos, S.; Barrientos, P.

2006-03-01

A photochemical model of the atmosphere constitutes a non-linear, non-autonomous dynamical system, enforced by the Earth's rotation. Some studies have shown that the region of the mesopause tends towards non-linear responses such as period-doubling cascades and chaos. In these studies, simple go approximations for the diurnal variations of the photolysis rates are assumed. The goal of this article is to investigate what happens if the more realistic, calculated photolysis rates are introduced. It is found that, if the usual approximations-sinusoidal and step functions-are assumed, the responses of the system are similar: it converges to a 2-day periodic solution. If the more realistic, calculated diurnal cycle is introduced, a new 4-day subharmonic appear.

A robust direct-integration method for rotorcraft maneuver and periodic response

NASA Technical Reports Server (NTRS)

Panda, Brahmananda

1992-01-01

The Newmark-Beta method and the Newton-Raphson iteration scheme are combined to develop a direct-integration method for evaluating the maneuver and periodic-response expressions for rotorcraft. The method requires the generation of Jacobians and includes higher derivatives in the formulation of the geometric stiffness matrix to enhance the convergence of the system. The method leads to effective convergence with nonlinear structural dynamics and aerodynamic terms. Singularities in the matrices can be addressed with the method as they arise from a Lagrange multiplier approach for coupling equations with nonlinear constraints. The method is also shown to be general enough to handle singularities from quasisteady control-system models. The method is shown to be more general and robust than the similar 2GCHAS method for analyzing rotorcraft dynamics.

Linear and nonlinear analysis of fluid slosh dampers

NASA Astrophysics Data System (ADS)

Sayar, B. A.; Baumgarten, J. R.

1982-11-01

A vibrating structure and a container partially filled with fluid are considered coupled in a free vibration mode. To simplify the mathematical analysis, a pendulum model to duplicate the fluid motion and a mass-spring dashpot representing the vibrating structure are used. The equations of motion are derived by Lagrange's energy approach and expressed in parametric form. For a wide range of parametric values the logarithmic decrements of the main system are calculated from theoretical and experimental response curves in the linear analysis. However, for the nonlinear analysis the theoretical and experimental response curves of the main system are compared. Theoretical predictions are justified by experimental observations with excellent agreement. It is concluded finally that for a proper selection of design parameters, containers partially filled with viscous fluids serve as good vibration dampers.

Further Results of Soft-Inplane Tiltrotor Aeromechanics Investigation Using Two Multibody Analyses

NASA Technical Reports Server (NTRS)

Masarati, Pierangelo; Quaranta, Giuseppe; Piatak, David J.; Singleton, Jeffrey D.

2004-01-01

This investigation focuses on the development of multibody analytical models to predict the dynamic response, aeroelastic stability, and blade loading of a soft-inplane tiltrotor wind-tunnel model. Comprehensive rotorcraft-based multibody analyses enable modeling of the rotor system to a high level of detail such that complex mechanics and nonlinear effects associated with control system geometry and joint deadband may be considered. The influence of these and other nonlinear effects on the aeromechanical behavior of the tiltrotor model are examined. A parametric study of the design parameters which may have influence on the aeromechanics of the soft-inplane rotor system are also included in this investigation.

Design of Life Extending Controls Using Nonlinear Parameter Optimization

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Holmes, Michael S.; Ray, Asok

1998-01-01

This report presents the conceptual development of a life extending control system where the objective is to achieve high performance and structural durability of the plant. A life extending controller is designed for a reusable rocket engine via damage mitigation in both the fuel and oxidizer turbines while achieving high performance for transient responses of the combustion chamber pressure and the O2/H2 mixture ratio. This design approach makes use of a combination of linear and nonlinear controller synthesis techniques and also allows adaptation of the life extending controller module to augment a conventional performance controller of a rocket engine. The nonlinear aspect of the design is achieved using nonlinear parameter optimization of a prescribed control structure.

Optical solitons in nematic liquid crystals: model with saturation effects

NASA Astrophysics Data System (ADS)

Borgna, Juan Pablo; Panayotaros, Panayotis; Rial, Diego; de la Vega, Constanza Sánchez F.

2018-04-01

We study a 2D system that couples a Schrödinger evolution equation to a nonlinear elliptic equation and models the propagation of a laser beam in a nematic liquid crystal. The nonlinear elliptic equation describes the response of the director angle to the laser beam electric field. We obtain results on well-posedness and solitary wave solutions of this system, generalizing results for a well-studied simpler system with a linear elliptic equation for the director field. The analysis of the nonlinear elliptic problem shows the existence of an isolated global branch of solutions with director angles that remain bounded for arbitrary electric field. The results on the director equation are also used to show local and global existence, as well as decay for initial conditions with sufficiently small L 2-norm. For sufficiently large L 2-norm we show the existence of energy minimizing optical solitons with radial, positive and monotone profiles.

On-line estimation of nonlinear physical systems

USGS Publications Warehouse

Christakos, G.

1988-01-01

Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared. ?? 1988 International Association for Mathematical Geology.

Enhanced absorption in a reverse saturable absorbing dye blended with carbon nanotubes.

PubMed

Webster, Scott; Reyes-Reyes, Marisol; Williams, Richard; Carroll, David L

2008-12-01

Using nonlinear absorption at 532 nm in the nanosecond temporal regime, we have measured the low fluence nonlinear transmittance properties of the reverse saturable absorbing carbocyanine dye, 1,1',3,3,3',3'-hexamethylindotricarbocyanine iodide (HITCI), blended with well dispersed carbon nanotubes. The nonlinear optical properties of the blends are strongly dependent on the ratio of dye to nanotubes in solution. In the case where the nanotubes per dye molecule ratio is large, we see a distinctive enhancement in optical fluence limiting properties of the system, suggesting enhanced absorption of the excited states. However, when the nanotube to dye ratio decreases, the system's response is dominated by the behavior of the dye. We suggest that this can be understood as a two component system in which sensitized dye molecules associated with the nanotubes have an effectively different optical cross-section from the dye molecules far from the nanotubes. From classical antennae considerations, this is expected.

A new approach for designing self-organizing systems and application to adaptive control

NASA Technical Reports Server (NTRS)

Ramamoorthy, P. A.; Zhang, Shi; Lin, Yueqing; Huang, Song

1993-01-01

There is tremendous interest in the design of intelligent machines capable of autonomous learning and skillful performance under complex environments. A major task in designing such systems is to make the system plastic and adaptive when presented with new and useful information and stable in response to irrelevant events. A great body of knowledge, based on neuro-physiological concepts, has evolved as a possible solution to this problem. Adaptive resonance theory (ART) is a classical example under this category. The system dynamics of an ART network is described by a set of differential equations with nonlinear functions. An approach for designing self-organizing networks characterized by nonlinear differential equations is proposed.

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

NASA Astrophysics Data System (ADS)

Zhu, Z. W.; Zhang, W. D.; Xu, J.

2014-03-01

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

The iso-response method: measuring neuronal stimulus integration with closed-loop experiments

PubMed Central

Gollisch, Tim; Herz, Andreas V. M.

2012-01-01

Throughout the nervous system, neurons integrate high-dimensional input streams and transform them into an output of their own. This integration of incoming signals involves filtering processes and complex non-linear operations. The shapes of these filters and non-linearities determine the computational features of single neurons and their functional roles within larger networks. A detailed characterization of signal integration is thus a central ingredient to understanding information processing in neural circuits. Conventional methods for measuring single-neuron response properties, such as reverse correlation, however, are often limited by the implicit assumption that stimulus integration occurs in a linear fashion. Here, we review a conceptual and experimental alternative that is based on exploring the space of those sensory stimuli that result in the same neural output. As demonstrated by recent results in the auditory and visual system, such iso-response stimuli can be used to identify the non-linearities relevant for stimulus integration, disentangle consecutive neural processing steps, and determine their characteristics with unprecedented precision. Automated closed-loop experiments are crucial for this advance, allowing rapid search strategies for identifying iso-response stimuli during experiments. Prime targets for the method are feed-forward neural signaling chains in sensory systems, but the method has also been successfully applied to feedback systems. Depending on the specific question, “iso-response” may refer to a predefined firing rate, single-spike probability, first-spike latency, or other output measures. Examples from different studies show that substantial progress in understanding neural dynamics and coding can be achieved once rapid online data analysis and stimulus generation, adaptive sampling, and computational modeling are tightly integrated into experiments. PMID:23267315

Coherence resonance in low-density jets

NASA Astrophysics Data System (ADS)

Zhu, Yuanhang; Gupta, Vikrant; Li, Larry K. B.

2017-11-01

Coherence resonance is a phenomenon in which the response of a stable nonlinear system to noise exhibits a peak in coherence at an intermediate noise amplitude. We report the first experimental evidence of coherence resonance in a purely hydrodynamic system, a low-density jet whose variants can be found in many natural and engineering systems. This evidence comprises four parts: (i) the jet's response amplitude increases as the Reynolds number approaches the instability boundary under a constant noise amplitude; (ii) as the noise amplitude increases, the amplitude distribution of the jet response first becomes unimodal, then bimodal, and finally unimodal again; (iii) a distinct peak emerges in the coherence factor at an intermediate noise amplitude; and (iv) for a subcritical Hopf bifurcation, the decay rate of the autocorrelation function exhibits a maximum at an intermediate noise amplitude, but for a supercritical Hopf bifurcation, the decay rate decreases monotonically with increasing noise amplitude. It is clear that coherence resonance can provide valuable information about a system's nonlinearity even in the unconditionally stable regime, opening up new possibilities for its use in system identification and flow control. This work was supported by the Research Grants Council of Hong Kong (Project No. 16235716 and 26202815).

Earthquake Ground Motion Selection

DOT National Transportation Integrated Search

2012-05-01

Nonlinear analyses of soils, structures, and soil-structure systems offer the potential for more accurate characterization of geotechnical and structural response under strong earthquake shaking. The increasing use of advanced performance-based desig...

Neural activation in the "reward circuit" shows a nonlinear response to facial attractiveness.

PubMed

Liang, Xiaoyun; Zebrowitz, Leslie A; Zhang, Yi

2010-01-01

Positive behavioral responses to attractive faces have led neuroscientists to investigate underlying neural mechanisms in a "reward circuit" that includes brain regions innervated by dopamine pathways. Using male faces ranging from attractive to extremely unattractive, disfigured ones, this study is the first to demonstrate heightened responses to both rewarding and aversive faces in numerous areas of this putative reward circuit. Parametric analyses employing orthogonal linear and nonlinear regressors revealed positive nonlinear effects in anterior cingulate cortex, lateral orbital frontal cortex (LOFC), striatum (nucleus accumbens, caudate, putamen), and ventral tegmental area, in addition to replicating previously documented linear effects in medial orbital frontal cortex (MOFC) and LOFC and nonlinear effects in amygdala and MOFC. The widespread nonlinear responses are consistent with single cell recordings in animals showing responses to both rewarding and aversive stimuli, and with some human fMRI investigations of non-face stimuli. They indicate that the reward circuit does not process face valence with any simple dissociation of function across structures. Perceiver gender modulated some responses to our male faces: Women showed stronger linear effects, and men showed stronger nonlinear effects, which may have functional implications. Our discovery of nonlinear responses to attractiveness throughout the reward circuit echoes the history of amygdala research: Early work indicated a linear response to threatening stimuli, including faces; later work also revealed a nonlinear response with heightened activation to affectively salient stimuli regardless of valence. The challenge remains to determine how such dual coding influences feelings, such as pleasure and pain, and guides goal-related behavioral responses, such as approach and avoidance.

Solution for the nonuniformity correction of infrared focal plane arrays.

PubMed

Zhou, Huixin; Liu, Shangqian; Lai, Rui; Wang, Dabao; Cheng, Yubao

2005-05-20

Based on the S-curve model of the detector response of infrared focal plan arrays (IRFPAs), an improved two-point correction algorithm is presented. The algorithm first transforms the nonlinear image data into linear data and then uses the normal two-point algorithm to correct the linear data. The algorithm can effectively overcome the influence of nonlinearity of the detector's response, and it enlarges the correction precision and the dynamic range of the response. A real-time imaging-signal-processing system for IRFPAs that is based on a digital signal processor and field-programmable gate arrays is also presented. The nonuniformity correction capability of the presented solution is validated by experimental imaging procedures of a 128 x 128 pixel IRFPA camera prototype.

Unbalance response of a two spool gas turbine engine with squeeze film bearings

NASA Technical Reports Server (NTRS)

Gunter, E. J.; Barrett, L. E.; Li, D. F.

1981-01-01

This paper presents a dynamic analysis of a two-spool gas turbine helicopter engine incorporating intershaft rolling element bearings between the gas generator and power turbine rotors. The analysis includes the nonlinear effects of a squeeze film bearing incorporated on the gas generator rotor. The analysis includes critical speeds and forced response of the system and indicates that substantial dynamic loads may be imposed on the intershaft bearings and main bearing supports with an improperly designed squeeze film bearing. A comparison of theoretical and experimental gas generator rotor response is presented illustrating the nonlinear characteristics of the squeeze film bearing. It was found that large intershaft bearing forces may occur even though the engine is not operating at a resonant condition.

Dispersion compensation of fiber optic communication system with direct detection using artificial neural networks (ANNs)

NASA Astrophysics Data System (ADS)

Maghrabi, Mahmoud M. T.; Kumar, Shiva; Bakr, Mohamed H.

2018-02-01

This work introduces a powerful digital nonlinear feed-forward equalizer (NFFE), exploiting multilayer artificial neural network (ANN). It mitigates impairments of optical communication systems arising due to the nonlinearity introduced by direct photo-detection. In a direct detection system, the detection process is nonlinear due to the fact that the photo-current is proportional to the absolute square of the electric field intensity. The proposed equalizer provides the most efficient computational cost with high equalization performance. Its performance is comparable to the benchmark compensation performance achieved by maximum-likelihood sequence estimator. The equalizer trains an ANN to act as a nonlinear filter whose impulse response removes the intersymbol interference (ISI) distortions of the optical channel. Owing to the proposed extensive training of the equalizer, it achieves the ultimate performance limit of any feed-forward equalizer (FFE). The performance and efficiency of the equalizer is investigated by applying it to various practical short-reach fiber optic communication system scenarios. These scenarios are extracted from practical metro/media access networks and data center applications. The obtained results show that the ANN-NFFE compensates for the received BER degradation and significantly increases the tolerance to the chromatic dispersion distortion.

Nonlinear Reduced-Order Simulation Using An Experimentally Guided Modal Basis

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2012-01-01

A procedure is developed for using nonlinear experimental response data to guide the modal basis selection in a nonlinear reduced-order simulation. The procedure entails using nonlinear acceleration response data to first identify proper orthogonal modes. Special consideration is given to cases in which some of the desired response data is unavailable. Bases consisting of linear normal modes are then selected to best represent the experimentally determined transverse proper orthogonal modes and either experimentally determined inplane proper orthogonal modes or the special case of numerically computed in-plane companions. The bases are subsequently used in nonlinear modal reduction and dynamic response simulations. The experimental data used in this work is simulated to allow some practical considerations, such as the availability of in-plane response data and non-idealized test conditions, to be explored. Comparisons of the nonlinear reduced-order simulations are made with the surrogate experimental data to demonstrate the effectiveness of the approach.

Third order nonlinear optical response exhibited by mono- and few-layers of WS 2

DOE PAGES

Torres-Torres, Carlos; Perea-López, Néstor; Elías, Ana Laura; ...

2016-04-13

In this work, strong third order nonlinear optical properties exhibited by WS 2 layers are presented. Optical Kerr effect was identified as the dominant physical mechanism responsible for these third order optical nonlinearities. An extraordinary nonlinear refractive index together with an important contribution of a saturated absorptive response was observed to depend on the atomic layer stacking. Comparative experiments performed in mono- and few-layer samples of WS 2 revealed that this material is potentially capable of modulating nonlinear optical processes by selective near resonant induced birefringence. In conclusion, we envision applications for developing all-optical bidimensional nonlinear optical devices.

Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

NASA Astrophysics Data System (ADS)

Zhu, Ping; Yan, Xingting; Huang, Wenlong

2017-10-01

Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

NASA Technical Reports Server (NTRS)

Mei, Chuh; Moorthy, Jayashree

1995-01-01

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Flight flutter testing technology at Grumman. [automated telemetry station for on line data reduction

NASA Technical Reports Server (NTRS)

Perangelo, H. J.; Milordi, F. W.

1976-01-01

Analysis techniques used in the automated telemetry station (ATS) for on line data reduction are encompassed in a broad range of software programs. Concepts that form the basis for the algorithms used are mathematically described. The control the user has in interfacing with various on line programs is discussed. The various programs are applied to an analysis of flight data which includes unimodal and bimodal response signals excited via a swept frequency shaker and/or random aerodynamic forces. A nonlinear response error modeling analysis approach is described. Preliminary results in the analysis of a hard spring nonlinear resonant system are also included.

Formulation of the nonlinear analysis of shell-like structures, subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, George J.; Carlson, Robert L.; Riff, Richard

1991-01-01

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.

Nonlinear characterization of elasticity using quantitative optical coherence elastography.

PubMed

Qiu, Yi; Zaki, Farzana R; Chandra, Namas; Chester, Shawn A; Liu, Xuan

2016-11-01

Optical coherence elastography (OCE) has been used to perform mechanical characterization on biological tissue at the microscopic scale. In this work, we used quantitative optical coherence elastography (qOCE), a novel technology we recently developed, to study the nonlinear elastic behavior of biological tissue. The qOCE system had a fiber-optic probe to exert a compressive force to deform tissue under the tip of the probe. Using the space-division multiplexed optical coherence tomography (OCT) signal detected by a spectral domain OCT engine, we were able to simultaneously quantify the probe deformation that was proportional to the force applied, and to quantify the tissue deformation. In other words, our qOCE system allowed us to establish the relationship between mechanical stimulus and tissue response to characterize the stiffness of biological tissue. Most biological tissues have nonlinear elastic behavior, and the apparent stress-strain relationship characterized by our qOCE system was nonlinear an extended range of strain, for a tissue-mimicking phantom as well as biological tissues. Our experimental results suggested that the quantification of force in OCE was critical for accurate characterization of tissue mechanical properties and the qOCE technique was capable of differentiating biological tissues based on the elasticity of tissue that is generally nonlinear.

A Simplified Model of ARIS for Optimal Controller Design

NASA Technical Reports Server (NTRS)

Beech, Geoffrey S.; Hampton, R. David; Kross, Denny (Technical Monitor)

2001-01-01

Many space-science experiments require active vibration isolation. Boeing's Active Rack Isolation System (ARIS) isolates experiments at the rack (vs. experiment or sub-experiment) level, with multi e experiments per rack. An ARIS-isolated rack typically employs eight actuators and thirteen umbilicals; the umbilicals provide services such as power, data transmission, and cooling. Hampton, et al., used "Kane's method" to develop an analytical, nonlinear, rigid-body model of ARIS that includes full actuator dynamics (inertias). This model, less the umbilicals, was first implemented for simulation by Beech and Hampton; they developed and tested their model using two commercial-off-the-shelf (COTS) software packages. Rupert, et al., added umbilical-transmitted disturbances to this nonlinear model. Because the nonlinear model, even for the untethered system, is both exceedingly complex and "encapsulated" inside these COTS tools, it is largely inaccessible to ARIS controller designers. This paper shows that ISPR rattle-space constraints and small ARIS actuator masses permit considerable model simplification, without significant loss of fidelity. First, for various loading conditions, comparisons are made between the dynamic responses of the nonlinear model (untethered) and a truth model. Then comparisons are made among nonlinear, linearized, and linearized reduced-mass models. It is concluded that these three models all capture the significant system rigid-body dynamics, with the third being preferred due to its relative simplicity.

Chaos and Beyond in a Water Filled Ultrasonic Resonance System

NASA Technical Reports Server (NTRS)

Lazlo, Adler; Yost, W.; Cantrell, John H.

2013-01-01

Finite amplitude ultrasonic wave resonances in a one-dimensional liquid-filled cavity, formed by a narrow band transducer and a plane reflector, are reported. The resonances are observed to include not only the expected harmonic and subharmonic signals (1,2) but chaotic signals as well. The generation mechanism requires attaining a threshold value of the driving amplitude that the liquid-filled cavity system becomes sufficiently nonlinear in response. The nonlinear features of the system were recently investigated via the construction of an ultrasonic interferometer having optical precision. The transducers were compressional, undamped quartz and lithium niobate crystals having the frequency range 1-10 MHz, driven by a high power amplifier. Both an optical diffraction system to characterize the diffraction pattern of laser light normally incident to the cavity and a receiving transducer attached to an aligned reflector with lapped flat and parallel surfaces were used to assess the generated resonance response in the cavity. At least 5 regions of excitation are identified.

Nonlinear dynamics of global atmospheric and Earth system processes

NASA Technical Reports Server (NTRS)

Saltzman, Barry

1993-01-01

During the past eight years, we have been engaged in a NASA-supported program of research aimed at establishing the connection between satellite signatures of the earth's environmental state and the nonlinear dynamics of the global weather and climate system. Thirty-five publications and four theses have resulted from this work, which included contributions in five main areas of study: (1) cloud and latent heat processes in finite-amplitude baroclinic waves; (2) application of satellite radiation data in global weather analysis; (3) studies of planetary waves and low-frequency weather variability; (4) GCM studies of the atmospheric response to variable boundary conditions measurable from satellites; and (5) dynamics of long-term earth system changes. Significant accomplishments from the three main lines of investigation pursued during the past year are presented and include the following: (1) planetary atmospheric waves and low frequency variability; (2) GCM studies of the atmospheric response to changed boundary conditions; and (3) dynamics of long-term changes in the global earth system.

Analytical stability and simulation response study for a coupled two-body system

NASA Technical Reports Server (NTRS)

Tao, K. M.; Roberts, J. R.

1975-01-01

An analytical stability study and a digital simulation response study of two connected rigid bodies are documented. Relative rotation of the bodies at the connection is allowed, thereby providing a model suitable for studying system stability and response during a soft-dock regime. Provisions are made of a docking port axes alignment torque and a despin torque capability for encountering spinning payloads. Although the stability analysis is based on linearized equations, the digital simulation is based on nonlinear models.

PLATSIM: A Simulation and Analysis Package for Large-Order Flexible Systems. Version 2.0

NASA Technical Reports Server (NTRS)

Maghami, Peiman G.; Kenny, Sean P.; Giesy, Daniel P.

1997-01-01

The software package PLATSIM provides efficient time and frequency domain analysis of large-order generic space platforms. PLATSIM can perform open-loop analysis or closed-loop analysis with linear or nonlinear control system models. PLATSIM exploits the particular form of sparsity of the plant matrices for very efficient linear and nonlinear time domain analysis, as well as frequency domain analysis. A new, original algorithm for the efficient computation of open-loop and closed-loop frequency response functions for large-order systems has been developed and is implemented within the package. Furthermore, a novel and efficient jitter analysis routine which determines jitter and stability values from time simulations in a very efficient manner has been developed and is incorporated in the PLATSIM package. In the time domain analysis, PLATSIM simulates the response of the space platform to disturbances and calculates the jitter and stability values from the response time histories. In the frequency domain analysis, PLATSIM calculates frequency response function matrices and provides the corresponding Bode plots. The PLATSIM software package is written in MATLAB script language. A graphical user interface is developed in the package to provide convenient access to its various features.

Noise in nonlinear nanoelectromechanical resonators

NASA Astrophysics Data System (ADS)

Guerra Vidal, Diego N.

Nano-Electro-Mechanical Systems (NEMS), due to their nanometer scale size, possess a number of desirable attributes: high sensitivity to applied forces, fast response times, high resonance frequencies and low power consumption. However, ultra small size and low power handling result in unwanted consequences: smaller signal size and higher dissipation, making the NEMS devices more susceptible to external and intrinsic noise. The simplest version of a NEMS, a suspended nanomechanical structure with two distinct excitation states, can be used as an archetypal two state system to study a plethora of fundamental phenomena such as Duffing nonlinearity, stochastic resonance, and macroscopic quantum tunneling at low temperatures. From a technical perspective, there are numerous applications such nanomechanical memory elements, microwave switches and nanomechanical computation. The control and manipulation of the mechanical response of these two state systems can be realized by exploiting a (seemingly) counterintuitive physical phenomenon, Stochastic Resonance: in a noisy nonlinear mechanical system, the presence of noise can enhance the system response to an external stimulus. This Thesis is mainly dedicated to study possible applications of Stochastic Resonance in two-state nanomechanical systems. First, on chip signal amplification by 1/falpha is observed. The effectiveness of the noise assisted amplification is observed to decrease with increasing a. Experimental evidence shows an increase in asymmetry between the two states with increasing noise color. Considering the prevalence of 1/f alpha noise in the materials in integrated circuits, the signal enhancement demonstrated here, suggests beneficial use of the otherwise detrimental noise. Finally, a nanomechanical device, operating as a reprogrammable logic gate, and performing fundamental logic functions such as AND/OR and NAND/NOR is presented. The logic function can be programmed (from AND to OR) dynamically, by adjusting the resonator's operating parameters. The device can access one of two stable steady states, according to a specific logic function; this operation is mediated by the noise floor, which can be directly adjusted, or dynamically "tuned" via an adjustment of the underlying nonlinearity of the resonator. The demonstration of this reprogrammable nanomechanical logic gate affords a path to the practical realization of a new generation of mechanical computer.

Noise-induced transitions in a double-well oscillator with nonlinear dissipation.

PubMed

Semenov, Vladimir V; Neiman, Alexander B; Vadivasova, Tatyana E; Anishchenko, Vadim S

2016-05-01

We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise intensity the system undergoes multiple qualitative changes in the structure of its steady-state probability density function (PDF). In particular, the PDF exhibits two pitchfork bifurcations versus noise intensity, which we describe using an effective potential and corresponding normal form of the bifurcation. These stochastic effects are explained by the partition of the phase space by the nullclines of the deterministic oscillator.

Parametric Analytical Studies for the Nonlinear Dynamic Response of the Tile/Pad Space Shuttle Thermal Protection System

NASA Technical Reports Server (NTRS)

Edighoffer, H.

1981-01-01

The studies examined for imposed sinusoidal and random motions of the shuttle skin and/or applied tile pressure. Studies are performed using the computer code DYNOTA which takes into account the highly nonlinear stiffening hysteresis and viscous behavior of the pad joining the tile to the shuttle skin. Where available, experimental data are used to confirm the validity of the analysis. Both analytical and experimental studies reveal that the system resonant frequency is very high for low amplitude oscillations but decreases rapidly to a minimum value with increasing amplitude.

Broad band nonlinear optical absorption measurements of the laser dye IR26 using white light continuum Z-scan

NASA Astrophysics Data System (ADS)

Dey, Soumyodeep; Bongu, Sudhakara Reddy; Bisht, Prem Ballabh

2017-03-01

We study the nonlinear optical response of a standard dye IR26 using the Z-scan technique, but with the white light continuum. The continuum source of wavelength from 450 nm to 1650 nm has been generated from the photonic crystal fiber on pumping with 772 nm of Ti:Sapphire oscillator. The use of broadband incident pulse enables us to probe saturable absorption (SA) and reverse saturable absorption (RSA) over the large spectral range with a single Z-scan measurement. The system shows SA in the resonant region while it turns to RSA in the non-resonant regions. The low saturation intensity of the dye can be explained based on the simultaneous excitation from ground states to various higher energy levels with the help of composite energy level diagram. The cumulative effects of excited state absorption and thermal induced nonlinear optical effects are responsible for the observed RSA.

Analysis of Nonlinear Dynamics in Linear Compressors Driven by Linear Motors

NASA Astrophysics Data System (ADS)

Chen, Liangyuan

2018-03-01

The analysis of dynamic characteristics of the mechatronics system is of great significance for the linear motor design and control. Steady-state nonlinear response characteristics of a linear compressor are investigated theoretically based on the linearized and nonlinear models. First, the influence factors considering the nonlinear gas force load were analyzed. Then, a simple linearized model was set up to analyze the influence on the stroke and resonance frequency. Finally, the nonlinear model was set up to analyze the effects of piston mass, spring stiffness, driving force as an example of design parameter variation. The simulating results show that the stroke can be obtained by adjusting the excitation amplitude, frequency and other adjustments, the equilibrium position can be adjusted by adjusting the DC input, and to make the more efficient operation, the operating frequency must always equal to the resonance frequency.

Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits.

PubMed

Ujfalussy, Balázs B; Makara, Judit K; Branco, Tiago; Lengyel, Máté

2015-12-24

Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

NASA Astrophysics Data System (ADS)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Active synchronization between two different chaotic dynamical system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maheri, M.; Arifin, N. Md; Ismail, F.

2015-05-15

In this paper we investigate on the synchronization problem between two different chaotic dynamical system based on the Lyapunov stability theorem by using nonlinear control functions. Active control schemes are used for synchronization Liu system as drive and Rossler system as response. Numerical simulation by using Maple software are used to show effectiveness of the proposed schemes.

Impulsive response of an automatic transmission system with multiple clearances: Formulation, simulation and experiment

NASA Astrophysics Data System (ADS)

Crowther, Ashley R.; Singh, Rajendra; Zhang, Nong; Chapman, Chris

2007-10-01

Impulsive responses in geared systems with multiple clearances are studied when the mean torque excitation and system load change abruptly, with application to a vehicle driveline with an automatic transmission. First, torsional lumped-mass models of the planetary and differential gear sets are formulated using matrix elements. The model is then reduced to address tractable nonlinear problems while successfully retaining the main modes of interest. Second, numerical simulations for the nonlinear model are performed for transient conditions and a typical driving situation that induces an impulsive behaviour simulated. However, initial conditions and excitation and load profiles have to be carefully defined before the model can be numerically solved. It is shown that the impacts within the planetary or differential gears may occur under combinations of engine, braking and vehicle load transients. Our analysis shows that the shaping of the engine transient by the torque converter before reaching the clearance locations is more critical. Third, a free vibration experiment is developed for an analogous driveline with multiple clearances and three experiments that excite different response regimes have been carried out. Good correlations validate the proposed methodology.

Nonlinear damage identification of breathing cracks in Truss system

NASA Astrophysics Data System (ADS)

Zhao, Jie; DeSmidt, Hans

2014-03-01

The breathing cracks in truss system are detected by Frequency Response Function (FRF) based damage identification method. This method utilizes damage-induced changes of frequency response functions to estimate the severity and location of structural damage. This approach enables the possibility of arbitrary interrogation frequency and multiple inputs/outputs which greatly enrich the dataset for damage identification. The dynamical model of truss system is built using the finite element method and the crack model is based on fracture mechanics. Since the crack is driven by tensional and compressive forces of truss member, only one damage parameter is needed to represent the stiffness reduction of each truss member. Assuming that the crack constantly breathes with the exciting frequency, the linear damage detection algorithm is developed in frequency/time domain using Least Square and Newton Raphson methods. Then, the dynamic response of the truss system with breathing cracks is simulated in the time domain and meanwhile the crack breathing status for each member is determined by the feedback from real-time displacements of member's nodes. Harmonic Fourier Coefficients (HFCs) of dynamical response are computed by processing the data through convolution and moving average filters. Finally, the results show the effectiveness of linear damage detection algorithm in identifying the nonlinear breathing cracks using different combinations of HFCs and sensors.

High amplitude nonlinear acoustic wave driven flow fields in cylindrical and conical resonators.

PubMed

Antao, Dion Savio; Farouk, Bakhtier

2013-08-01

A high fidelity computational fluid dynamic model is used to simulate the flow, pressure, and density fields generated in a cylindrical and a conical resonator by a vibrating end wall/piston producing high-amplitude standing waves. The waves in the conical resonator are found to be shock-less and can generate peak acoustic overpressures that exceed the initial undisturbed pressure by two to three times. A cylindrical (consonant) acoustic resonator has limitations to the output response observed at one end when the opposite end is acoustically excited. In the conical geometry (dissonant acoustic resonator) the linear acoustic input is converted to high energy un-shocked nonlinear acoustic output. The model is validated using past numerical results of standing waves in cylindrical resonators. The nonlinear nature of the harmonic response in the conical resonator system is further investigated for two different working fluids (carbon dioxide and argon) operating at various values of piston amplitude. The high amplitude nonlinear oscillations observed in the conical resonator can potentially enhance the performance of pulse tube thermoacoustic refrigerators and these conical resonators can be used as efficient mixers.

Nonlinear ultrasonic wave modulation for online fatigue crack detection

NASA Astrophysics Data System (ADS)

Sohn, Hoon; Lim, Hyung Jin; DeSimio, Martin P.; Brown, Kevin; Derriso, Mark

2014-02-01

This study presents a fatigue crack detection technique using nonlinear ultrasonic wave modulation. Ultrasonic waves at two distinctive driving frequencies are generated and corresponding ultrasonic responses are measured using permanently installed lead zirconate titanate (PZT) transducers with a potential for continuous monitoring. Here, the input signal at the lower driving frequency is often referred to as a 'pumping' signal, and the higher frequency input is referred to as a 'probing' signal. The presence of a system nonlinearity, such as a crack formation, can provide a mechanism for nonlinear wave modulation, and create spectral sidebands around the frequency of the probing signal. A signal processing technique combining linear response subtraction (LRS) and synchronous demodulation (SD) is developed specifically to extract the crack-induced spectral sidebands. The proposed crack detection method is successfully applied to identify actual fatigue cracks grown in metallic plate and complex fitting-lug specimens. Finally, the effect of pumping and probing frequencies on the amplitude of the first spectral sideband is investigated using the first sideband spectrogram (FSS) obtained by sweeping both pumping and probing signals over specified frequency ranges.

Identification and modeling of the electrohydraulic systems of the main gun of a main battle tank

NASA Astrophysics Data System (ADS)

Campos, Luiz C. A.; Menegaldo, Luciano L.

2012-11-01

The black-box mathematical models of the electrohydraulic systems responsible for driving the two degrees of freedom (elevation and azimuth) of the main gun of a main battle tank (MBT) were identified. Such systems respond to gunner's inputs while acquiring and tracking targets. Identification experiments were designed to collect simultaneous data from two inertial measurement units (IMU) installed at the gunner's handle (input) and at the center of rotation of the turret (output), for the identification of the azimuth system. For the elevation system, IMUs were installed at the gunner's handle (input) and at the breech of the gun (output). Linear accelerations and angular rates were collected for both input and output. Several black-box model architectures were investigated. As a result, nonlinear autoregressive with exogenous variables (NARX) second order model and nonlinear finite impulse response (NFIR) fourth order model, demonstrate to best fit the experimental data, with low computational costs. The derived models are being employed in a broader research, aiming to reproduce such systems in a laboratory virtual main gun simulator.

Application of chaotic attractor analysis in crack assessment of plates

NASA Astrophysics Data System (ADS)

Jalili, Sina; Daneshmehr, A. R.

2018-03-01

Part-through crack presence with limited length is one of the prevalent defects in plate structures. However, this type of damage has only a slight effect on the dynamic response of the structures. In this paper the modified line spring method (MLSM) is used to develop a nonlinear multi-degree of freedom model of part through cracked rectangular plate and chaotic interrogation is implemented to assess crack-induced degradation in the nonlinear model. After a convergence study of the proposed model in time series domain in which the plate subjected to Lorenz-type chaotic excitation, the tuning of interrogation is conducted by crossing the Lyapunov exponents' spectrums of the nonlinear model of the plate and chaotic signal. In this research nonlinear prediction error (NPE) is proposed as a damage sensitive feature which deals with the chaotic attractor of the excited system response. It is found that there are ranges of tuning parameter that result in higher damage sensitivity of the NPE. Damage characteristics such as: length, angle, location and depth of crack are considered as parameters to be varied to scrutinize the response of the plates. Results show that NPE generally has significantly higher sensitivity in comparison with conventional frequency-based methods; however this property has different levels for various boundary conditions.

Optical response of semiconductors in a dc-electric field

NASA Astrophysics Data System (ADS)

Prussel, Lucie; Veniard, Valerie

A deep understanding of the optical properties of solids is crucial for the improvement of nonlinear materials and devices. It offers the opportunity to search for new materials with specific properties. One way to tune some of those properties is to apply an electrostatic field. This gives rise to electro-optic effects. The most known among those is the Pockel or linear electro-optic effect (LEO), which is a second order response property described by the susceptibility χ (2) (- ω ω , 0) . An important nonlinear process is the second harmonic generation (SHG), where two photons are absorbed by the material. While this process is sensitive to the symmetry of the material, adding a static field would enable a nonlinear response from every material, including centrosymmetric ones. This happens through a third order process, named EFISH (Electric Field Induced Second Harmonic) for which the susceptibility of interest is χ (3) (- 2 ω ω , ω , 0) . We have developed a theoretical approach and a numerical tool to study these two nonlinear properties (LEO and EFISH) in the context of Time-dependent Density Functional Theory (TDDFT), and we have applied it to the case of bulk SiC and GaAs as well as layered systems such as Ge/SiGe.

A colloquium on the influence of versatile class of saturable nonlinear responses in the instability induced supercontinuum generation

NASA Astrophysics Data System (ADS)

Nithyanandan, K.; Vasantha Jayakantha Raja, R.; Porsezian, K.; Uthayakumar, T.

2013-08-01

We investigate the modulational instability induced supercontinuum generation (MI-SCG) under versatile saturable nonlinear (SNL) responses. We identify and discuss the salient features of saturable nonlinear responses of various functional forms such as exponential, conventional and coupled type on modulational instability (MI) and the subsequent supercontinuum (SC) process. Firstly, we analyze the impact of SNL on the MI spectrum and found both analytically and numerically that MI gain and bandwidth is maximum for exponential nonlinearity in comparison to other types of SNL's. We also reported the unique behavior of the SNL system in the MI dynamics. Following the MI analysis, the proceeding section deals with the supercontinuum generation (SCG) process by virtue of MI. We examine exclusively the impact of each form of SNL on the SC spectrum and predicted numerically that exponential case attains the phase matching earlier and thus enable to achieve broad spectrum at a relatively shorter distance of propagation than the other cases of SNL's. Thus a direct evidence of SCG from MI is emphasized and the impact of SNL in MI-SCG is highlighted. To analyze the quality of the output continuum spectrum, we performed the coherence analysis for MI-SCG in the presence of SNL.

Microscopic Approach to the Nonlinear Elasticity of Compressed Emulsions

NASA Astrophysics Data System (ADS)

Jorjadze, Ivane; Pontani, Lea-Laetitia; Brujic, Jasna

2013-01-01

Using confocal microscopy, we measure the packing geometry and interdroplet forces as a function of the osmotic pressure in a 3D emulsion system. We assume a harmonic interaction potential over a wide range of volume fractions and attribute the observed nonlinear elastic response of the pressure with density to the first corrections to the scaling laws of the microstructure away from the critical point. The bulk modulus depends on the excess contacts created under compression, which leads to the correction exponent α=1.5. Microscopically, the nonlinearities manifest themselves as a narrowing of the distribution of the pressure per particle as a function of the global pressure.

Nonlinear identification of the total baroreflex arc: chronic hypertension model.

PubMed

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru; Mukkamala, Ramakrishna

2016-05-01

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). Its linear dynamic functioning has been shown to be preserved in spontaneously hypertensive rats (SHR). However, the system is known to exhibit nonlinear dynamic behaviors. The aim of this study was to establish nonlinear dynamic models of the total arc (and its subsystems) in hypertensive rats and to compare these models with previously published models for normotensive rats. Hypertensive rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned. The carotid sinus regions were isolated and attached to a servo-controlled piston pump. AP and sympathetic nerve activity were measured while CSP was controlled via the pump using Gaussian white noise stimulation. Second-order, nonlinear dynamics models were developed by application of nonparametric system identification to a portion of the measurements. The models of the total arc predicted AP 21-43% better (P < 0.005) than conventional linear dynamic models in response to a new portion of the CSP measurement. The linear and nonlinear terms of these validated models were compared with the corresponding terms of an analogous model for normotensive rats. The nonlinear gains for the hypertensive rats were significantly larger than those for the normotensive rats [-0.38 ± 0.04 (unitless) vs. -0.22 ± 0.03, P < 0.01], whereas the linear gains were similar. Hence, nonlinear dynamic functioning of the sympathetically mediated total arc may enhance baroreflex buffering of AP increases more in SHR than normotensive rats. Copyright © 2016 the American Physiological Society.

Effects of Initial Geometric Imperfections On the Non-Linear Response of the Space Shuttle Superlightweight Liquid-Oxygen Tank

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H., Jr.

2002-01-01

The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.

The Vestibular System Implements a Linear–Nonlinear Transformation In Order to Encode Self-Motion

PubMed Central

Massot, Corentin; Schneider, Adam D.; Chacron, Maurice J.; Cullen, Kathleen E.

2012-01-01

Although it is well established that the neural code representing the world changes at each stage of a sensory pathway, the transformations that mediate these changes are not well understood. Here we show that self-motion (i.e. vestibular) sensory information encoded by VIIIth nerve afferents is integrated nonlinearly by post-synaptic central vestibular neurons. This response nonlinearity was characterized by a strong (∼50%) attenuation in neuronal sensitivity to low frequency stimuli when presented concurrently with high frequency stimuli. Using computational methods, we further demonstrate that a static boosting nonlinearity in the input-output relationship of central vestibular neurons accounts for this unexpected result. Specifically, when low and high frequency stimuli are presented concurrently, this boosting nonlinearity causes an intensity-dependent bias in the output firing rate, thereby attenuating neuronal sensitivities. We suggest that nonlinear integration of afferent input extends the coding range of central vestibular neurons and enables them to better extract the high frequency features of self-motion when embedded with low frequency motion during natural movements. These findings challenge the traditional notion that the vestibular system uses a linear rate code to transmit information and have important consequences for understanding how the representation of sensory information changes across sensory pathways. PMID:22911113

Sweep excitation with order tracking: A new tactic for beam crack analysis

NASA Astrophysics Data System (ADS)

Wei, Dongdong; Wang, KeSheng; Zhang, Mian; Zuo, Ming J.

2018-04-01

Crack detection in beams and beam-like structures is an important issue in industry and has attracted numerous investigations. A local crack leads to global system dynamics changes and produce non-linear vibration responses. Many researchers have studied these non-linearities for beam crack diagnosis. However, most reported methods are based on impact excitation and constant frequency excitation. Few studies have focused on crack detection through external sweep excitation which unleashes abundant dynamic characteristics of the system. Together with a signal resampling technique inspired by Computed Order Tracking, this paper utilize vibration responses under sweep excitations to diagnose crack status of beams. A data driven method for crack depth evaluation is proposed and window based harmonics extracting approaches are studied. The effectiveness of sweep excitation and the proposed method is experimentally validated.

Generation of linear dynamic models from a digital nonlinear simulation

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Krosel, S. M.

1979-01-01

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Decoupling nonclassical nonlinear behavior of elastic wave types

DOE PAGES

Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cedric; ...

2016-03-01

In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. As a result, this could lead to furthermore » understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.« less

Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties

PubMed Central

Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon

2014-01-01

Purpose The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency during anterior-posterior stretching. Method Three materially linear and three materially nonlinear models were created and stretched up to 10 mm in 1 mm increments. Phonation onset pressure (Pon) and fundamental frequency (F0) at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1 mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Results Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Conclusions Nonlinear synthetic models appear to more accurately represent the human vocal folds than linear models, especially with respect to F0 response. PMID:22271874

Frequency response of synthetic vocal fold models with linear and nonlinear material properties.

PubMed

Shaw, Stephanie M; Thomson, Scott L; Dromey, Christopher; Smith, Simeon

2012-10-01

The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F0) during anterior-posterior stretching. Three materially linear and 3 materially nonlinear models were created and stretched up to 10 mm in 1-mm increments. Phonation onset pressure (Pon) and F0 at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1-mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Nonlinear synthetic models appear to more accurately represent the human vocal folds than do linear models, especially with respect to F0 response.

Quantifying non-linear dynamics of mass-springs in series oscillators via asymptotic approach

NASA Astrophysics Data System (ADS)

Starosta, Roman; Sypniewska-Kamińska, Grażyna; Awrejcewicz, Jan

2017-05-01

Dynamical regular response of an oscillator with two serially connected springs with nonlinear characteristics of cubic type and governed by a set of differential-algebraic equations (DAEs) is studied. The classical approach of the multiple scales method (MSM) in time domain has been employed and appropriately modified to solve the governing DAEs of two systems, i.e. with one- and two degrees-of-freedom. The approximate analytical solutions have been verified by numerical simulations.

Preisach modeling of temperature-dependent ferroelectric response of piezoceramics at sub-switching regime

NASA Astrophysics Data System (ADS)

Ochoa, Diego Alejandro; García, Jose Eduardo

2016-04-01

The Preisach model is a classical method for describing nonlinear behavior in hysteretic systems. According to this model, a hysteretic system contains a collection of simple bistable units which are characterized by an internal field and a coercive field. This set of bistable units exhibits a statistical distribution that depends on these fields as parameters. Thus, nonlinear response depends on the specific distribution function associated with the material. This model is satisfactorily used in this work to describe the temperature-dependent ferroelectric response in PZT- and KNN-based piezoceramics. A distribution function expanded in Maclaurin series considering only the first terms in the internal field and the coercive field is proposed. Changes in coefficient relations of a single distribution function allow us to explain the complex temperature dependence of hard piezoceramic behavior. A similar analysis based on the same form of the distribution function shows that the KNL-NTS properties soften around its orthorhombic to tetragonal phase transition.

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity [PowerPoint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mayes, Randall L.; Pacini, Benjamin Robert; Roettgen, Dan

2016-01-01

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combinationmore » with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.« less

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pacini, Benjamin Robert; Mayes, Randall L.; Roettgen, Daniel R

2015-10-01

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combinationmore » with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.« less

Autocorrelation measurement of femtosecond laser pulses based on two-photon absorption in GaP photodiode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chong, E. Z.; Watson, T. F.; Festy, F., E-mail: frederic.festy@kcl.ac.uk

2014-08-11

Semiconductor materials which exhibit two-photon absorption characteristic within a spectral region of interest can be useful in building an ultra-compact interferometric autocorrelator. In this paper, we report on the evidence of a nonlinear absorption process in GaP photodiodes which was exploited to measure the temporal profile of femtosecond Ti:sapphire laser pulses with a tunable peak wavelength above 680 nm. The two-photon mediated conductivity measurements were performed at an average laser power of less than a few tenths of milliwatts. Its suitability as a single detector in a broadband autocorrelator setup was assessed by investigating the nonlinear spectral sensitivity bandwidth of amore » GaP photodiode. The highly favourable nonlinear response was found to cover the entire tuning range of our Ti:sapphire laser and can potentially be extended to wavelengths below 680 nm. We also demonstrated the flexibility of GaP in determining the optimum compensation value of the group delay dispersion required to restore the positively chirped pulses inherent in our experimental optical system to the shortest pulse width possible. With the rise in the popularity of nonlinear microscopy, the broad two-photon response of GaP and the simplicity of this technique can provide an alternative way of measuring the excitation laser pulse duration at the focal point of any microscopy systems.« less

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

High Speed Civil Transport Aircraft Simulation: Reference-H Cycle 1, MATLAB Implementation

NASA Technical Reports Server (NTRS)

Sotack, Robert A.; Chowdhry, Rajiv S.; Buttrill, Carey S.

1999-01-01

The mathematical model and associated code to simulate a high speed civil transport aircraft - the Boeing Reference H configuration - are described. The simulation was constructed in support of advanced control law research. In addition to providing time histories of the dynamic response, the code includes the capabilities for calculating trim solutions and for generating linear models. The simulation relies on the nonlinear, six-degree-of-freedom equations which govern the motion of a rigid aircraft in atmospheric flight. The 1962 Standard Atmosphere Tables are used along with a turbulence model to simulate the Earth atmosphere. The aircraft model has three parts - an aerodynamic model, an engine model, and a mass model. These models use the data from the Boeing Reference H cycle 1 simulation data base. Models for the actuator dynamics, landing gear, and flight control system are not included in this aircraft model. Dynamic responses generated by the nonlinear simulation are presented and compared with results generated from alternate simulations at Boeing Commercial Aircraft Company and NASA Langley Research Center. Also, dynamic responses generated using linear models are presented and compared with dynamic responses generated using the nonlinear simulation.

Buckling Behavior of Compression-Loaded Composite Cylindrical Shells with Reinforced Cutouts

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Starnes, James H., Jr.

2002-01-01

Results from a numerical study of the response of thin-wall compression-loaded quasi-isotropic laminated composite cylindrical shells with reinforced and unreinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A high-fidelity nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate how a compression-loaded shell with an unreinforced cutout can exhibit a complex nonlinear response. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, the addition of reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell, as expected. However, results are presented that show how certain reinforcement configurations can actually cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved response characteristics.

Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.

1993-11-01

Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.

Stages of chaotic synchronization.

PubMed

Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.

1998-09-01

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.

Nonlinearities and noise in micromechanical resonators: From understanding to characterization and design tools

NASA Astrophysics Data System (ADS)

Polunin, Pavel M.

In this work we consider several nonlinearity-based and/or noise-related phenomena that have been recently observed in micro-electromechanical vibratory systems. The main goals are to closely examine these phenomena, develop an understanding of their underlying physics, derive techniques for characterizing parameters in relevant mathematical models, and determine ways to improve the performance of specific classes of micro-electromechanical systems (MEMS) used in applications. The general perspective of this work is based on the fact that nonlinearity and noise represent integral parts of the models needed to describe the response of these systems, and the focus is on situations where these generally undesirable features can be utilized or accounted for in design. We consider three different, but related, topics in this general area. The first topic uses the slowly varying states in a rotating frame of reference where we analyze the stationary probability distribution of a nonlinear parametrically-driven resonator subjected to Poisson pulses and thermal noise. We show that Poisson pulses with low pulse rates, as compared with the resonator decay rate, cause a power-law divergence of the probability density at the resonator equilibrium in both the underdamped (overdamped) regimes, in which the response does (does not) spiral in the rotating frame. We have also found that the shape of the probability distribution away from the equilibrium position is qualitatively different for the overdamped and underdamped cases. In particular, in the overdamped regime, the form of the secondary singularity in the probability distribution depends strongly on the reference phase of the resonator response and the pulse modulation phase, while in the underdamped regime several singular peaks occur in the distribution, and their locations are determined by the resonator frequency and decay rate in the rotating frame. Finally, we show that even weak Gaussian noise smoothens out the singular peaks in the probability distribution. The theoretical results are successfully compared experimental results obtained from collaborators at the Hong Kong University of Science and Technology. Second, we discuss a time-domain technique for characterizing parameters for models that describe the response of a single vibrational mode of micromechanical resonators with symmetric restoring and damping forces. These parameters include coefficients of conservative and dissipative linear and nonlinear terms, as well as the strengths of various noise sources acting on the mode of interest. The method relies on measurements taken during a ringdown response, that is, free vibration, in which the nonlinearities result in an amplitude-dependent frequency and a non-exponential decay of the amplitude, while noise sources cause fluctuations in the resonator amplitude and phase. Analysis of the amplitude of the ringdown response allows one to estimate the quality factor and the dissipative nonlinearity, and the zero-crossing points in the ringdown measurement can be used to characterize the linear natural frequency and the cubic and quintic nonlinearities of the vibrational mode, which typically arise from a combination of mechanical and electrostatic effects. Additionally, we develop and demonstrate a statistical analysis of the zero-crossing points in the resonator response that allows one to separate the effects of additive, multiplicative, and measurement noises and estimate their corresponding intensities. These characterization methods are demonstrated using experimental measurements obtained from collaborators at Stanford University. Finally, we examine the problem of self-induced parametric amplification in ring/disk resonating gyroscopes. We model the dynamics of these gyroscopes by considering flexural (elliptical) vibrations of a thin elastic ring subjected to electrostatic transduction and show that the parametric amplification arises naturally from nonlinear intermodal coupling between the drive and sense modes of the gyroscope. Analysis shows that this coupling results in a substantial increase in the sensitivity of the gyroscope to the external angular rate. This improvement in the gyroscope performance depends strongly on both the modal coupling strength and the operating point of the gyroscope, features which depend on details of nonlinear kinematics of, and forces acting on, the ring. Using the results from this model, we explore ways to enhance the amplification effect by changing the shape of the resonator body and attendant electrodes, and by electrostatic tuning. These results suggest new designs for ring gyros, and a general approach for other geometries, such as disk-resonator-gyros (DRGs), that should offer significant improvements in device sensitivity.

Superradiance Effects in the Linear and Nonlinear Optical Response of Quantum Dot Molecules

NASA Astrophysics Data System (ADS)

Sitek, A.; Machnikowski, P.

2008-11-01

We calculate the linear optical response from a single quantum dot molecule and the nonlinear, four-wave-mixing response from an inhomogeneously broadened ensemble of such molecules. We show that both optical signals are affected by the coupling-dependent superradiance effect and by optical interference between the two polarizations. As a result, the linear and nonlinear responses are not identical.

Theta phase precession and phase selectivity: a cognitive device description of neural coding

NASA Astrophysics Data System (ADS)

Zalay, Osbert C.; Bardakjian, Berj L.

2009-06-01

Information in neural systems is carried by way of phase and rate codes. Neuronal signals are processed through transformative biophysical mechanisms at the cellular and network levels. Neural coding transformations can be represented mathematically in a device called the cognitive rhythm generator (CRG). Incoming signals to the CRG are parsed through a bank of neuronal modes that orchestrate proportional, integrative and derivative transformations associated with neural coding. Mode outputs are then mixed through static nonlinearities to encode (spatio) temporal phase relationships. The static nonlinear outputs feed and modulate a ring device (limit cycle) encoding output dynamics. Small coupled CRG networks were created to investigate coding functionality associated with neuronal phase preference and theta precession in the hippocampus. Phase selectivity was found to be dependent on mode shape and polarity, while phase precession was a product of modal mixing (i.e. changes in the relative contribution or amplitude of mode outputs resulted in shifting phase preference). Nonlinear system identification was implemented to help validate the model and explain response characteristics associated with modal mixing; in particular, principal dynamic modes experimentally derived from a hippocampal neuron were inserted into a CRG and the neuron's dynamic response was successfully cloned. From our results, small CRG networks possessing disynaptic feedforward inhibition in combination with feedforward excitation exhibited frequency-dependent inhibitory-to-excitatory and excitatory-to-inhibitory transitions that were similar to transitions seen in a single CRG with quadratic modal mixing. This suggests nonlinear modal mixing to be a coding manifestation of the effect of network connectivity in shaping system dynamic behavior. We hypothesize that circuits containing disynaptic feedforward inhibition in the nervous system may be candidates for interpreting upstream rate codes to guide downstream processes such as phase precession, because of their demonstrated frequency-selective properties.

Analysis of periodically excited non-linear systems by a parametric continuation technique

NASA Astrophysics Data System (ADS)

Padmanabhan, C.; Singh, R.

1995-07-01

The dynamic behavior and frequency response of harmonically excited piecewise linear and/or non-linear systems has been the subject of several recent investigations. Most of the prior studies employed harmonic balance or Galerkin schemes, piecewise linear techniques, analog simulation and/or direct numerical integration (digital simulation). Such techniques are somewhat limited in their ability to predict all of the dynamic characteristics, including bifurcations leading to the occurrence of unstable, subharmonic, quasi-periodic and/or chaotic solutions. To overcome this problem, a parametric continuation scheme, based on the shooting method, is applied specifically to a periodically excited piecewise linear/non-linear system, in order to improve understanding as well as to obtain the complete dynamic response. Parameter regions exhibiting bifurcations to harmonic, subharmonic or quasi-periodic solutions are obtained quite efficiently and systematically. Unlike other techniques, the proposed scheme can follow period-doubling bifurcations, and with some modifications obtain stable quasi-periodic solutions and their bifurcations. This knowledge is essential in establishing conditions for the occurrence of chaotic oscillations in any non-linear system. The method is first validated through the Duffing oscillator example, the solutions to which are also obtained by conventional one-term harmonic balance and perturbation methods. The second example deals with a clearance non-linearity problem for both harmonic and periodic excitations. Predictions from the proposed scheme match well with available analog simulation data as well as with multi-term harmonic balance results. Potential savings in computational time over direct numerical integration is demonstrated for some of the example cases. Also, this work has filled in some of the solution regimes for an impact pair, which were missed previously in the literature. Finally, one main limitation associated with the proposed procedure is discussed.

Nonlinear response of unidirectional boron/aluminum

NASA Technical Reports Server (NTRS)

Pindera, M.-J.; Herakovich, C. T.; Becker, W.; Aboudi, J.

1990-01-01

Experimental results obtained for unidirectional boron/aluminum subjected to combined loading using off-axis tension, compression and Iosipescu shear specimens are correlated with a nonlinear micromechanics model. It is illustrated that the nonlinear response in the principal material directions is markedly influenced by the different loading modes and different ratios of the applied stress components. The observed nonlinear response under pure and combined loading is discussed in terms of initial yielding, subsequent hardening, stress-interaction effects and unloading-reloading characteristics. The micromechanics model is based on the concept of a repeating unit cell representative of the composite-at-large and employs the unified theory of Bodner and Partom to model the inelastic response of the matrix. It is shown that the employed micromechanics model is sufficiently general to predict the observed nonlinear response of unidirectional boron/aluminum with good accuracy.

Nonlinear 2D arm dynamics in response to continuous and pulse-shaped force perturbations.

PubMed

Happee, Riender; de Vlugt, Erwin; van Vliet, Bart

2015-01-01

Ample evidence exists regarding the nonlinearity of the neuromuscular system but linear models are widely applied to capture postural dynamics. This study quantifies the nonlinearity of human arm postural dynamics applying 2D continuous force perturbations (0.2-40 Hz) inducing three levels of hand displacement (5, 15, 45 mm RMS) followed by force-pulse perturbations inducing large hand displacements (up to 250 mm) in a position task (PT) and a relax task (RT) recording activity of eight shoulder and elbow muscles. The continuous perturbation data were used to analyze the 2D endpoint dynamics in the frequency domain and to identify reflexive and intrinsic parameters of a linear neuromuscular shoulder-elbow model. Subsequently, it was assessed to what extent the large displacements in response to force pulses could be predicted from the 'small amplitude' linear neuromuscular model. Continuous and pulse perturbation responses with varying amplitudes disclosed highly nonlinear effects. In PT, a larger continuous perturbation induced stiffening with a factor of 1.5 attributed to task adaptation evidenced by increased co-contraction and reflexive activity. This task adaptation was even more profound in the pulse responses where reflexes and displacements were strongly affected by the presence and amplitude of preceding continuous perturbations. In RT, a larger continuous perturbation resulted in yielding with a factor of 3.8 attributed to nonlinear mechanical properties as no significant reflexive activity was found. Pulse perturbations always resulted in yielding where a model fitted to the preceding 5-mm continuous perturbations predicted only 37% of the recorded peak displacements in RT and 79% in PT. This demonstrates that linear neuromuscular models, identified using continuous perturbations with small amplitudes, strongly underestimate displacements in pulse-shaped (e.g., impact) loading conditions. The data will be used to validate neuromuscular models including nonlinear muscular (e.g., Hill and Huxley) and reflexive components.

Nonlinear effects of respiration on the crosstalk between cardiovascular and cerebrovascular control systems

NASA Astrophysics Data System (ADS)

Bari, Vlasta; Marchi, Andrea; De Maria, Beatrice; Rossato, Gianluca; Nollo, Giandomenico; Faes, Luca; Porta, Alberto

2016-05-01

Cardiovascular and cerebrovascular regulatory systems are vital control mechanisms responsible for guaranteeing homeostasis and are affected by respiration. This work proposes the investigation of cardiovascular and cerebrovascular control systems and the nonlinear influences of respiration on both regulations through joint symbolic analysis (JSA), conditioned or unconditioned on respiration. Interactions between cardiovascular and cerebrovascular regulatory systems were evaluated as well by performing correlation analysis between JSA indexes describing the two control systems. Heart period, systolic and mean arterial pressure, mean cerebral blood flow velocity and respiration were acquired on a beat-to-beat basis in 13 subjects experiencing recurrent syncope episodes (SYNC) and 13 healthy individuals (non-SYNC) in supine resting condition and during head-up tilt test at 60° (TILT). Results showed that JSA distinguished conditions and groups, whereas time domain parameters detected only the effect of TILT. Respiration affected cardiovascular and cerebrovascular regulatory systems in a nonlinear way and was able to modulate the interactions between the two control systems with different outcome in non-SYNC and SYNC groups, thus suggesting that the analysis of the impact of respiration on cardiovascular and cerebrovascular regulatory systems might improve our understanding of the mechanisms underpinning the development of postural-related syncope.

Transient chaos and crisis phenomena in butterfly valves driven by solenoid actuators

NASA Astrophysics Data System (ADS)

Naseradinmousavi, Peiman; Nataraj, C.

2012-11-01

Chilled water systems used in the industry and on board ships are critical for safe and reliable operation. It is hence important to understand the fundamental physics of these systems. This paper focuses in particular on a critical part of the automation system, namely, actuators and valves that are used in so-called "smart valve" systems. The system is strongly nonlinear, and necessitates a nonlinear dynamic analysis to be able to predict all critical phenomena that affect effective operation and efficient design. The derived mathematical model includes electromagnetics, fluid mechanics, and mechanical dynamics. Nondimensionalization has been carried out in order to reduce the large number of parameters to a few critical independent sets to help carry out a broad parametric analysis. The system stability analysis is then carried out with the aid of the tools from nonlinear dynamic analysis. This reveals that the system is unstable in a certain region of the parameter space. The system is also shown to exhibit crisis and transient chaotic responses; this is characterized using Lyapunov exponents and power spectra. Knowledge and avoidance of these dangerous regimes is necessary for successful and safe operation.

Nonlinear resonances and antiresonances of a forced sonic vacuum

DOE PAGES

Pozharskiy, D.; Zhang, Y.; Williams, M. O.; ...

2015-12-23

We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., ofmore » period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) “nonlinear spectrum” in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). As a result, we rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves.« less

Aeroservoelastic Model Validation and Test Data Analysis of the F/A-18 Active Aeroelastic Wing

NASA Technical Reports Server (NTRS)

Brenner, Martin J.; Prazenica, Richard J.

2003-01-01

Model validation and flight test data analysis require careful consideration of the effects of uncertainty, noise, and nonlinearity. Uncertainty prevails in the data analysis techniques and results in a composite model uncertainty from unmodeled dynamics, assumptions and mechanics of the estimation procedures, noise, and nonlinearity. A fundamental requirement for reliable and robust model development is an attempt to account for each of these sources of error, in particular, for model validation, robust stability prediction, and flight control system development. This paper is concerned with data processing procedures for uncertainty reduction in model validation for stability estimation and nonlinear identification. F/A-18 Active Aeroelastic Wing (AAW) aircraft data is used to demonstrate signal representation effects on uncertain model development, stability estimation, and nonlinear identification. Data is decomposed using adaptive orthonormal best-basis and wavelet-basis signal decompositions for signal denoising into linear and nonlinear identification algorithms. Nonlinear identification from a wavelet-based Volterra kernel procedure is used to extract nonlinear dynamics from aeroelastic responses, and to assist model development and uncertainty reduction for model validation and stability prediction by removing a class of nonlinearity from the uncertainty.

Nonlinear Response of the Stratosphere and the North Atlantic-European Climate to Global Warming

NASA Astrophysics Data System (ADS)

Manzini, E.; Karpechko, A. Yu.; Kornblueh, L.

2018-05-01

The response of the northern winter atmospheric circulation for two consecutive global warming periods of 2 K is examined in a grand ensemble (68 members) of idealized CO2 increase experiments performed with the same climate model. The comparison of the atmospheric responses for the two periods shows remarkable differences, indicating the nonlinearity of the response. The nonlinear signature of the atmospheric and surface responses is reminiscent of the positive phase of the annular mode of variability. The stratospheric vortex response shifts from an easterly wind change for the first 2 K to a westerly wind change for the second 2 K. The North Atlantic storm track shifts poleward only in the second period. A weaker November Arctic amplification during the second period suggests that differences in Arctic sea ice changes can act to trigger the atmospheric nonlinear response. Stratosphere-troposphere coupling thereafter can provide for the persistence of this nonlinearity throughout the winter.

Mechanistic analysis of challenge-response experiments.

PubMed

Shotwell, M S; Drake, K J; Sidorov, V Y; Wikswo, J P

2013-09-01

We present an application of mechanistic modeling and nonlinear longitudinal regression in the context of biomedical response-to-challenge experiments, a field where these methods are underutilized. In this type of experiment, a system is studied by imposing an experimental challenge, and then observing its response. The combination of mechanistic modeling and nonlinear longitudinal regression has brought new insight, and revealed an unexpected opportunity for optimal design. Specifically, the mechanistic aspect of our approach enables the optimal design of experimental challenge characteristics (e.g., intensity, duration). This article lays some groundwork for this approach. We consider a series of experiments wherein an isolated rabbit heart is challenged with intermittent anoxia. The heart responds to the challenge onset, and recovers when the challenge ends. The mean response is modeled by a system of differential equations that describe a candidate mechanism for cardiac response to anoxia challenge. The cardiac system behaves more variably when challenged than when at rest. Hence, observations arising from this experiment exhibit complex heteroscedasticity and sharp changes in central tendency. We present evidence that an asymptotic statistical inference strategy may fail to adequately account for statistical uncertainty. Two alternative methods are critiqued qualitatively (i.e., for utility in the current context), and quantitatively using an innovative Monte-Carlo method. We conclude with a discussion of the exciting opportunities in optimal design of response-to-challenge experiments. © 2013, The International Biometric Society.

The Effect of Basis Selection on Static and Random Acoustic Response Prediction Using a Nonlinear Modal Simulation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2005-01-01

An investigation of the effect of basis selection on geometric nonlinear response prediction using a reduced-order nonlinear modal simulation is presented. The accuracy is dictated by the selection of the basis used to determine the nonlinear modal stiffness. This study considers a suite of available bases including bending modes only, bending and membrane modes, coupled bending and companion modes, and uncoupled bending and companion modes. The nonlinear modal simulation presented is broadly applicable and is demonstrated for nonlinear quasi-static and random acoustic response of flat beam and plate structures with isotropic material properties. Reduced-order analysis predictions are compared with those made using a numerical simulation in physical degrees-of-freedom to quantify the error associated with the selected modal bases. Bending and membrane responses are separately presented to help differentiate the bases.

Off-resonant third-order optical nonlinearities of squarylium and croconium dyes

NASA Astrophysics Data System (ADS)

Li, Zhongyu; Xu, Song; Niu, Lihong; Zhang, Zhi; Chen, Zihui; Zhang, Fushi

2008-01-01

The magnitude and dynamic response of the third-order optical nonlinearities of squarylium and croconium dyes in methanol solution were measured by femtosecond degenerate four-wave mixing (DFWM) technique at 800 nm. Ultrafast nonlinear optical responses have been observed, and the magnitude of the second-order hyperpolarizabilities was evaluated to be 5.80 × 10 -31 esu for the squarylium dye and 8.69 × 10 -31 esu for the croconium dye, respectively. The large optical nonlinearities of the dyes can be attributed to their rigid and intramolecular charge transfer structure, and the instantaneous NLO responses of dyes are shorter than the experimental time resolution (50 fs), which is mainly contributed from the electron delocalization. The fast nonlinear response and large third-order optical nonlinearities show that the studied squarylium and croconium dyes might a kind of promising materials for the applications in all-optical switching and modulator.

Nonlinear Response of Thin Cylindrical Shells with Longitudinal Cracks and Subjected to Internal Pressure and Axial compression Loads

NASA Technical Reports Server (NTRS)

Starnes, James H.; Rose, Cheryl A.

1998-01-01

The results of an analytical study of the nonlinear response of a thin unstiffened aluminum cylindrical shell with a longitudinal crack are presented. The shell is analyzed with a nonlinear shell analysis code that maintains the shell in a nonlinear equilibrium state while the crack is grown. The analysis accurately accounts for global and local structural response phenomena. Results are presented for internal pressure, axial compression, and combined internal pressure and axial compression loads. The effects of varying crack length on the nonlinear response of the shell subjected to internal pressure are described. The effects of varying crack length on the prebuckling, buckling and postbuckling responses of the shell subjected to axial compression, and subjected to combined internal pressure and axial compression are also described. The results indicate that the nonlinear interaction between the in-plane stress resultants and the out-of-plane displacements near a crack can significantly affect the structural response of the shell. The results also indicate that crack growth instabilities and shell buckling instabilities can both affect the response of the shell as the crack length is increased.

On the nonlinear forced response of the North Atlantic atmosphere to meridional shifts of the Gulf Stream path

NASA Astrophysics Data System (ADS)

Seo, H.; Kwon, Y. O.; Joyce, T. M.; Ummenhofer, C.

2016-12-01

This study examines the North Atlantic atmospheric circulation response to the meridional shift of Gulf Stream path using a large-ensemble, high-resolution, and hemispheric-scale WRF simulations. The model is forced with wintertime SST anomalies derived from a wide range of Gulf Stream shift scenarios. The key result of the model experiments, supported in part by an independent analysis of a reanalysis data set, is that the large-scale, quasi-steady North Atlantic circulation response is unambiguously nonlinear about the sign and amplitude of chosen SST anomalies. This nonlinear response prevails over the weak linear response and resembles the negative North Atlantic Oscillation, the leading intrinsic mode of variability in the model and the observations. Further analysis of the associated dynamics reveals that the nonlinear responses are accompanied by the anomalous southward shift of the North Atlantic eddy-driven jet stream, which is reinforced nearly equally by the high-frequency transient eddy feedback and the low-frequency high-latitude wave breaking events. The result highlights the importance of the intrinsically nonlinear transient eddy dynamics and eddy-mean flow interactions in generating the nonlinear forced response to the meridional shift in the Gulf Stream.

Linear dynamic coupling in geared rotor systems

NASA Technical Reports Server (NTRS)

David, J. W.; Mitchell, L. D.

1986-01-01

The effects of high frequency oscillations caused by the gear mesh, on components of a geared system that can be modeled as rigid discs are analyzed using linear dynamic coupling terms. The coupled, nonlinear equations of motion for a disc attached to a rotating shaft are presented. The results of a trial problem analysis show that the inclusion of the linear dynamic coupling terms can produce significant changes in the predicted response of geared rotor systems, and that the produced sideband responses are greater than the unbalanced response. The method is useful in designing gear drives for heavy-lift helicopters, industrial speed reducers, naval propulsion systems, and heavy off-road equipment.

Optimization of a pressure control valve for high power automatic transmission considering stability

NASA Astrophysics Data System (ADS)

Jian, Hongchao; Wei, Wei; Li, Hongcai; Yan, Qingdong

2018-02-01

The pilot-operated electrohydraulic clutch-actuator system is widely utilized by high power automatic transmission because of the demand of large flowrate and the excellent pressure regulating capability. However, a self-excited vibration induced by the inherent non-linear characteristics of valve spool motion coupled with the fluid dynamics can be generated during the working state of hydraulic systems due to inappropriate system parameters, which causes sustaining instability in the system and leads to unexpected performance deterioration and hardware damage. To ensure a stable and fast response performance of the clutch actuator system, an optimal design method for the pressure control valve considering stability is proposed in this paper. A non-linear dynamic model of the clutch actuator system is established based on the motion of the valve spool and coupling fluid dynamics in the system. The stability boundary in the parameter space is obtained by numerical stability analysis. Sensitivity of the stability boundary and output pressure response time corresponding to the valve parameters are identified using design of experiment (DOE) approach. The pressure control valve is optimized using particle swarm optimization (PSO) algorithm with the stability boundary as constraint. The simulation and experimental results reveal that the optimization method proposed in this paper helps in improving the response characteristics while ensuring the stability of the clutch actuator system during the entire gear shift process.

Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.

2006-01-01

Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn; Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin; Zhang, W. D., E-mail: zhangwenditju@126.com

2014-03-15

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposedmore » in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.« less

Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems.

PubMed

Sapsis, Themistoklis P; Majda, Andrew J

2013-08-20

A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems is developed here. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear nonnormal dynamics in the unperturbed system and energy-conserving nonlinear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. In the Lorenz 96 model, the ROMQG algorithm with just a single mode captures the transient response to random or deterministic forcing. For the baroclinic ocean turbulence models, the inexpensive ROMQG algorithm with 252 modes, less than 0.2% of the total, captures the nonlinear response of the energy, the heat flux, and even the one-dimensional energy and heat flux spectra.

A robust hybrid fuzzy-simulated annealing-intelligent water drops approach for tuning a distribution static compensator nonlinear controller in a distribution system

NASA Astrophysics Data System (ADS)

Bagheri Tolabi, Hajar; Hosseini, Rahil; Shakarami, Mahmoud Reza

2016-06-01

This article presents a novel hybrid optimization approach for a nonlinear controller of a distribution static compensator (DSTATCOM). The DSTATCOM is connected to a distribution system with the distributed generation units. The nonlinear control is based on partial feedback linearization. Two proportional-integral-derivative (PID) controllers regulate the voltage and track the output in this control system. In the conventional scheme, the trial-and-error method is used to determine the PID controller coefficients. This article uses a combination of a fuzzy system, simulated annealing (SA) and intelligent water drops (IWD) algorithms to optimize the parameters of the controllers. The obtained results reveal that the response of the optimized controlled system is effectively improved by finding a high-quality solution. The results confirm that using the tuning method based on the fuzzy-SA-IWD can significantly decrease the settling and rising times, the maximum overshoot and the steady-state error of the voltage step response of the DSTATCOM. The proposed hybrid tuning method for the partial feedback linearizing (PFL) controller achieved better regulation of the direct current voltage for the capacitor within the DSTATCOM. Furthermore, in the event of a fault the proposed controller tuned by the fuzzy-SA-IWD method showed better performance than the conventional controller or the PFL controller without optimization by the fuzzy-SA-IWD method with regard to both fault duration and clearing times.

Volterra Series Approach for Nonlinear Aeroelastic Response of 2-D Lifting Surfaces

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Marzocca, Piergiovanni; Librescu, Liviu

2001-01-01

The problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via Volterra series approach is addressed. The related aeroelastic governing equations are based upon the inclusion of structural nonlinearities, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of geometric nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

The spatial structure of a nonlinear receptive field.

PubMed

Schwartz, Gregory W; Okawa, Haruhisa; Dunn, Felice A; Morgan, Josh L; Kerschensteiner, Daniel; Wong, Rachel O; Rieke, Fred

2012-11-01

Understanding a sensory system implies the ability to predict responses to a variety of inputs from a common model. In the retina, this includes predicting how the integration of signals across visual space shapes the outputs of retinal ganglion cells. Existing models of this process generalize poorly to predict responses to new stimuli. This failure arises in part from properties of the ganglion cell response that are not well captured by standard receptive-field mapping techniques: nonlinear spatial integration and fine-scale heterogeneities in spatial sampling. Here we characterize a ganglion cell's spatial receptive field using a mechanistic model based on measurements of the physiological properties and connectivity of only the primary excitatory circuitry of the retina. The resulting simplified circuit model successfully predicts ganglion-cell responses to a variety of spatial patterns and thus provides a direct correspondence between circuit connectivity and retinal output.

Partitioning strategy for efficient nonlinear finite element dynamic analysis on multiprocessor computers

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Peters, Jeanne M.

1989-01-01

A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.

Nonlinearity in the vertical transmissibility of seating: the role of the human body apparent mass and seat dynamic stiffness

NASA Astrophysics Data System (ADS)

Tufano, Saverio; Griffin, Michael J.

2013-01-01

The efficiency of a seat in reducing vibration depends on the characteristics of the vibration, the dynamic characteristics of the seat, and the dynamic characteristics of the person sitting on the seat. However, it is not known whether seat cushions influence the dynamic response of the human body, whether the human body influences the dynamic response of seat cushions, or the relative importance of human body nonlinearity and seat nonlinearity in causing nonlinearity in measures of seat transmissibility. This study was designed to investigate the nonlinearity of the coupled seat and human body systems and to compare the apparent mass of the human body supported on rigid and foam seats. A frequency domain model was used to identify the dynamic parameters of seat foams and investigate their dependence on the subject-sitting weight and hip breadth. With 15 subjects, the force and acceleration at the seat base and acceleration at the subject interface were measured during random vertical vibration excitation (0.25-25 Hz) at each of five vibration magnitudes, (0.25-1.6 ms-2 r.m.s.) with four seating conditions (rigid flat seat and three foam cushions). The measurements are presented in terms of the subject's apparent mass on the rigid and foam seat surfaces, and the transmissibility and dynamic stiffness of each of the foam cushions. Both the human body and the foams showed nonlinear softening behaviour, which resulted in nonlinear cushion transmissibility. The apparent masses of subjects sitting on the rigid seat and on foam cushions were similar, but with an apparent increase in damping when sitting on the foams. The foam dynamic stiffness showed complex correlations with characteristics of the human body, which differed between foams. The nonlinearities in cushion transmissibilities, expressed in terms of changes in resonance frequencies and moduli, were more dependent on human body nonlinearity than on cushion nonlinearity.

Growth and nonlinear response of driven water bells

NASA Astrophysics Data System (ADS)

Kolinski, John M.; Aharoni, Hillel; Fineberg, Jay; Sharon, Eran

2017-04-01

A water bell forms when a fluid jet impacts upon a target and separates into a two-dimensional sheet. Depending on the angle of separation from the target, the sheet can curve into a variety of different geometries. We show analytically that harmonic perturbations of water bells have linear wave solutions with geometry-dependent growth. We test the predictions of this model experimentally with a custom target system, and observe growth in agreement with the model below a critical forcing amplitude. Once the critical forcing amplitude is exceeded, a nonlinear transcritical bifurcation occurs; the response amplitude increases linearly with increasing forcing amplitude, albeit with a fundamentally different spatial form, and distinct nodes appear in the amplitude envelope.

A displacement-based approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

NASA Astrophysics Data System (ADS)

Giaccu, Gian Felice; Caracoglia, Luca

2017-04-01

Pre-tensioned-cable bracing systems are widely employed in structural engineering to limit lateral deflections and stabilize structures. A suitable configuration of the pre-tensioned-cable bracing systems in a structure is an important issue since the internal force distribution, emerging from the interaction with the existing structure, significantly affects the structural dynamic behavior. The design, however, is often based on the intuition and the previous experience of the engineer. In recent years, the authors have been investigating the non-linear dynamic response of cable systems, installed on cable-stayed bridges, and in particular the so-called "cable-cross-tie systems" forming a cable network. The bracing cables (cross-ties) can exhibit slackening or snapping. Therefore, a non-linear unilateral model, combined with the taut-cable theory, is required to simulate the incipient slackening conditions in the stays. Capitalizing from this work on non-linear cable dynamics, this paper proposes a new approach to analyze, in laterally- braced truss structures, the unilateral effects and dynamic response accounting for the loss in the pre-tensioning force imparted to the bracing cables. This effect leads to non-linear vibration of the structure. In this preliminary study, the free vibrations of the structure are investigated by using the "Equivalent Linearization Method". A performance coefficient, a real positive number between 0.5 and 1.0, is defined and employed to monitor the relative reduction in the apparent stiffness of the braces during structural vibration, "mode by mode". It is shown that the system can exhibit alternate unilateral behavior of the cross-braces. A reduction of the performance coefficient close to fifty percent is observed in the braces when the initial pre-tensioning force is small. On the other hand the performance coefficient tends to one in the case of a high level of pre-stress. It is concluded that the performance coefficient may possibly be used as an indicator for the design of the braces since a suitable selection of the initial pre-tensioning force can avoid slackening in the braces.

Coherent motion of chaotic attractors

NASA Astrophysics Data System (ADS)

Louodop, Patrick; Saha, Suman; Tchitnga, Robert; Muruganandam, Paulsamy; Dana, Syamal K.; Cerdeira, Hilda A.

2017-10-01

We report a simple model of two drive-response-type coupled chaotic oscillators, where the response system copies the nonlinearity of the driver system. It leads to a coherent motion of the trajectories of the coupled systems that establishes a constant separating distance in time between the driver and the response attractors, and their distance depends upon the initial state. The coupled system responds to external obstacles, modeled by short-duration pulses acting either on the driver or the response system, by a coherent shifting of the distance, and it is able to readjust their distance as and when necessary via mutual exchange of feedback information. We confirm these behaviors with examples of a jerk system, the paradigmatic Rössler system, a tunnel diode system and a Josephson junction-based jerk system, analytically, to an extent, and mostly numerically.

Linearity and nonlinearity of basin response as a function of scale: Discussion of alternative definitions

NASA Astrophysics Data System (ADS)

Sivapalan, M.; Jothityangkoon, C.; Menabde, M.

2002-02-01

Two uses of the terms ``linearity'' and ``nonlinearity'' appear in recent literature. The first definition of nonlinearity is with respect to the dynamical property such as the rainfall-runoff response of a catchment, and nonlinearity in this sense refers to a nonlinear dependence of the storm response on the magnitude of the rainfall inputs [Minshall, 1960; Wang et al., 1981]. The second definition of nonlinearity [Huang and Willgoose, 1993; Goodrich et al., 1997] is with respect to the dependence of a catchment statistical property, such as the mean annual flood, on the area of the catchment. They are both linked to important and interconnected hydrologic concepts, and furthermore, the change of nonlinearity with area (scale) has been an important motivation for hydrologic research. While both definitions are correct mathematically, they refer to hydrologically different concepts. In this paper we show that nonlinearity in the dynamical sense and that in the statistical sense can exist independently of each other (i.e., can be unrelated). If not carefully distinguished, the existence of these two definitions can lead to a catchment's response being described as being both linear and nonlinear at the same time. We therefore recommend separating these definitions by reserving the term ``nonlinearity'' for the classical, dynamical definition with respect to rainfall inputs, while adopting the term ``scaling relationship'' for the dependence of a catchment hydrological property on catchment area.

Design and verification of a hybrid nonlinear MRE vibration absorber for controllable broadband performance

NASA Astrophysics Data System (ADS)

Sun, S. S.; Yildirim, T.; Wu, Jichu; Yang, J.; Du, H.; Zhang, S. W.; Li, W. H.

2017-09-01

In this work, a hybrid nonlinear magnetorheological elastomer (MRE) vibration absorber has been designed, theoretically investigated and experimentally verified. The proposed nonlinear MRE absorber has the dual advantages of a nonlinear force-displacement relationship and variable stiffness technology; the purpose for coupling these two technologies is to achieve a large broadband vibration absorber with controllable capability. To achieve a nonlinear stiffness in the device, two pairs of magnets move at a rotary angle against each other, and the theoretical nonlinear force-displacement relationship has been theoretically calculated. For the experimental investigation, the effects of base excitation, variable currents applied to the device (i.e. variable stiffness of the MRE) and semi-active control have been conducted to determine the enhanced broadband performance of the designed device. It was observed the device was able to change resonance frequency with the applied current; moreover, the hybrid nonlinear MRE absorber displayed a softening-type nonlinear response with clear discontinuous bifurcations observed. Furthermore, the performance of the device under a semi-active control algorithm displayed the optimal performance in attenuating the vibration from a primary system to the absorber over a large frequency bandwidth from 4 to 12 Hz. By coupling nonlinear stiffness attributes with variable stiffness MRE technology, the performance of a vibration absorber is substantially improved.

Phase-resolved two-dimensional terahertz spectroscopy - a probe of highly nonlinear light-matter interactions

NASA Astrophysics Data System (ADS)

Elsaesser, Thomas

Terahertz (THz) spectroscopy gives insight into low-frequency excitations and charge dynamics in condensed matter. So far, most experiments in a frequency range from 0.5 to 30 THz have focused on the linear THz response to determine linear absorption and disperion spectra, and/or electric conductivities. The generation of ultrashort THz transients with peak electric fields up to megavolts/cm has allowed for addressing nonlinear light-matter interactions and inducing excitations far from equilibrium. The novel method of two-dimensional THz (2D-THz) spectroscopy allows for mapping ultrafast dynamics and couplings of elementary excitations up to arbitrary nonlinear order in the electric field, both under resonant and nonresonant excitation conditions. In particular, different contributions to the overall nonlinear response are separated by dissecting it as a function of excitation and detection frequencies and for different waiting times after excitation. This talk gives an introduction in 2D-THz spectroscopy, including its recent extension to 3-pulse sequences and interaction schemes. To illustrate the potential of the method, recent results on two-phonon coherences and high-order interband excitations in the semiconductor InSb will be presented. Nonlinear THz excitation of two-phonon coherences exploits a resonance enhancement by the large electronic interband dipole of InSb and is, thus, far more efficient than linear excitation via resonant two-phonon absorption. As a second application, the nonlinear softmode response in a crystal consisting of aspirin molecules will be discussed. At moderate THz driving fields, the pronounced correlation of rotational modes of CH3 groups with collective oscillations of π-electrons drives the system into the regime of nonperturbative light-matter interaction. Nonlinear absorption around 1.1 THz leads to a blue-shifted coherent emission at 1.5 THz, revealing a dynamic breakup of the strong electron-phonon correlations.

Practical guidelines to select and scale earthquake records for nonlinear response history analysis of structures

USGS Publications Warehouse

Kalkan, Erol; Chopra, Anil K.

2010-01-01

Earthquake engineering practice is increasingly using nonlinear response history analysis (RHA) to demonstrate performance of structures. This rigorous method of analysis requires selection and scaling of ground motions appropriate to design hazard levels. Presented herein is a modal-pushover-based scaling (MPS) method to scale ground motions for use in nonlinear RHA of buildings and bridges. In the MPS method, the ground motions are scaled to match (to a specified tolerance) a target value of the inelastic deformation of the first-'mode' inelastic single-degree-of-freedom (SDF) system whose properties are determined by first-'mode' pushover analysis. Appropriate for first-?mode? dominated structures, this approach is extended for structures with significant contributions of higher modes by considering elastic deformation of second-'mode' SDF system in selecting a subset of the scaled ground motions. Based on results presented for two bridges, covering single- and multi-span 'ordinary standard' bridge types, and six buildings, covering low-, mid-, and tall building types in California, the accuracy and efficiency of the MPS procedure are established and its superiority over the ASCE/SEI 7-05 scaling procedure is demonstrated.

Analysis for delamination initiation in postbuckled dropped-ply laminates

NASA Technical Reports Server (NTRS)

Davila, Carlos G.; Johnson, Eric R.

1992-01-01

The compression strength of dropped-ply, graphite-epoxy laminated plates for the delamination mode of failure is studied by analysis and corroborated with experiments. The nonlinear response of the test specimens is modeled by a geometrically nonlinear finite element analysis. The methodology for predicting delamination is based on a quadratic interlaminar stress criterion evaluated at a characteristic distance from the ply drop-off. The compression strength of specimens exhibiting a linear response is greater than the compression strength of specimens with the same layup exhibiting a geometrically nonlinear response. The analyses for both linear and nonlinear response show that severe interlaminar stress gradients occur in the interfaces at the drop-off because of the thickness/stiffness discontinuity. However, these interlaminar stress distributions are altered in the geometrically nonlinear response such that, with increasing load, their growth at the center of the laminate is retarded while their growth near the unloaded supported edge is increased.

Response of a 2-story test-bed structure for the seismic evaluation of nonstructural systems

NASA Astrophysics Data System (ADS)

Soroushian, Siavash; Maragakis, E. "Manos"; Zaghi, Arash E.; Rahmanishamsi, Esmaeel; Itani, Ahmad M.; Pekcan, Gokhan

2016-03-01

A full-scale, two-story, two-by-one bay, steel braced-frame was subjected to a number of unidirectional ground motions using three shake tables at the UNR-NEES site. The test-bed frame was designed to study the seismic performance of nonstructural systems including steel-framed gypsum partition walls, suspended ceilings and fire sprinkler systems. The frame can be configured to perform as an elastic or inelastic system to generate large floor accelerations or large inter story drift, respectively. In this study, the dynamic performance of the linear and nonlinear test-beds was comprehensively studied. The seismic performance of nonstructural systems installed in the linear and nonlinear test-beds were assessed during extreme excitations. In addition, the dynamic interactions of the test-bed and installed nonstructural systems are investigated.

Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes

NASA Astrophysics Data System (ADS)

Zhang, W.; Liu, T.; Xi, A.; Wang, Y. N.

2018-06-01

This paper is focused on the resonant responses and chaotic dynamics of a composite laminated circular cylindrical shell with radially pre-stretched membranes at both ends and clamped along a generatrix. Based on the two-degree-of-freedom non-autonomous nonlinear equations of this system, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equation. The resonant case considered here is the primary parametric resonance-1/2 subharmonic resonance and 1:1 internal resonance. Corresponding to several selected parameters, the frequency-response curves are obtained. From the numerical results, we find that the hardening-spring-type behaviors and jump phenomena are exhibited. The jump phenomena also occur in the amplitude curves of the temperature parameter excitation. Moreover, it is found that the temperature parameter excitation, the coupling degree of two order modes and the detuning parameters can effect the nonlinear oscillations of this system. The periodic and chaotic motions of the composite laminated circular cylindrical shell clamped along a generatrix are demonstrated by the bifurcation diagrams, the maximum Lyapunov exponents, the phase portraits, the waveforms, the power spectrums and the Poincaré map. The temperature parameter excitation shows that the Pomeau-Manneville type intermittent chaos occur under the certain initial conditions. It is also found that there exist the twin phenomena between the Pomeau-Manneville type intermittent chaos and the period-doubling bifurcation.

Nonlinear analysis of shock absorbers with amplitude-dependent damping

NASA Astrophysics Data System (ADS)

Łuczko, Jan; Ferdek, Urszula; Łatas, Waldemar

2018-01-01

This paper contains an analysis of a quarter-car model representing a vehicle equipped with a hydraulic damper whose characteristics are dependent on the piston stroke. The damper, compared to a classical mono-tube damper, has additional internal chambers. Oil flow in those chambers is controlled by relative piston displacement. The proposed nonlinear model of the system is aimed to test the effect of key design parameters of the damper on the quality indices representing ride comfort and driving safety. Numerical methods were used to determine the characteristic curves of the damper and responses of the system to harmonic excitations with their amplitude decreasing as the values of frequency increase.

Estimation of nonlinear pilot model parameters including time delay.

NASA Technical Reports Server (NTRS)

Schiess, J. R.; Roland, V. R.; Wells, W. R.

1972-01-01

Investigation of the feasibility of using a Kalman filter estimator for the identification of unknown parameters in nonlinear dynamic systems with a time delay. The problem considered is the application of estimation theory to determine the parameters of a family of pilot models containing delayed states. In particular, the pilot-plant dynamics are described by differential-difference equations of the retarded type. The pilot delay, included as one of the unknown parameters to be determined, is kept in pure form as opposed to the Pade approximations generally used for these systems. Problem areas associated with processing real pilot response data are included in the discussion.

Multivariable control of the Space Shuttle Remote Manipulator System using linearization by state feedback. M.S. Thesis

NASA Technical Reports Server (NTRS)

Gettman, Chang-Ching LO

1993-01-01

This thesis develops and demonstrates an approach to nonlinear control system design using linearization by state feedback. The design provides improved transient response behavior allowing faster maneuvering of payloads by the SRMS. Modeling uncertainty is accounted for by using a second feedback loop designed around the feedback linearized dynamics. A classical feedback loop is developed to provide the easy implementation required for the relatively small on board computers. Feedback linearization also allows the use of higher bandwidth model based compensation in the outer loop, since it helps maintain stability in the presence of the nonlinearities typically neglected in model based designs.

Charging power optimization for nonlinear vibration energy harvesting systems subjected to arbitrary, persistent base excitations

NASA Astrophysics Data System (ADS)

Dai, Quanqi; Harne, Ryan L.

2018-01-01

The vibrations of mechanical systems and structures are often a combination of periodic and random motions. Emerging interest to exploit nonlinearities in vibration energy harvesting systems for charging microelectronics may be challenged by such reality due to the potential to transition between favorable and unfavorable dynamic regimes for DC power delivery. Therefore, a need exists to devise an optimization method whereby charging power from nonlinear energy harvesters remains maximized when excitation conditions are neither purely harmonic nor purely random, which have been the attention of past research. This study meets the need by building from an analytical approach that characterizes the dynamic response of nonlinear energy harvesting platforms subjected to combined harmonic and stochastic base accelerations. Here, analytical expressions are formulated and validated to optimize charging power while the influences of the relative proportions of excitation types are concurrently assessed. It is found that about a 2 times deviation in optimal resistive loads can reduce the charging power by 20% when the system is more prominently driven by harmonic base accelerations, whereas a greater proportion of stochastic excitation results in a 11% reduction in power for the same resistance deviation. In addition, the results reveal that when the frequency of a predominantly harmonic excitation deviates by 50% from optimal conditions the charging power reduces by 70%, whereas the same frequency deviation for a more stochastically dominated excitation reduce total DC power by only 20%. These results underscore the need for maximizing direct current power delivery for nonlinear energy harvesting systems in practical operating environments.

Nonlinear identification of the total baroreflex arc: higher-order nonlinearity

PubMed Central

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru

2016-01-01

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). The nonlinear dynamics of this system were recently characterized. First, Gaussian white noise CSP stimulation was employed in open-loop conditions in normotensive and hypertensive rats with sectioned vagal and aortic depressor nerves. Nonparametric system identification was then applied to measured CSP and AP to establish a second-order nonlinear Uryson model. The aim in this study was to assess the importance of higher-order nonlinear dynamics via development and evaluation of a third-order nonlinear model of the total arc using the same experimental data. Third-order Volterra and Uryson models were developed by employing nonparametric and parametric identification methods. The R2 values between the AP predicted by the best third-order Volterra model and measured AP in response to Gaussian white noise CSP not utilized in developing the model were 0.69 ± 0.03 and 0.70 ± 0.03 for normotensive and hypertensive rats, respectively. The analogous R2 values for the best third-order Uryson model were 0.71 ± 0.03 and 0.73 ± 0.03. These R2 values were not statistically different from the corresponding values for the previously established second-order Uryson model, which were both 0.71 ± 0.03 (P > 0.1). Furthermore, none of the third-order models predicted well-known nonlinear behaviors including thresholding and saturation better than the second-order Uryson model. Additional experiments suggested that the unexplained AP variance was partly due to higher brain center activity. In conclusion, the second-order Uryson model sufficed to represent the sympathetically mediated total arc under the employed experimental conditions. PMID:27629885

Optical spatial solitons: historical overview and recent advances.

PubMed

Chen, Zhigang; Segev, Mordechai; Christodoulides, Demetrios N

2012-08-01

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

Nonlinear optical investigation of the Tris(2‧,2-bipyridyl)iron(II) tetrafluoroborate using z-scan technique

NASA Astrophysics Data System (ADS)

Zidan, M. D.; Al-Ktaifani, M. M.; Allahham, A.

2017-05-01

Z-scan measurements were performed with a CW diode laser at 635 nm to investigate the nonlinear optical properties of Tris(2‧,2-bipyridyl)iron(II) tetrafluoroborate in ethanol at two concentrations. Theoretical fit was carried out to evaluate the nonlinear absorption coefficient (β) and the negative nonlinear refractive index (n2) for the studied complex. Furthermore, the ground-state absorption cross sections (σg), the excited-state absorption cross sections (σex) and thermo-optic coefficient were also estimated. The investigations show large NLO response, which is predominantly associated with substantial conjugation between the aromatic ring π-electron system and d-electron set metal center. The obtained results give a strong indication that Tris(2‧,2-bipyridyl)iron(II) tetrafluoroborate have a potential application in optical domain.

Nonlinear Conductive Behaviour of Silver Nanowires/Silicone Rubber Composites

NASA Astrophysics Data System (ADS)

Lu, Pin; Qu, Zhaoming; Wang, Qingguo; Bai, Liyun; Zhao, Shiyang

2018-01-01

Silver nanowires with an average length of 10 μm and diameter of about 90 nm have been synthesized by polyol reduction of silver nitrate in the presence of polyvinylpyrrolidone(PVP). Silver nanowires (AgNWs)/silicone rubber (SR) composites have been made by mixing silver nanowires into silicone rubber. The nonlinear response of AgNWs/SR composites under high electric field is investigated. The nonlinear Conductive behavior of composites is considered as a competitive process of several effects. From the perspective of the microstructure of composites, the conductive path is established by the quantum tunnel effect between silver nanowires. The influence factors on the conductivity of composites are discussed and analyzed. The results show that the AgNWs/SR composites with nonlinear conductive properties are of great potential application in electromagnetic protection of electron device and system.

Constrained hierarchical least square nonlinear equation solvers. [for indefinite stiffness and large structural deformations

NASA Technical Reports Server (NTRS)

Padovan, J.; Lackney, J.

1986-01-01

The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

Complex Dynamics of Wetland Ecosystem with Nonlinear Harvesting: Application to Chilika Lake in Odisha, India

NASA Astrophysics Data System (ADS)

Upadhyay, Ranjit Kumar; Tiwari, S. K.; Roy, Parimita

2015-06-01

In this paper, an attempt has been made to study the spatial and temporal dynamical interactions among the species of wetland ecosystem through a mathematical model. The model represents the population dynamics of phytoplankton, zooplankton and fish species found in Chilika lake, Odisha, India. Nonlinear stability analysis of both the temporal and spatial models has been carried out. Maximum sustainable yield and optimal harvesting policy have been studied for a nonspatial model system. Numerical simulation has been performed to figure out the parameters responsible for the complex dynamics of the wetland system. Significant outcomes of our numerical findings and their interpretations from an ecological point of view are provided in this paper. Numerical simulation of spatial model exhibits some interesting and beautiful patterns. We have also pointed out the parameters that are responsible for the good health of wetland ecosystem.

Insight into the effect of screw dislocations and oxygen vacancy defects on the optical nonlinear refraction response in chemically grown ZnO/Al2O3 films

NASA Astrophysics Data System (ADS)

Agrawal, Arpana; Saroj, Rajendra K.; Dar, Tanveer A.; Baraskar, Priyanka; Sen, Pratima; Dhar, Subhabrata

2017-11-01

We report the effect of screw dislocations and oxygen vacancy defects on the optical nonlinear refraction response of ZnO films grown on a sapphire substrate at various oxygen flow rates using the chemical vapor deposition technique. The nonlinear refraction response was investigated in the off-resonant regime using a CW He-Ne laser source to examine the role of the intermediate bandgap states. It has been observed that the structural defects strongly influence the optical nonlinearity in the off-resonant regime. Nonlinearity has been found to improve as the oxygen flow rate is lowered from 2 sccm to 0.3 sccm. From photoluminescence studies, we observe that the enhanced defect density of the electronic defect levels due to the increased concentration of structural defects (with the decrease in the oxygen flow rate) is responsible for this improved optical nonlinearity along with the thermal effect. This suggests that defect engineering is an effective way to tailor the nonlinearity of ZnO films and their utility for optoelectronic device applications.

Nonlinear dynamics of planetary gears using analytical and finite element models

NASA Astrophysics Data System (ADS)

Ambarisha, Vijaya Kumar; Parker, Robert G.

2007-05-01

Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.

Research in nonlinear structural and solid mechanics

NASA Technical Reports Server (NTRS)

Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)

1980-01-01

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

The preparation of a new type of ferrocene-based compounds with large conjugated system containing symmetrical aromatic vinyl with Schiff base moieties and the study of their third-order nonlinear optical properties

NASA Astrophysics Data System (ADS)

Yu, Weiguo; Jia, Jianhong; Gao, Jianrong; Han, Liang; Li, Yujin

2016-09-01

Herein we reported the preparation of a new type of ferrocene-based compounds with large conjugated system containing symmetrical aromatic vinyl and Schiff base moieties and the study of their third-order nonlinear optical (NLO) properties. Their third-order NLO properties were measured using femtosecond laser and degenerate four-wave mixing (DFWM) technique. The obtained χ(3), n2 and γ values of these molecules were found in the range of 0.998-1.429 × 10-12 esu,1.847-2.646 × 10-11 esu and 1.026-1.449 × 10-30 esu, respectively. The response time ranged from 43.65 fs to 61.71 fs. The results indicate that these compounds have potential nonlinear optical applications.

Measurement of nonlinear normal modes using multi-harmonic stepped force appropriation and free decay

NASA Astrophysics Data System (ADS)

Ehrhardt, David A.; Allen, Matthew S.

2016-08-01

Nonlinear Normal Modes (NNMs) offer tremendous insight into the dynamic behavior of a nonlinear system, extending many concepts that are familiar in linear modal analysis. Hence there is interest in developing methods to experimentally and numerically determine a system's NNMs for model updating or simply to characterize its dynamic response. Previous experimental work has shown that a mono-harmonic excitation can be used to isolate a system's dynamic response in the neighborhood of a NNM along the main backbones of a system. This work shows that a multi-harmonic excitation is needed to isolate a NNM when well separated linear modes of a structure couple to produce an internal resonance. It is shown that one can tune the multiple harmonics of the input excitation using a plot of the input force versus the response velocity until the area enclosed by the force-velocity curve is minimized. Once an appropriated NNM is measured, one can increase the force level and retune the frequency to obtain a NNM at a higher amplitude or remove the excitation and measure the structure's decay down a NNM backbone. This work explores both methods using simulations and measurements of a nominally-flat clamped-clamped beam excited at a single point with a magnetic force. Numerical simulations are used to validate the method in a well defined environment and to provide comparison with the experimentally measured NNMs. The experimental results seem to produce a good estimate of two NNMs along their backbone and part of an internal resonance branch. Full-field measurements are then used to further explore the couplings between the underlying linear modes along the identified NNMs.

Retrieval of all effective susceptibilities in nonlinear metamaterials

NASA Astrophysics Data System (ADS)

Larouche, Stéphane; Radisic, Vesna

2018-04-01

Electromagnetic metamaterials offer a great avenue to engineer and amplify the nonlinear response of materials. Their electric, magnetic, and magnetoelectric linear and nonlinear response are related to their structure, providing unprecedented liberty to control those properties. Both the linear and the nonlinear properties of metamaterials are typically anisotropic. While the methods to retrieve the effective linear properties are well established, existing nonlinear retrieval methods have serious limitations. In this work, we generalize a nonlinear transfer matrix approach to account for all nonlinear susceptibility terms and show how to use this approach to retrieve all effective nonlinear susceptibilities of metamaterial elements. The approach is demonstrated using sum frequency generation, but can be applied to other second-order or higher-order processes.

Analysis of randomly time varying systems by gaussian closure technique

NASA Astrophysics Data System (ADS)

Dash, P. K.; Iyengar, R. N.

1982-07-01

The Gaussian probability closure technique is applied to study the random response of multidegree of freedom stochastically time varying systems under non-Gaussian excitations. Under the assumption that the response, the coefficient and the excitation processes are jointly Gaussian, deterministic equations are derived for the first two response moments. It is further shown that this technique leads to the best Gaussian estimate in a minimum mean square error sense. An example problem is solved which demonstrates the capability of this technique for handling non-linearity, stochastic system parameters and amplitude limited responses in a unified manner. Numerical results obtained through the Gaussian closure technique compare well with the exact solutions.

Short Time Impulse Response Function (STIRF) for automatic evaluation of the variation of the dynamic parameters of reinforced concrete framed structures during strong earthquakes.

NASA Astrophysics Data System (ADS)

Carlo Ponzo, Felice; Ditommaso, Rocco

2015-04-01

This study presents an innovative strategy for automatic evaluation of the variable fundamental frequency and related damping factor of nonlinear structures during strong motion phases. Most of methods for damage detection are based on the assessment of the variations of the dynamic parameters characterizing the monitored structure. A crucial aspect of these methods is the automatic and accurate estimation of both structural eigen-frequencies and related damping factors also during the nonlinear behaviour. A new method, named STIRF (Short-Time Impulse Response Function - STIRF), based on the nonlinear interferometric analysis combined with the Fourier Transform (FT) here is proposed in order to allow scientists and engineers to characterize frequencies and damping variations of a monitored structure. The STIRF approach helps to overcome some limitation derived from the use of techniques based on simple Fourier Transform. These latter techniques provide good results when the response of the monitored system is stationary, but fails when the system exhibits a non-stationary, time-varying behaviour: even non-stationary input, soil-foundation and/or adjacent structures interaction phenomena can show the inadequacy of classic techniques to analysing the nonlinear and/or non-stationary behaviour of structures. In fact, using this kind of approach it is possible to improve some of the existing methods for the automatic damage detection providing stable results also during the strong motion phase. Results are consistent with those expected if compared with other techniques. The main advantage derived from the use of the proposed approach (STIRF) for Structural Health Monitoring is based on the simplicity of the interpretation of the nonlinear variations of the fundamental frequency and the related equivalent viscous damping factor. The proposed methodology has been tested on both numerical and experimental models also using data retrieved from shaking table tests. Based on the results provided in this study, the methodology seems to be able to evaluate fast variations (over time) of dynamic parameters of a generic reinforced concrete framed structure. Further analyses are necessary to better calibrate the length of the moving time-window (in order to minimize the spurious frequency within each Interferometric Response Function evaluated on both weak and strong motion phases) and to verify the possibility to use the STIRF to analyse the nonlinear behaviour of general systems. Acknowledgements This study was partially funded by the Italian Civil Protection Department within the project DPC-RELUIS 2014 - RS4 ''Seismic observatory of structures and health monitoring''. References R. Ditommaso, F.C. Ponzo (2015). Automatic evaluation of the fundamental frequency variations and related damping factor of reinforced concrete framed structures using the Short Time Impulse Response Function (STIRF). Engineering Structures, 82 (2015), 104-112. http://dx.doi.org/10.1016/j.engstruct.2014.10.023.

Comparison of linear and nonlinear models for coherent hemodynamics spectroscopy (CHS)

NASA Astrophysics Data System (ADS)

Sassaroli, Angelo; Kainerstorfer, Jana; Fantini, Sergio

2015-03-01

A recently proposed linear time-invariant hemodynamic model for coherent hemodynamics spectroscopy1 (CHS) relates the tissue concentrations of oxy- and deoxy-hemoglobin (outputs of the system) to given dynamics of the tissue blood volume, blood flow and rate constant of oxygen diffusion (inputs of the system). This linear model was derived in the limit of "small" perturbations in blood flow velocity. We have extended this model to a more general model (which will be referred to as the nonlinear extension to the original model) that yields the time-dependent changes of oxy and deoxy-hemoglobin concentrations in response to arbitrary dynamic changes in capillary blood flow velocity. The nonlinear extension to the model relies on a general solution of the partial differential equation that governs the spatio-temporal behavior of oxygen saturation of hemoglobin in capillaries and venules on the basis of dynamic (or time resolved) blood transit time. We show preliminary results where the CHS spectra obtained from the linear and nonlinear models are compared to quantify the limits of applicability of the linear model.

Nonlinear dynamic modeling of rotor system supported by angular contact ball bearings

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Zhou, Daning

2017-02-01

In current bearing dynamic models, the displacement coordinate relations are usually utilized to approximately obtain the contact deformations between the rolling element and raceways, and then the nonlinear restoring forces of the rolling bearing could be calculated accordingly. Although the calculation efficiency is relatively higher, the accuracy is lower as the contact deformations should be solved through iterative analysis. Thus, an improved nonlinear dynamic model is presented in this paper. Considering the preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication, load distribution analysis is solved iteratively to more accurately obtain the contact deformations and angles between the rolling balls and raceways. The bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. Dynamic tests upon a typical rotor system supported by two angular contact ball bearings are conducted to verify the model. Through comparisons, the differences between the nonlinear dynamic model and current models are also pointed out. The effects of axial preload, rotor eccentricity and inner/outer waviness amplitudes on the dynamic response are discussed in detail.

Chemical reaction for Carreau-Yasuda nanofluid flow past a nonlinear stretching sheet considering Joule heating

NASA Astrophysics Data System (ADS)

Khan, Mair; Shahid, Amna; Malik, M. Y.; Salahuddin, T.

2018-03-01

Current analysis has been made to scrutinize the consequences of chemical response against magneto-hydrodynamic Carreau-Yasuda nanofluid flow induced by a non-linear stretching surface considering zero normal flux, slip and convective boundary conditions. Joule heating effect is also considered. Appropriate similarity approach is used to convert leading system of PDE's for Carreau-Yasuda nanofluid into nonlinear ODE's. Well known mathematical scheme namely shooting method is utilized to solve the system numerically. Physical parameters, namely Weissenberg number We , thermal slip parameter δ , thermophoresis number NT, non-linear stretching parameter n, magnetic field parameter M, velocity slip parameter k , Lewis number Le, Brownian motion parameter NB, Prandtl number Pr, Eckert number Ec and chemical reaction parameter γ upon temperature, velocity and concentration profiles are visualized through graphs and tables. Numerical influence of mass and heat transfer rates and friction factor are also represented in tabular as well as graphical form respectively. Skin friction coefficient reduces when Weissenberg number We is incremented. Rate of heat transfer enhances for large values of Brownian motion constraint NB. By increasing Lewis quantity Le rate of mass transfer declines.

Exploring 4D quantum Hall physics with a 2D topological charge pump

NASA Astrophysics Data System (ADS)

Lohse, Michael; Schweizer, Christian; Price, Hannah M.; Zilberberg, Oded; Bloch, Immanuel

2018-01-01

The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant—the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.

Exploring 4D quantum Hall physics with a 2D topological charge pump.

PubMed

Lohse, Michael; Schweizer, Christian; Price, Hannah M; Zilberberg, Oded; Bloch, Immanuel

2018-01-03

The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant-the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.

Route to thermalization in the α-Fermi–Pasta–Ulam system

PubMed Central

Onorato, Miguel; Vozella, Lara; Lvov, Yuri V.

2015-01-01

We study the original α-Fermi–Pasta–Ulam (FPU) system with N = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave–wave interaction theory; i.e., we assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the α-FPU equation of motion, we find that the first nontrivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that, for small-amplitude random waves, the timescale of such interactions is extremely large and it is of the order of 1/ϵ8, where ϵ is the small parameter in the system. The wave–wave interaction theory is not based on any threshold: Equipartition is predicted for arbitrary small nonlinearity. Our results are supported by extensive numerical simulations. A key role in our finding is played by the Umklapp (flip-over) resonant interactions, typical of discrete systems. The thermodynamic limit is also briefly discussed. PMID:25805822

Steady-state mechanical squeezing and ground-state cooling of a Duffing anharmonic oscillator in an optomechanical cavity assisted by a nonlinear medium

NASA Astrophysics Data System (ADS)

Momeni, F.; Naderi, M. H.

2018-05-01

In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric nonlinearity can be exploited to drive the system toward the multistability region. We also show that for appropriate values of the mechanical anharmonicity strength the steady-state mechanical squeezing and the ground-state cooling of the mechanical resonator can be achieved. Moreover, we find that the presence of the nonlinear gain medium can lead to the improvement of the mechanical anharmonicity-induced cooling of the mechanical motion, as well as to the mechanical squeezing beyond the standard quantum limit of 3 dB.

On the orthogonalised reverse path method for nonlinear system identification

NASA Astrophysics Data System (ADS)

Muhamad, P.; Sims, N. D.; Worden, K.

2012-09-01

The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach - the orthogonalised reverse path (ORP) method - is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.

RF Spectrum Sensing Based on an Overdamped Nonlinear Oscillator Ring for Cognitive Radios.

PubMed

Tang, Zhi-Ling; Li, Si-Min; Yu, Li-Juan

2016-06-09

Existing spectrum-sensing techniques for cognitive radios require an analog-to-digital converter (ADC) to work at high dynamic range and a high sampling rate, resulting in high cost. Therefore, in this paper, a spectrum-sensing method based on a unidirectionally coupled, overdamped nonlinear oscillator ring is proposed. First, the numerical model of such a system is established based on the circuit of the nonlinear oscillator. Through numerical analysis of the model, the critical condition of the system's starting oscillation is determined, and the simulation results of the system's response to Gaussian white noise and periodic signal are presented. The results show that once the radio signal is input into the system, it starts oscillating when in the critical region, and the oscillating frequency of each element is fo/N, where fo is the frequency of the radio signal and N is the number of elements in the ring. The oscillation indicates that the spectrum resources at fo are occupied. At the same time, the sampling rate required for an ADC is reduced to the original value, 1/N. A prototypical circuit to verify the functionality of the system is designed, and the sensing bandwidth of the system is measured.

Aeroelastic Response of Nonlinear Wing Section By Functional Series Technique

NASA Technical Reports Server (NTRS)

Marzocca, Piergiovanni; Librescu, Liviu; Silva, Walter A.

2000-01-01

This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indicial functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Aeroelastic Response of Nonlinear Wing Section by Functional Series Technique

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Marzocca, Piergiovanni

2001-01-01

This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indicial functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Linear and Non-Linear Visual Feature Learning in Rat and Humans

PubMed Central

Bossens, Christophe; Op de Beeck, Hans P.

2016-01-01

The visual system processes visual input in a hierarchical manner in order to extract relevant features that can be used in tasks such as invariant object recognition. Although typically investigated in primates, recent work has shown that rats can be trained in a variety of visual object and shape recognition tasks. These studies did not pinpoint the complexity of the features used by these animals. Many tasks might be solved by using a combination of relatively simple features which tend to be correlated. Alternatively, rats might extract complex features or feature combinations which are nonlinear with respect to those simple features. In the present study, we address this question by starting from a small stimulus set for which one stimulus-response mapping involves a simple linear feature to solve the task while another mapping needs a well-defined nonlinear combination of simpler features related to shape symmetry. We verified computationally that the nonlinear task cannot be trivially solved by a simple V1-model. We show how rats are able to solve the linear feature task but are unable to acquire the nonlinear feature. In contrast, humans are able to use the nonlinear feature and are even faster in uncovering this solution as compared to the linear feature. The implications for the computational capabilities of the rat visual system are discussed. PMID:28066201

Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems

NASA Astrophysics Data System (ADS)

Mahdi Alavi, S. M.; Saif, Mehrdad

2013-12-01

This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

NASA Astrophysics Data System (ADS)

Bache, Morten; Lavrinenko, Andrei V.

2017-09-01

Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.

Energy dynamics in a simulation of LAPD turbulence

NASA Astrophysics Data System (ADS)

Friedman, B.; Carter, T. A.; Umansky, M. V.; Schaffner, D.; Dudson, B.

2012-10-01

Energy dynamics calculations in a 3D fluid simulation of drift wave turbulence in the linear Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] illuminate processes that drive and dissipate the turbulence. These calculations reveal that a nonlinear instability dominates the injection of energy into the turbulence by overtaking the linear drift wave instability that dominates when fluctuations about the equilibrium are small. The nonlinear instability drives flute-like (k∥=0) density fluctuations using free energy from the background density gradient. Through nonlinear axial wavenumber transfer to k∥≠0 fluctuations, the nonlinear instability accesses the adiabatic response, which provides the requisite energy transfer channel from density to potential fluctuations as well as the phase shift that causes instability. The turbulence characteristics in the simulations agree remarkably well with experiment. When the nonlinear instability is artificially removed from the system through suppressing k∥=0 modes, the turbulence develops a coherent frequency spectrum which is inconsistent with experimental data. This indicates the importance of the nonlinear instability in producing experimentally consistent turbulence.

Micro-/nanoscale multi-field coupling in nonlinear photonic devices

NASA Astrophysics Data System (ADS)

Yang, Qing; Wang, Yubo; Tang, Mingwei; Xu, Pengfei; Xu, Yingke; Liu, Xu

2017-08-01

The coupling of mechanics/electronics/photonics may improve the performance of nanophotonic devices not only in the linear region but also in the nonlinear region. This review letter mainly presents the recent advances on multi-field coupling in nonlinear photonic devices. The nonlinear piezoelectric effect and piezo-phototronic effects in quantum wells and fibers show that large second-order nonlinear susceptibilities can be achieved, and second harmonic generation and electro-optic modulation can be enhanced and modulated. Strain engineering can tune the lattice structures and induce second order susceptibilities in central symmetry semiconductors. By combining the absorption-based photoacoustic effect and intensity-dependent photobleaching effect, subdiffraction imaging can be achieved. This review will also discuss possible future applications of these novel effects and the perspective of their research. The review can help us develop a deeper knowledge of the substance of photon-electron-phonon interaction in a micro-/nano- system. Moreover, it can benefit the design of nonlinear optical sensors and imaging devices with a faster response rate, higher efficiency, more sensitivity and higher spatial resolution which could be applied in environmental detection, bio-sensors, medical imaging and so on.

Simulation Study of the Localization of a Near-Surface Crack Using an Air-Coupled Ultrasonic Sensor Array

PubMed Central

Delrue, Steven; Aleshin, Vladislav; Sørensen, Mikael; De Lathauwer, Lieven

2017-01-01

The importance of Non-Destructive Testing (NDT) to check the integrity of materials in different fields of industry has increased significantly in recent years. Actually, industry demands NDT methods that allow fast (preferably non-contact) detection and localization of early-stage defects with easy-to-interpret results, so that even a non-expert field worker can carry out the testing. The main challenge is to combine as many of these requirements into one single technique. The concept of acoustic cameras, developed for low frequency NDT, meets most of the above-mentioned requirements. These cameras make use of an array of microphones to visualize noise sources by estimating the Direction Of Arrival (DOA) of the impinging sound waves. Until now, however, because of limitations in the frequency range and the lack of integrated nonlinear post-processing, acoustic camera systems have never been used for the localization of incipient damage. The goal of the current paper is to numerically investigate the capabilities of locating incipient damage by measuring the nonlinear airborne emission of the defect using a non-contact ultrasonic sensor array. We will consider a simple case of a sample with a single near-surface crack and prove that after efficient excitation of the defect sample, the nonlinear defect responses can be detected by a uniform linear sensor array. These responses are then used to determine the location of the defect by means of three different DOA algorithms. The results obtained in this study can be considered as a first step towards the development of a nonlinear ultrasonic camera system, comprising the ultrasonic sensor array as the hardware and nonlinear post-processing and source localization software. PMID:28441738

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

This research should lead to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle-of-attack aircraft such as the F18 (HARV). The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis and simulation is performed in some detail as well. Various models under investigation for different purposes are summarized in tabular form. Models and simulation for the longitudinal dynamics have been developed for all types except the nonlinear ordinary differential equation model. Briefly, studies completed indicate that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in alpha. The transient responses are compared where the desired alpha varies from 5 degrees to 60 degrees to 30 degrees and back to 5 degrees in all about 16 sec. Here, the horizontal stabilator is the only control used with an assumed first-order linear actuator with a 1/30 sec time constant.

Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits

PubMed Central

Ujfalussy, Balázs B; Makara, Judit K; Branco, Tiago; Lengyel, Máté

2015-01-01

Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits. DOI: http://dx.doi.org/10.7554/eLife.10056.001 PMID:26705334

Nonlinear and Synchronous Dissolved Organic Matter Dynamics in Streams Across an Agriculture Land Use and Climate Setting

NASA Astrophysics Data System (ADS)

Xenopoulos, M. A.; Vogt, R. J.

2014-12-01

There is now increasing evidence that non-linearity is a common response in ecological systems to pressures caused by human activities. There is also increasing evidence that exogenous environmental drivers, such as climate, induce spatial and temporal synchrony in a wide range of ecological variables. Using Moran's I and Pearson's correlation, we quantified the synchrony of dissolved organic carbon concentration (DOC) and quality (DOM; e.g., specific UV absorbance, Fluorescence Index, PARAFAC), nutrients, discharge and temperature in 40 streams that span an agriculture gradient (0 to >70% cropland), over 10 years. We then used breakpoint regression, 2D-Kolmogorov-Smirnov test and significant zero crossings (SiZer) analyses to quantify the prevalence of nonlinearity and ecological thresholds (breakpoints) where applicable. There was a high degree of synchrony in DOM quality (r > 0.7) but not DOC (r < 0.4). The degree of synchrony was driven in part by the catchment's land use. With respect to the nonlinear analyses we found non-linearity in ~50% of bivariate datasets analyzed. Non-linearity was also driven in part by the catchment's land use. Breakpoints defined different DOM properties. Nonlinearity and synchronous behaviour in DOM are intimately linked to land use.

Nonlinear dynamic modeling of a simple flexible rotor system subjected to time-variable base motions

NASA Astrophysics Data System (ADS)

Chen, Liqiang; Wang, Jianjun; Han, Qinkai; Chu, Fulei

2017-09-01

Rotor systems carried in transportation system or under seismic excitations are considered to have a moving base. To study the dynamic behavior of flexible rotor systems subjected to time-variable base motions, a general model is developed based on finite element method and Lagrange's equation. Two groups of Euler angles are defined to describe the rotation of the rotor with respect to the base and that of the base with respect to the ground. It is found that the base rotations would cause nonlinearities in the model. To verify the proposed model, a novel test rig which could simulate the base angular-movement is designed. Dynamic experiments on a flexible rotor-bearing system with base angular motions are carried out. Based upon these, numerical simulations are conducted to further study the dynamic response of the flexible rotor under harmonic angular base motions. The effects of base angular amplitude, rotating speed and base frequency on response behaviors are discussed by means of FFT, waterfall, frequency response curve and orbits of the rotor. The FFT and waterfall plots of the disk horizontal and vertical vibrations are marked with multiplications of the base frequency and sum and difference tones of the rotating frequency and the base frequency. Their amplitudes will increase remarkably when they meet the whirling frequencies of the rotor system.

Towards a unifying theory for the first-, second-, and third-order molecular (non)linear optical response

NASA Astrophysics Data System (ADS)

Pérez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.

2010-05-01

We present a procedure for the modeling of the dispersion of the nonlinear optical response of complex molecular structures that is based strictly on the results from experimental characterization. We show how under some general conditions, the use of the Thomas-Kuhn sum-rules leads to a successful modeling of the nonlinear response of complex molecular structures.

The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.

Nonlinear ionic transport through microstructured solid electrolytes: homogenization estimates

NASA Astrophysics Data System (ADS)

Curto Sillamoni, Ignacio J.; Idiart, Martín I.

2016-10-01

We consider the transport of multiple ionic species by diffusion and migration through microstructured solid electrolytes in the presence of strong electric fields. The assumed constitutive relations for the constituent phases follow from convex energy and dissipation potentials which guarantee thermodynamic consistency. The effective response is heuristically deduced from a multi-scale convergence analysis of the relevant field equations. The resulting homogenized response involves an effective dissipation potential per species. Each potential is mathematically akin to that of a standard nonlinear heterogeneous conductor. A ‘linear-comparison’ homogenization technique is then used to generate estimates for these nonlinear potentials in terms of available estimates for corresponding linear conductors. By way of example, use is made of the Maxwell-Garnett and effective-medium linear approximations to generate estimates for two-phase systems with power-law dissipation. Explicit formulas are given for some limiting cases. In the case of threshold-type behavior, the estimates exhibit non-analytical dilute limits and seem to be consistent with fields localized in low energy paths.

Seismic performance of arch dams on non-homogeneous and discontinuous foundations (a case study: Karun 4 Dam)

NASA Astrophysics Data System (ADS)

Ferdousi, A.

2017-06-01

The present study set out to investigate the nonlinear seismic response of the dam-reservoir-rock foundation system, taking into consideration the effects of change in the material properties of discontinuous foundation. To this end, it is important to provide the proper modeling of truncated boundary conditions at the far-end of rock foundation and reservoir fluid domain and to correctly apply the in situ stresses for rock foundation. The nonlinear seismic response of an arch dam mainly depends on the opening and sliding of the dam body's contraction joints and foundation discontinuities, failure of the jointed rock and concrete materials, etc. In this paper, a time domain dynamic analysis of the 3D dam-reservoir-foundation interaction problem was performed by developing a nonlinear Finite Element program. The results of the analysis of Karun-4 Dam revealed the essential role of modeling discontinuities and boundary conditions of rock foundation under seismic excitation.

Inducing in situ, nonlinear soil response applying an active source

USGS Publications Warehouse

Johnson, P.A.; Bodin, P.; Gomberg, J.; Pearce, F.; Lawrence, Z.; Menq, F.-Y.

2009-01-01

[1] It is well known that soil sites have a profound effect on ground motion during large earthquakes. The complex structure of soil deposits and the highly nonlinear constitutive behavior of soils largely control nonlinear site response at soil sites. Measurements of nonlinear soil response under natural conditions are critical to advancing our understanding of soil behavior during earthquakes. Many factors limit the use of earthquake observations to estimate nonlinear site response such that quantitative characterization of nonlinear behavior relies almost exclusively on laboratory experiments and modeling of wave propagation. Here we introduce a new method for in situ characterization of the nonlinear behavior of a natural soil formation using measurements obtained immediately adjacent to a large vibrator source. To our knowledge, we are the first group to propose and test such an approach. Employing a large, surface vibrator as a source, we measure the nonlinear behavior of the soil by incrementally increasing the source amplitude over a range of frequencies and monitoring changes in the output spectra. We apply a homodyne algorithm for measuring spectral amplitudes, which provides robust signal-to-noise ratios at the frequencies of interest. Spectral ratios are computed between the receivers and the source as well as receiver pairs located in an array adjacent to the source, providing the means to separate source and near-source nonlinearity from pervasive nonlinearity in the soil column. We find clear evidence of nonlinearity in significant decreases in the frequency of peak spectral ratios, corresponding to material softening with amplitude, observed across the array as the source amplitude is increased. The observed peak shifts are consistent with laboratory measurements of soil nonlinearity. Our results provide constraints for future numerical modeling studies of strong ground motion during earthquakes.

Modelling, validation and analysis of a three-dimensional railway vehicle-track system model with linear and nonlinear track properties in the presence of wheel flats

NASA Astrophysics Data System (ADS)

Uzzal, R. U. A.; Ahmed, A. K. W.; Bhat, R. B.

2013-11-01

This paper presents dynamic contact loads at wheel-rail contact point in a three-dimensional railway vehicle-track model as well as dynamic response at vehicle-track component levels in the presence of wheel flats. The 17-degrees of freedom lumped mass vehicle is modelled as a full car body, two bogies and four wheelsets, whereas the railway track is modelled as two parallel Timoshenko beams periodically supported by lumped masses representing the sleepers. The rail beam is also supported by nonlinear spring and damper elements representing the railpad and ballast. In order to ensure the interactions between the railpads, a shear parameter beneath the rail beams has also been considered into the model. The wheel-rail contact is modelled using nonlinear Hertzian contact theory. In order to solve the coupled partial and ordinary differential equations of the vehicle-track system, modal analysis method is employed. Idealised Haversine wheel flats with the rounded corner are included in the wheel-rail contact model. The developed model is validated with the existing measured and analytical data available in the literature. The nonlinear model is then employed to investigate the wheel-rail impact forces that arise in the wheel-rail interface due to the presence of wheel flats. The validated model is further employed to investigate the dynamic responses of vehicle and track components in terms of displacement, velocity, and acceleration in the presence of single wheel flat.

Thrust generation by a heaving flexible foil: Resonance, nonlinearities, and optimality

NASA Astrophysics Data System (ADS)

Paraz, Florine; Schouveiler, Lionel; Eloy, Christophe

2016-01-01

Flexibility of marine animal fins has been thought to enhance swimming performance. However, despite numerous experimental and numerical studies on flapping flexible foils, there is still no clear understanding of the effect of flexibility and flapping amplitude on thrust generation and swimming efficiency. Here, to address this question, we combine experiments on a model system and a weakly nonlinear analysis. Experiments consist in immersing a flexible rectangular plate in a uniform flow and forcing this plate into a heaving motion at its leading edge. A complementary theoretical model is developed assuming a two-dimensional inviscid problem. In this model, nonlinear effects are taken into account by considering a transverse resistive drag. Under these hypotheses, a modal decomposition of the system motion allows us to predict the plate response amplitude and the generated thrust, as a function of the forcing amplitude and frequency. We show that this model can correctly predict the experimental data on plate kinematic response and thrust generation, as well as other data found in the literature. We also discuss the question of efficiency in the context of bio-inspired propulsion. Using the proposed model, we show that the optimal propeller for a given thrust and a given swimming speed is achieved when the actuating frequency is tuned to a resonance of the system, and when the optimal forcing amplitude scales as the square root of the required thrust.

Optimal Self-Tuning PID Controller Based on Low Power Consumption for a Server Fan Cooling System.

PubMed

Lee, Chengming; Chen, Rongshun

2015-05-20

Recently, saving the cooling power in servers by controlling the fan speed has attracted considerable attention because of the increasing demand for high-density servers. This paper presents an optimal self-tuning proportional-integral-derivative (PID) controller, combining a PID neural network (PIDNN) with fan-power-based optimization in the transient-state temperature response in the time domain, for a server fan cooling system. Because the thermal model of the cooling system is nonlinear and complex, a server mockup system simulating a 1U rack server was constructed and a fan power model was created using a third-order nonlinear curve fit to determine the cooling power consumption by the fan speed control. PIDNN with a time domain criterion is used to tune all online and optimized PID gains. The proposed controller was validated through experiments of step response when the server operated from the low to high power state. The results show that up to 14% of a server's fan cooling power can be saved if the fan control permits a slight temperature response overshoot in the electronic components, which may provide a time-saving strategy for tuning the PID controller to control the server fan speed during low fan power consumption.

A nonlinear propagation model-based phase calibration technique for membrane hydrophones.

PubMed

Cooling, Martin P; Humphrey, Victor F

2008-01-01

A technique for the phase calibration of membrane hydrophones in the frequency range up to 80 MHz is described. This is achieved by comparing measurements and numerical simulation of a nonlinearly distorted test field. The field prediction is obtained using a finite-difference model that solves the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation in the frequency domain. The measurements are made in the far field of a 3.5 MHz focusing circular transducer in which it is demonstrated that, for the high drive level used, spatial averaging effects due to the hydrophone's finite-receive area are negligible. The method provides a phase calibration of the hydrophone under test without the need for a device serving as a phase response reference, but it requires prior knowledge of the amplitude sensitivity at the fundamental frequency. The technique is demonstrated using a 50-microm thick bilaminar membrane hydrophone, for which the results obtained show functional agreement with predictions of a hydrophone response model. Further validation of the results is obtained by application of the response to the measurement of the high amplitude waveforms generated by a modern biomedical ultrasonic imaging system. It is demonstrated that full deconvolution of the calculated complex frequency response of a nonideal hydrophone results in physically realistic measurements of the transmitted waveforms.

Dose-response-a challenge for allelopathy?

PubMed

Belz, Regina G; Hurle, Karl; Duke, Stephen O

2005-04-01

The response of an organism to a chemical depends, among other things, on the dose. Nonlinear dose-response relationships occur across a broad range of research fields, and are a well established tool to describe the basic mechanisms of phytotoxicity. The responses of plants to allelochemicals as biosynthesized phytotoxins, relate as well to nonlinearity and, thus, allelopathic effects can be adequately quantified by nonlinear mathematical modeling. The current paper applies the concept of nonlinearity to assorted aspects of allelopathy within several bioassays and reveals their analysis by nonlinear regression models. Procedures for a valid comparison of effective doses between different allelopathic interactions are presented for both, inhibitory and stimulatory effects. The dose-response applications measure and compare the responses produced by pure allelochemicals [scopoletin (7-hydroxy-6-methoxy-2H-1-benzopyran-2-one); DIBOA (2,4-dihydroxy-2H-1,4-benzoxaxin-3(4H)-one); BOA (benzoxazolin-2(3H)-one); MBOA (6-methoxy-benzoxazolin-2(3H)-one)], involved in allelopathy of grain crops, to demonstrate how some general principles of dose responses also relate to allelopathy. Hereupon, dose-response applications with living donor plants demonstrate the validity of these principles for density-dependent phytotoxicity of allelochemicals produced and released by living plants (Avena sativa L., Secale cereale L., Triticum L. spp.), and reveal the use of such experiments for initial considerations about basic principles of allelopathy. Results confirm that nonlinearity applies to allelopathy, and the study of allelopathic effects in dose-response experiments allows for new and challenging insights into allelopathic interactions.

Effects of Combined Loads on the Nonlinear Response and Residual Strength of Damaged Stiffened Shells

NASA Technical Reports Server (NTRS)

Starnes, James H., Jr.; Rose, Cheryl A.; Rankin, Charles C.

1996-01-01

The results of an analytical study of the nonlinear response of stiffened fuselage shells with long cracks are presented. The shells are modeled with a hierarchical modeling strategy and analyzed with a nonlinear shell analysis code that maintains the shell in a nonlinear equilibrium state while the crack is grown. The analysis accurately accounts for global and local structural response phenomena. Results are presented for various combinations of internal pressure and mechanical loads, and the effects of crack orientation on the shell response are described. The effects of combined loading conditions and the effects of varying structural parameters on the stress-intensity factors associated with a crack are presented.

Trajectory following and stabilization control of fully actuated AUV using inverse kinematics and self-tuning fuzzy PID.

PubMed

Hammad, Mohanad M; Elshenawy, Ahmed K; El Singaby, M I

2017-01-01

In this work a design for self-tuning non-linear Fuzzy Proportional Integral Derivative (FPID) controller is presented to control position and speed of Multiple Input Multiple Output (MIMO) fully-actuated Autonomous Underwater Vehicles (AUV) to follow desired trajectories. Non-linearity that results from the hydrodynamics and the coupled AUV dynamics makes the design of a stable controller a very difficult task. In this study, the control scheme in a simulation environment is validated using dynamic and kinematic equations for the AUV model and hydrodynamic damping equations. An AUV configuration with eight thrusters and an inverse kinematic model from a previous work is utilized in the simulation. In the proposed controller, Mamdani fuzzy rules are used to tune the parameters of the PID. Nonlinear fuzzy Gaussian membership functions are selected to give better performance and response in the non-linear system. A control architecture with two feedback loops is designed such that the inner loop is for velocity control and outer loop is for position control. Several test scenarios are executed to validate the controller performance including different complex trajectories with and without injection of ocean current disturbances. A comparison between the proposed FPID controller and the conventional PID controller is studied and shows that the FPID controller has a faster response to the reference signal and more stable behavior in a disturbed non-linear environment.

Trajectory following and stabilization control of fully actuated AUV using inverse kinematics and self-tuning fuzzy PID

PubMed Central

Elshenawy, Ahmed K.; El Singaby, M.I.

2017-01-01

In this work a design for self-tuning non-linear Fuzzy Proportional Integral Derivative (FPID) controller is presented to control position and speed of Multiple Input Multiple Output (MIMO) fully-actuated Autonomous Underwater Vehicles (AUV) to follow desired trajectories. Non-linearity that results from the hydrodynamics and the coupled AUV dynamics makes the design of a stable controller a very difficult task. In this study, the control scheme in a simulation environment is validated using dynamic and kinematic equations for the AUV model and hydrodynamic damping equations. An AUV configuration with eight thrusters and an inverse kinematic model from a previous work is utilized in the simulation. In the proposed controller, Mamdani fuzzy rules are used to tune the parameters of the PID. Nonlinear fuzzy Gaussian membership functions are selected to give better performance and response in the non-linear system. A control architecture with two feedback loops is designed such that the inner loop is for velocity control and outer loop is for position control. Several test scenarios are executed to validate the controller performance including different complex trajectories with and without injection of ocean current disturbances. A comparison between the proposed FPID controller and the conventional PID controller is studied and shows that the FPID controller has a faster response to the reference signal and more stable behavior in a disturbed non-linear environment. PMID:28683071

Current transformer model with hysteresis for improving the protection response in electrical transmission systems

NASA Astrophysics Data System (ADS)

Matussek, Robert; Dzienis, Cezary; Blumschein, Jörg; Schulte, Horst

2014-12-01

In this paper, a generic enhanced protection current transformer (CT) model with saturation effects and transient behavior is presented. The model is used for the purpose of analysis and design of power system protection algorithms. Three major classes of protection CT have been modeled which all take into account the nonlinear inductance with remanence effects. The transient short-circuit currents in power systems are simulated under CT saturation condition. The response of a common power system protection algorithm with respect to robustness to nominal parameter variations and sensitivity against maloperation is demonstrated by simulation studies.

Nonlinear theory of diffusive acceleration of particles by shock waves

NASA Astrophysics Data System (ADS)

Malkov, M. A.; Drury, L. O'C.

2001-04-01

Among the various acceleration mechanisms which have been suggested as responsible for the nonthermal particle spectra and associated radiation observed in many astrophysical and space physics environments, diffusive shock acceleration appears to be the most successful. We review the current theoretical understanding of this process, from the basic ideas of how a shock energizes a few reactionless particles to the advanced nonlinear approaches treating the shock and accelerated particles as a symbiotic self-organizing system. By means of direct solution of the nonlinear problem we set the limit to the test-particle approximation and demonstrate the fundamental role of nonlinearity in shocks of astrophysical size and lifetime. We study the bifurcation of this system, proceeding from the hydrodynamic to kinetic description under a realistic condition of Bohm diffusivity. We emphasize the importance of collective plasma phenomena for the global flow structure and acceleration efficiency by considering the injection process, an initial stage of acceleration and, the related aspects of the physics of collisionless shocks. We calculate the injection rate for different shock parameters and different species. This, together with differential acceleration resulting from nonlinear large-scale modification, determines the chemical composition of accelerated particles. The review concentrates on theoretical and analytical aspects but our strategic goal is to link the fundamental theoretical ideas with the rapidly growing wealth of observational data.

Traveling waves in an optimal velocity model of freeway traffic.

PubMed

Berg, P; Woods, A

2001-03-01

Car-following models provide both a tool to describe traffic flow and algorithms for autonomous cruise control systems. Recently developed optimal velocity models contain a relaxation term that assigns a desirable speed to each headway and a response time over which drivers adjust to optimal velocity conditions. These models predict traffic breakdown phenomena analogous to real traffic instabilities. In order to deepen our understanding of these models, in this paper, we examine the transition from a linear stable stream of cars of one headway into a linear stable stream of a second headway. Numerical results of the governing equations identify a range of transition phenomena, including monotonic and oscillating travelling waves and a time- dependent dispersive adjustment wave. However, for certain conditions, we find that the adjustment takes the form of a nonlinear traveling wave from the upstream headway to a third, intermediate headway, followed by either another traveling wave or a dispersive wave further downstream matching the downstream headway. This intermediate value of the headway is selected such that the nonlinear traveling wave is the fastest stable traveling wave which is observed to develop in the numerical calculations. The development of these nonlinear waves, connecting linear stable flows of two different headways, is somewhat reminiscent of stop-start waves in congested flow on freeways. The different types of adjustments are classified in a phase diagram depending on the upstream and downstream headway and the response time of the model. The results have profound consequences for autonomous cruise control systems. For an autocade of both identical and different vehicles, the control system itself may trigger formations of nonlinear, steep wave transitions. Further information is available [Y. Sugiyama, Traffic and Granular Flow (World Scientific, Singapore, 1995), p. 137].

Traveling waves in an optimal velocity model of freeway traffic

NASA Astrophysics Data System (ADS)

Berg, Peter; Woods, Andrew

2001-03-01

Car-following models provide both a tool to describe traffic flow and algorithms for autonomous cruise control systems. Recently developed optimal velocity models contain a relaxation term that assigns a desirable speed to each headway and a response time over which drivers adjust to optimal velocity conditions. These models predict traffic breakdown phenomena analogous to real traffic instabilities. In order to deepen our understanding of these models, in this paper, we examine the transition from a linear stable stream of cars of one headway into a linear stable stream of a second headway. Numerical results of the governing equations identify a range of transition phenomena, including monotonic and oscillating travelling waves and a time- dependent dispersive adjustment wave. However, for certain conditions, we find that the adjustment takes the form of a nonlinear traveling wave from the upstream headway to a third, intermediate headway, followed by either another traveling wave or a dispersive wave further downstream matching the downstream headway. This intermediate value of the headway is selected such that the nonlinear traveling wave is the fastest stable traveling wave which is observed to develop in the numerical calculations. The development of these nonlinear waves, connecting linear stable flows of two different headways, is somewhat reminiscent of stop-start waves in congested flow on freeways. The different types of adjustments are classified in a phase diagram depending on the upstream and downstream headway and the response time of the model. The results have profound consequences for autonomous cruise control systems. For an autocade of both identical and different vehicles, the control system itself may trigger formations of nonlinear, steep wave transitions. Further information is available [Y. Sugiyama, Traffic and Granular Flow (World Scientific, Singapore, 1995), p. 137].

Non-linear vibrating systems excited by a nonideal energy source with a large slope characteristic

NASA Astrophysics Data System (ADS)

González-Carbajal, Javier; Domínguez, Jaime

2017-11-01

This paper revisits the problem of an unbalanced motor attached to a fixed frame by means of a nonlinear spring and a linear damper. The excitation provided by the motor is, in general, nonideal, which means it is affected by the vibratory response. Since the system behaviour is highly dependent on the order of magnitude of the motor characteristic slope, the case of large slope is considered herein. Some Perturbation Methods are applied to the system of equations, which allows transforming the original 4D system into a much simpler 2D system. The fixed points of this reduced system and their stability are carefully studied. We find the existence of a Hopf bifurcation which, to the authors' knowledge, has not been addressed before in the literature. These analytical results are supported by numerical simulations. We also compare our approach and results with those published by other authors.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Lei; Kruk, Sergey; Koshelev, Kirill

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Nonlinear Wavefront Control with All-Dielectric Metasurfaces.

PubMed

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; Kravchenko, Ivan; Luther-Davies, Barry; Kivshar, Yuri

2018-06-13

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront of parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Our nonlinear metasurfaces produce phase gradients over a full 0-2π phase range with a 92% diffraction efficiency.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE PAGES

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; ...

2018-05-11

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less