A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

NASA Technical Reports Server (NTRS)

Ball, R. E.

1972-01-01

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

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.

User document for computer programs for ring-stiffened shells of revolution

NASA Technical Reports Server (NTRS)

Cohen, G. A.

1973-01-01

A user manual and related program documentation is presented for six compatible computer programs for structural analysis of axisymmetric shell structures. The programs apply to a common structural model but analyze different modes of structural response. In particular, they are: (1) Linear static response under asymmetric loads; (2) Buckling of linear states under asymmetric loads; (3) Nonlinear static response under axisymmetric loads; (4) Buckling nonlinear states under axisymmetric (5) Imperfection sensitivity of buckling modes under axisymmetric loads; and (6) Vibrations about nonlinear states under axisymmetric loads. These programs treat branched shells of revolution with an arbitrary arrangement of a large number of open branches but with at most one closed branch.

Analysis of Pull-In Instability of Geometrically Nonlinear Microbeam Using Radial Basis Artificial Neural Network Based on Couple Stress Theory

PubMed Central

Heidari, Mohammad; Heidari, Ali; Homaei, Hadi

2014-01-01

The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS. PMID:24860602

Uncertainty Analysis of the Grazing Flow Impedance Tube

NASA Technical Reports Server (NTRS)

Brown, Martha C.; Jones, Michael G.; Watson, Willie R.

2012-01-01

This paper outlines a methodology to identify the measurement uncertainty of NASA Langley s Grazing Flow Impedance Tube (GFIT) over its operating range, and to identify the parameters that most significantly contribute to the acoustic impedance prediction. Two acoustic liners are used for this study. The first is a single-layer, perforate-over-honeycomb liner that is nonlinear with respect to sound pressure level. The second consists of a wire-mesh facesheet and a honeycomb core, and is linear with respect to sound pressure level. These liners allow for evaluation of the effects of measurement uncertainty on impedances educed with linear and nonlinear liners. In general, the measurement uncertainty is observed to be larger for the nonlinear liners, with the largest uncertainty occurring near anti-resonance. A sensitivity analysis of the aerodynamic parameters (Mach number, static temperature, and static pressure) used in the impedance eduction process is also conducted using a Monte-Carlo approach. This sensitivity analysis demonstrates that the impedance eduction process is virtually insensitive to each of these parameters.

An Aeroelastic Analysis of a Thin Flexible Membrane

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Bartels, Robert E.; Kandil, Osama A.

2007-01-01

Studies have shown that significant vehicle mass and cost savings are possible with the use of ballutes for aero-capture. Through NASA's In-Space Propulsion program, a preliminary examination of ballute sensitivity to geometry and Reynolds number was conducted, and a single-pass coupling between an aero code and a finite element solver was used to assess the static aeroelastic effects. There remain, however, a variety of open questions regarding the dynamic aeroelastic stability of membrane structures for aero-capture, with the primary challenge being the prediction of the membrane flutter onset. The purpose of this paper is to describe and begin addressing these issues. The paper includes a review of the literature associated with the structural analysis of membranes and membrane utter. Flow/structure analysis coupling and hypersonic flow solver options are also discussed. An approach is proposed for tackling this problem that starts with a relatively simple geometry and develops and evaluates analysis methods and procedures. This preliminary study considers a computationally manageable 2-dimensional problem. The membrane structural models used in the paper include a nonlinear finite-difference model for static and dynamic analysis and a NASTRAN finite element membrane model for nonlinear static and linear normal modes analysis. Both structural models are coupled with a structured compressible flow solver for static aeroelastic analysis. For dynamic aeroelastic analyses, the NASTRAN normal modes are used in the structured compressible flow solver and 3rd order piston theories were used with the finite difference membrane model to simulate utter onset. Results from the various static and dynamic aeroelastic analyses are compared.

Nonlinear Slewing Spacecraft Control Based on Exergy, Power Flow, and Static and Dynamic Stability

NASA Astrophysics Data System (ADS)

Robinett, Rush D.; Wilson, David G.

2009-10-01

This paper presents a new nonlinear control methodology for slewing spacecraft, which provides both necessary and sufficient conditions for stability by identifying the stability boundaries, rigid body modes, and limit cycles. Conservative Hamiltonian system concepts, which are equivalent to static stability of airplanes, are used to find and deal with the static stability boundaries: rigid body modes. The application of exergy and entropy thermodynamic concepts to the work-rate principle provides a natural partitioning through the second law of thermodynamics of power flows into exergy generator, dissipator, and storage for Hamiltonian systems that is employed to find the dynamic stability boundaries: limit cycles. This partitioning process enables the control system designer to directly evaluate and enhance the stability and performance of the system by balancing the power flowing into versus the power dissipated within the system subject to the Hamiltonian surface (power storage). Relationships are developed between exergy, power flow, static and dynamic stability, and Lyapunov analysis. The methodology is demonstrated with two illustrative examples: (1) a nonlinear oscillator with sinusoidal damping and (2) a multi-input-multi-output three-axis slewing spacecraft that employs proportional-integral-derivative tracking control with numerical simulation results.

Equivalent Linearization Analysis of Geometrically Nonlinear Random Vibrations Using Commercial Finite Element Codes

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2002-01-01

Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.

Static and dynamic stability analysis of the space shuttle vehicle-orbiter

NASA Technical Reports Server (NTRS)

Chyu, W. J.; Cavin, R. K.; Erickson, L. L.

1978-01-01

The longitudinal static and dynamic stability of a Space Shuttle Vehicle-Orbiter (SSV Orbiter) model is analyzed using the FLEXSTAB computer program. Nonlinear effects are accounted for by application of a correction technique in the FLEXSTAB system; the technique incorporates experimental force and pressure data into the linear aerodynamic theory. A flexible Orbiter model is treated in the static stability analysis for the flight conditions of Mach number 0.9 for rectilinear flight (1 g) and for a pull-up maneuver (2.5 g) at an altitude of 15.24 km. Static stability parameters and structural deformations of the Orbiter are calculated at trim conditions for the dynamic stability analysis, and the characteristics of damping in pitch are investigated for a Mach number range of 0.3 to 1.2. The calculated results for both the static and dynamic stabilities are compared with the available experimental data.

Computational aeroelastic analysis of aircraft wings including geometry nonlinearity

NASA Astrophysics Data System (ADS)

Tian, Binyu

The objective of the present study is to show the ability of solving fluid structural interaction problems more realistically by including the geometric nonlinearity of the structure so that the aeroelastic analysis can be extended into the onset of flutter, or in the post flutter regime. A nonlinear Finite Element Analysis software is developed based on second Piola-Kirchhoff stress and Green-Lagrange strain. The second Piola-Kirchhoff stress and Green-Lagrange strain is a pair of energetically conjugated tensors that can accommodate arbitrary large structural deformations and deflection, to study the flutter phenomenon. Since both of these tensors are objective tensors, i.e., the rigid-body motion has no contribution to their components, the movement of the body, including maneuvers and deformation, can be included. The nonlinear Finite Element Analysis software developed in this study is verified with ANSYS, NASTRAN, ABAQUS, and IDEAS for the linear static, nonlinear static, linear dynamic and nonlinear dynamic structural solutions. To solve the flow problems by Euler/Navier equations, the current nonlinear structural software is then embedded into ENSAERO, which is an aeroelastic analysis software package developed at NASA Ames Research Center. The coupling of the two software, both nonlinear in their own field, is achieved by domain decomposition method first proposed by Guruswamy. A procedure has been set for the aeroelastic analysis process. The aeroelastic analysis results have been obtained for fight wing in the transonic regime for various cases. The influence dynamic pressure on flutter has been checked for a range of Mach number. Even though the current analysis matches the general aeroelastic characteristic, the numerical value not match very well with previous studies and needs farther investigations. The flutter aeroelastic analysis results have also been plotted at several time points. The influences of the deforming wing geometry can be well seen in those plots. The movement of shock changes the aerodynamic load distribution on the wing. The effect of viscous on aeroelastic analysis is also discussed. Also compared are the flutter solutions with, or without the structural nonlinearity. As can be seen, linear structural solution goes to infinite, which can not be true in reality. The nonlinear solution is more realistic and can be used to understand the fluid and structure interaction behavior, to control, or prevent disastrous events. (Abstract shortened by UMI.)

A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: The Constrained Harmonic Balance Method, with application to disc brake squeal

NASA Astrophysics Data System (ADS)

Coudeyras, N.; Sinou, J.-J.; Nacivet, S.

2009-01-01

Brake squeal noise is still an issue since it generates high warranty costs for the automotive industry and irritation for customers. Key parameters must be known in order to reduce it. Stability analysis is a common method of studying nonlinear phenomena and has been widely used by the scientific and the engineering communities for solving disc brake squeal problems. This type of analysis provides areas of stability versus instability for driven parameters, thereby making it possible to define design criteria. Nevertheless, this technique does not permit obtaining the vibrating state of the brake system and nonlinear methods have to be employed. Temporal integration is a well-known method for computing the dynamic solution but as it is time consuming, nonlinear methods such as the Harmonic Balance Method (HBM) are preferred. This paper presents a novel nonlinear method called the Constrained Harmonic Balance Method (CHBM) that works for nonlinear systems subject to flutter instability. An additional constraint-based condition is proposed that omits the static equilibrium point (i.e. the trivial static solution of the nonlinear problem that would be obtained by applying the classical HBM) and therefore focuses on predicting both the Fourier coefficients and the fundamental frequency of the stationary nonlinear system. The effectiveness of the proposed nonlinear approach is illustrated by an analysis of disc brake squeal. The brake system under consideration is a reduced finite element model of a pad and a disc. Both stability and nonlinear analyses are performed and the results are compared with a classical variable order solver integration algorithm. Therefore, the objectives of the following paper are to present not only an extension of the HBM (CHBM) but also to demonstrate an application to the specific problem of disc brake squeal with extensively parametric studies that investigate the effects of the friction coefficient, piston pressure, nonlinear stiffness and structural damping.

Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector

NASA Technical Reports Server (NTRS)

Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)

2001-01-01

Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.

Theoretical and software considerations for nonlinear dynamic analysis

NASA Technical Reports Server (NTRS)

Schmidt, R. J.; Dodds, R. H., Jr.

1983-01-01

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

A nonlinear vibration isolator achieving high-static-low-dynamic stiffness and tunable anti-resonance frequency band

NASA Astrophysics Data System (ADS)

Sun, Xiuting; Jing, Xingjian

2016-12-01

This study investigates theoretically and experimentally a vibration isolator constructed by an n-layer Scissor-Like Structure (SLS), focusing on the analysis and design of nonlinear stiffness and damping characteristics for advantageous isolation performance in both orthogonal directions. With the mathematical modeling, the influence incurred by different structural parameters on system isolation performance is studied. It is shown that, (a) nonlinear high-static-low-dynamic stiffness and damping characteristics can be seen such that the system can achieve good isolation performance in both directions, (b) an anti-resonance frequency band exists due to the coupling effect between the linear and nonlinear stiffness in the two orthogonal directions within the structure, and (c) all these performances are designable with several structural parameters. The advantages of the proposed system are shown through comparisons with an existing quasi-zero-stiffness vibration isolator (QZS-VI) and a traditional mass-spring-damper vibration isolator (MSD-VI), and further validated by experimental results.

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.

High Temperature Composite Analyzer (HITCAN) demonstration manual, version 1.0

NASA Technical Reports Server (NTRS)

Singhal, S. N; Lackney, J. J.; Murthy, P. L. N.

1993-01-01

This manual comprises a variety of demonstration cases for the HITCAN (HIgh Temperature Composite ANalyzer) code. HITCAN is a general purpose computer program for predicting nonlinear global structural and local stress-strain response of arbitrarily oriented, multilayered high temperature metal matrix composite structures. HITCAN is written in FORTRAN 77 computer language and has been configured and executed on the NASA Lewis Research Center CRAY XMP and YMP computers. Detailed description of all program variables and terms used in this manual may be found in the User's Manual. The demonstration includes various cases to illustrate the features and analysis capabilities of the HITCAN computer code. These cases include: (1) static analysis, (2) nonlinear quasi-static (incremental) analysis, (3) modal analysis, (4) buckling analysis, (5) fiber degradation effects, (6) fabrication-induced stresses for a variety of structures; namely, beam, plate, ring, shell, and built-up structures. A brief discussion of each demonstration case with the associated input data file is provided. Sample results taken from the actual computer output are also included.

TORO II: A finite element computer program for nonlinear quasi-static problems in electromagnetics: Part 1, Theoretical background

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

Gartling, D.K.

The theoretical and numerical background for the finite element computer program, TORO II, is presented in detail. TORO II is designed for the multi-dimensional analysis of nonlinear, electromagnetic field problems described by the quasi-static form of Maxwell`s equations. A general description of the boundary value problems treated by the program is presented. The finite element formulation and the associated numerical methods used in TORO II are also outlined. Instructions for the use of the code are documented in SAND96-0903; examples of problems analyzed with the code are also provided in the user`s manual. 24 refs., 8 figs.

From Spiking Neuron Models to Linear-Nonlinear Models

PubMed Central

Ostojic, Srdjan; Brunel, Nicolas

2011-01-01

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates. PMID:21283777

From spiking neuron models to linear-nonlinear models.

PubMed

Ostojic, Srdjan; Brunel, Nicolas

2011-01-20

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

Estimation of Rotary Stability Derivatives at Subsonic and Transonic Speeds

NASA Technical Reports Server (NTRS)

Tobak, Murray; Lessing, Henry C.

1961-01-01

The first part of this paper pertains to the estimation of subsonic rotary stability derivatives of wings. The unsteady potential flow problem is solved by a superposition of steady flow solutions. Numerical results for the damping coefficients of triangular wings are presented as functions of aspect ratio and Mach number, and are compared with experimental results over the Mach number range 0 to 1. In the second part, experimental results are used. to point out a close correlation between the nonlinear variations with angle of attack of the static pitching-moment curve slope and the damping-in-pitch coefficient. The underlying basis for the correlation is found as a result of an analysis in which the indicial function concept and. the principle of super-position are adapted to apply to the nonlinear problem. The form of the result suggests a method of estimating nonlinear damping coefficients from results of static wind-tunnel measurements.

Self-adaptive predictor-corrector algorithm for static nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Padovan, J.

1981-01-01

A multiphase selfadaptive predictor corrector type algorithm was developed. This algorithm enables the solution of highly nonlinear structural responses including kinematic, kinetic and material effects as well as pro/post buckling behavior. The strategy involves three main phases: (1) the use of a warpable hyperelliptic constraint surface which serves to upperbound dependent iterate excursions during successive incremental Newton Ramphson (INR) type iterations; (20 uses an energy constraint to scale the generation of successive iterates so as to maintain the appropriate form of local convergence behavior; (3) the use of quality of convergence checks which enable various self adaptive modifications of the algorithmic structure when necessary. The restructuring is achieved by tightening various conditioning parameters as well as switch to different algorithmic levels to improve the convergence process. The capabilities of the procedure to handle various types of static nonlinear structural behavior are illustrated.

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

NASA Astrophysics Data System (ADS)

Chróścielewski, Jacek; Schmidt, Rüdiger; Eremeyev, Victor A.

2018-05-01

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

Finite element analysis of high aspect ratio wind tunnel wing model: A parametric study

NASA Astrophysics Data System (ADS)

Rosly, N. A.; Harmin, M. Y.

2017-12-01

Procedure for designing the wind tunnel model of a high aspect ratio (HAR) wing containing geometric nonlinearities is described in this paper. The design process begins with identification of basic features of the HAR wing as well as its design constraints. This enables the design space to be narrowed down and consequently, brings ease of convergence towards the design solution. Parametric studies in terms of the spar thickness, the span length and the store diameter are performed using finite element analysis for both undeformed and deformed cases, which respectively demonstrate the linear and nonlinear conditions. Two main criteria are accounted for in the selection of the wing design: the static deflections due to gravitational loading should be within the allowable margin of the size of the wind tunnel test section and the flutter speed of the wing should be much below the maximum speed of the wind tunnel. The findings show that the wing experiences a stiffness hardening effect under the nonlinear static solution and the presence of the store enables significant reduction in linear flutter speed.

Parametric Study on the Response of Compression-Loaded Composite Shells With Geometric and Material Imperfections

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Starnes, James H., Jr.

2004-01-01

The results of a parametric study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thinwalled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The imperfections considered include initial geometric shell-wall midsurface imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity nonlinear shell analysis procedure that accurately accounts for the effects of these imperfections on the nonlinear responses and buckling loads of the shells is described. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable response characteristics.

Nonlinear resonance of the rotating circular plate under static loads in magnetic field

NASA Astrophysics Data System (ADS)

Hu, Yuda; Wang, Tong

2015-11-01

The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.

A contact stress model for multifingered grasps of rough objects

NASA Technical Reports Server (NTRS)

Sinha, Pramath Raj; Abel, Jacob M.

1990-01-01

The model developed utilizes a contact-stress analysis of an arbitrarily shaped object in a multifingered grasp. The fingers and the object are all treated as elastic bodies, and the region of contact is modeled as a deformable surface patch. The relationship between the friction and normal forces is nonlocal and nonlinear in nature and departs from the Coulomb approximation. The nature of the constraints arising out of conditions for compatibility and static equilibrium motivated the formulation of the model as a nonlinear constrained minimization problem. The model is able to predict the magnitude of the inwardly directed normal forces and both the magnitude and direction of the tangential (friction) forces at each finger-object interface for grasped objects in static equilibrium.

Experimental and numerical investigation of the nonlinear dynamics of compliant mechanisms for deployable structures

NASA Astrophysics Data System (ADS)

Dewalque, Florence; Schwartz, Cédric; Denoël, Vincent; Croisier, Jean-Louis; Forthomme, Bénédicte; Brüls, Olivier

2018-02-01

This paper studies the dynamics of tape springs which are characterised by a highly geometrical nonlinear behaviour including buckling, the formation of folds and hysteresis. An experimental set-up is designed to capture these complex nonlinear phenomena. The experimental data are acquired by the means of a 3D motion analysis system combined with a synchronised force plate. Deployment tests show that the motion can be divided into three phases characterised by different types of folds, frequencies of oscillation and damping behaviours. Furthermore, the reproducibility quality of the dynamic and quasi-static results is validated by performing a large number of tests. In parallel, a nonlinear finite element model is developed. The required model parameters are identified based on simple experimental tests such as static deformed configurations and small amplitude vibration tests. In the end, the model proves to be well correlated with the experimental results in opposite sense bending, while in equal sense, both the experimental set-up and the numerical model are particularly sensitive to the initial conditions.

Discretization in time gives rise to noise-induced improvement of the signal-to-noise ratio in static nonlinearities.

PubMed

Davidović, A; Huntington, E H; Frater, M R

2009-07-01

For some nonlinear systems the performance can improve with an increasing noise level. Such noise-induced improvement in static nonlinearities is of great interest for practical applications since many systems can be modeled in that way (e.g., sensors, quantizers, limiters, etc.). We present experimental evidence that noise-induced performance improvement occurs in those systems as a consequence of discretization in time with the achievable signal-to-noise ratio (SNR) gain increasing with decreasing ratio of input noise bandwidth and total measurement bandwidth. By modifying the input noise bandwidth, noise-induced improvement with SNR gain larger than unity is demonstrated in a system where it was not previously thought possible. Our experimental results bring closer two different theoretical models for the same class of nonlinearities and shed light on the behavior of static nonlinear discrete-time systems.

Application of a Modal Approach in Solving the Static Stability Problem for Electric Power Systems

NASA Astrophysics Data System (ADS)

Sharov, J. V.

2017-12-01

Application of a modal approach in solving the static stability problem for power systems is examined. It is proposed to use the matrix exponent norm as a generalized transition function of the power system disturbed motion. Based on the concept of a stability radius and the pseudospectrum of Jacobian matrix, the necessary and sufficient conditions for existence of the static margins were determined. The capabilities and advantages of the modal approach in designing centralized or distributed control and the prospects for the analysis of nonlinear oscillations and rendering the dynamic stability are demonstrated.

Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations

NASA Technical Reports Server (NTRS)

Hodges, D. H.

1985-01-01

Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.

Numerical study on static component generation from the primary Lamb waves propagating in a plate with nonlinearity

NASA Astrophysics Data System (ADS)

Wan, Xiang; Tse, Peter W.; Zhang, Xuhui; Xu, Guanghua; Zhang, Qing; Fan, Hongwei; Mao, Qinghua; Dong, Ming; Wang, Chuanwei; Ma, Hongwei

2018-04-01

Under the discipline of nonlinear ultrasonics, in addition to second harmonic generation, static component generation is another frequently used nonlinear ultrasonic behavior in non-destructive testing (NDT) and structural health monitoring (SHM) communities. However, most previous studies on static component generation are mainly based on using longitudinal waves. It is desirable to extend static component generation from primary longitudinal waves to primary Lamb waves. In this paper, static component generation from the primary Lamb waves is studied. Two major issues are numerically investigated. First, the mode of static displacement component generated from different primary Lamb wave modes is identified. Second, cumulative effect of static displacement component from different primary Lamb wave modes is also discussed. Our study results show that the static component wave packets generated from the primary S0, A0 and S1 modes share the almost same group velocity equal to the phase velocity of S0 mode tending to zero frequency c plate . The finding indicates that whether the primary mode is S0, A0 or S1, the static components generated from these primary modes always share the nature of S0 mode. This conclusion is also verified by the displacement filed of these static components that the horizontal displacement field is almost uniform and the vertical displacement filed is antisymmetric across the thickness of the plate. The uniform distribution of horizontal displacement filed enables the static component, regardless of the primary Lamb modes, to be a promising technique for evaluating microstructural damages buried in the interior of a structure. Our study also illustrates that the static components are cumulative regardless of whether the phase velocity of the primary and secondary waves is matched or not. This observation indicates that the static component overcomes the limitations of the traditional nonlinear Lamb waves satisfying phase velocity matching condition to achieve cumulative second harmonic generation. This nature also enables the primary Lamb waves excited at a low center frequency to generate static component used for inspecting large-scale structures with micro-scale damages.

Assessment of current state of the art in modeling techniques and analysis methods for large space structures

NASA Technical Reports Server (NTRS)

Noor, A. K.

1983-01-01

Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.

Sensitivity analysis of static resistance of slender beam under bending

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

Valeš, Jan

2016-06-08

The paper deals with statical and sensitivity analyses of resistance of simply supported I-beams under bending. The resistance was solved by geometrically nonlinear finite element method in the programme Ansys. The beams are modelled with initial geometrical imperfections following the first eigenmode of buckling. Imperfections were, together with geometrical characteristics of cross section, and material characteristics of steel, considered as random quantities. The method Latin Hypercube Sampling was applied to evaluate statistical and sensitivity resistance analyses.

Estimation of Handgrip Force from SEMG Based on Wavelet Scale Selection.

PubMed

Wang, Kai; Zhang, Xianmin; Ota, Jun; Huang, Yanjiang

2018-02-24

This paper proposes a nonlinear correlation-based wavelet scale selection technology to select the effective wavelet scales for the estimation of handgrip force from surface electromyograms (SEMG). The SEMG signal corresponding to gripping force was collected from extensor and flexor forearm muscles during the force-varying analysis task. We performed a computational sensitivity analysis on the initial nonlinear SEMG-handgrip force model. To explore the nonlinear correlation between ten wavelet scales and handgrip force, a large-scale iteration based on the Monte Carlo simulation was conducted. To choose a suitable combination of scales, we proposed a rule to combine wavelet scales based on the sensitivity of each scale and selected the appropriate combination of wavelet scales based on sequence combination analysis (SCA). The results of SCA indicated that the scale combination VI is suitable for estimating force from the extensors and the combination V is suitable for the flexors. The proposed method was compared to two former methods through prolonged static and force-varying contraction tasks. The experiment results showed that the root mean square errors derived by the proposed method for both static and force-varying contraction tasks were less than 20%. The accuracy and robustness of the handgrip force derived by the proposed method is better than that obtained by the former methods.

A nonlinear auxetic structural vibration damper with metal rubber particles

NASA Astrophysics Data System (ADS)

Ma, Yanhong; Scarpa, Fabrizio; Zhang, Dayi; Zhu, Bin; Chen, Lulu; Hong, Jie

2013-08-01

The work describes the mechanical performance of a metal rubber particles (MRP) damper design based on an auxetic (negative Poisson’s ratio) cellular configuration. The auxetic damper configuration is constituted by an anti-tetrachiral honeycomb, where the cylinders are filled with the MRP material. The MRP samples have been subjected to quasi-static loading to measure the stiffness and loss factor from the static hysteresis curve. A parametric experimental analysis has been carried out to investigate the effect of relative density and filling percentage on the static performance of the MRP, and to identify design guidelines for best use of MRP devices. An experimental assessment of the integrated auxetic-MRP damper concept has been provided through static and dynamic force response techniques.

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.

Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother

NASA Astrophysics Data System (ADS)

Fillion, Anthony; Bocquet, Marc; Gratton, Serge

2018-04-01

The analysis in nonlinear variational data assimilation is the solution of a non-quadratic minimization. Thus, the analysis efficiency relies on its ability to locate a global minimum of the cost function. If this minimization uses a Gauss-Newton (GN) method, it is critical for the starting point to be in the attraction basin of a global minimum. Otherwise the method may converge to a local extremum, which degrades the analysis. With chaotic models, the number of local extrema often increases with the temporal extent of the data assimilation window, making the former condition harder to satisfy. This is unfortunate because the assimilation performance also increases with this temporal extent. However, a quasi-static (QS) minimization may overcome these local extrema. It accomplishes this by gradually injecting the observations in the cost function. This method was introduced by Pires et al. (1996) in a 4D-Var context. We generalize this approach to four-dimensional strong-constraint nonlinear ensemble variational (EnVar) methods, which are based on both a nonlinear variational analysis and the propagation of dynamical error statistics via an ensemble. This forces one to consider the cost function minimizations in the broader context of cycled data assimilation algorithms. We adapt this QS approach to the iterative ensemble Kalman smoother (IEnKS), an exemplar of nonlinear deterministic four-dimensional EnVar methods. Using low-order models, we quantify the positive impact of the QS approach on the IEnKS, especially for long data assimilation windows. We also examine the computational cost of QS implementations and suggest cheaper algorithms.

Remarkable Second-Order Optical Nonlinearity of Nano-Sized Au Cluster: A TDDFT Study

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

Wu, Kechen; Li, Jun; Lin, Chensheng

2004-04-21

The dipole polarizability, static first hyperpolarizability, and UV-vis spectrum of the recently identified nano-sized tetrahedral cluster of Au have been investigated by using time-dependent density functional response theory. We have discovered that the Au cluster possesses remarkably large molecular second-order optical nonlinearity with the first hyperpolarizabilty (xyz) calculated to be 14.3 x 10 electrostatic unit (esu). The analysis of the low-energy absorption band suggests that the charge transfer from the edged gold atoms to the vertex ones plays the key role in nonlinear optical (NLO) response of Au.

Influence of damped propagation of dopant on the static and frequency-dependent third nonlinear polarizability of quantum dot

NASA Astrophysics Data System (ADS)

Pal, Suvajit; Ghosh, Manas

2014-07-01

We investigate the profiles of diagonal components of static and frequency-dependent third nonlinear (γxxxx and γyyyy) polarizability of repulsive impurity doped quantum dots. The dopant impurity potential takes a GAUSSIAN form. We have considered propagation of the dopant within an environment that damps the motion. The study focuses on role of damping strength on the diagonal components of both static and frequency-dependent third nonlinear polarizability of the doped system. The doped system is further exposed to an external electric field of given intensity. Damping subtly modulates the dot-impurity interaction and fabricates the polarizability components in a noticeable manner.

Multiscale Static Analysis of Notched and Unnotched Laminates Using the Generalized Method of Cells

NASA Technical Reports Server (NTRS)

Naghipour Ghezeljeh, Paria; Arnold, Steven M.; Pineda, Evan J.; Stier, Bertram; Hansen, Lucas; Bednarcyk, Brett A.; Waas, Anthony M.

2016-01-01

The generalized method of cells (GMC) is demonstrated to be a viable micromechanics tool for predicting the deformation and failure response of laminated composites, with and without notches, subjected to tensile and compressive static loading. Given the axial [0], transverse [90], and shear [+45/-45] response of a carbon/epoxy (IM7/977-3) system, the unnotched and notched behavior of three multidirectional layups (Layup 1: [0,45,90,-45](sub 2S), Layup 2: [0,60,0](sub 3S), and Layup 3: [30,60,90,-30, -60](sub 2S)) are predicted under both tensile and compressive static loading. Matrix nonlinearity is modeled in two ways. The first assumes all nonlinearity is due to anisotropic progressive damage of the matrix only, which is modeled, using the multiaxial mixed-mode continuum damage model (MMCDM) within GMC. The second utilizes matrix plasticity coupled with brittle final failure based on the maximum principle strain criteria to account for matrix nonlinearity and failure within the Finite Element Analysis--Micromechanics Analysis Code (FEAMAC) software multiscale framework. Both MMCDM and plasticity models incorporate brittle strain- and stress-based failure criteria for the fiber. Upon satisfaction of these criteria, the fiber properties are immediately reduced to a nominal value. The constitutive response for each constituent (fiber and matrix) is characterized using a combination of vendor data and the axial, transverse, and shear responses of unnotched laminates. Then, the capability of the multiscale methodology is assessed by performing blind predictions of the mentioned notched and unnotched composite laminates response under tensile and compressive loading. Tabulated data along with the detailed results (i.e., stress-strain curves as well as damage evolution states at various ratios of strain to failure) for all laminates are presented.

Manual on the Flight of Flexible Aircraft in Turbulence (Manuel sur le Vol des Avions Non-rigides en Milieu Turbulent)

DTIC Science & Technology

1991-05-01

Static Non-Linearity 106 0 y = f(dx/dt) = -f(-dx/dt) = = > Static Non-Linearity • y = f(x,sign(dx/dt)) = = > Hysteresis-Type Non-Linearity = -f(-x,sign... Havilland Division Garratt Blvd., Downsview Ontario M3K I Y5 Canada CONTENTS ABSTRACT NOTATION 1. INTRODUCTION 2. THE SDG GUST MODEL 3. ESTABLISHING CRITICAL...VENT ETRE ADRESSEES DIRECTEMENT N AU SERVICE NATIONAL TECHNIQUE, Dh INFORMATION (NTIS) DONT LADRESSE SUIT AGENCES DE VENTE National Technical

Restoration of Static JPEG Images and RGB Video Frames by Means of Nonlinear Filtering in Conditions of Gaussian and Non-Gaussian Noise

NASA Astrophysics Data System (ADS)

Sokolov, R. I.; Abdullin, R. R.

2017-11-01

The use of nonlinear Markov process filtering makes it possible to restore both video stream frames and static photos at the stage of preprocessing. The present paper reflects the results of research in comparison of these types image filtering quality by means of special algorithm when Gaussian or non-Gaussian noises acting. Examples of filter operation at different values of signal-to-noise ratio are presented. A comparative analysis has been performed, and the best filtered kind of noise has been defined. It has been shown the quality of developed algorithm is much better than quality of adaptive one for RGB signal filtering at the same a priori information about the signal. Also, an advantage over median filter takes a place when both fluctuation and pulse noise filtering.

The Shock and Vibration Digest, Volume 17, Number 11

DTIC Science & Technology

1985-11-01

Jiang, C., and Chia , 1983). C.Y., "Dynamic and Static Nonlinear Analy- .sis of Cylindrically Orthotropic Circular 122. Nowinski, J.L., "On the...Rectilinearly Orthotropic Disk," Intl. J. (1984). Mech. Sci., j2 (3), pp 191-198 (1983). 132. Sathyamootthy, M. and Chia , C.Y., 123. Sathyamoorthy, M...34Geometrically Nonlinear Transient Analysis of Laminated Composite 139. Chia , C.Y., "Large Amplitude Vibra- Plates," AIAA J., 21 (4), pp 621-629 (Apr tions of

Symposium on Parallel Computational Methods for Large-scale Structural Analysis and Design, 2nd, Norfolk, VA, US

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O. (Editor); Housner, Jerrold M. (Editor)

1993-01-01

Computing speed is leaping forward by several orders of magnitude each decade. Engineers and scientists gathered at a NASA Langley symposium to discuss these exciting trends as they apply to parallel computational methods for large-scale structural analysis and design. Among the topics discussed were: large-scale static analysis; dynamic, transient, and thermal analysis; domain decomposition (substructuring); and nonlinear and numerical methods.

Stability of nonuniform rotor blades in hover using a mixed formulation

NASA Technical Reports Server (NTRS)

Stephens, W. B.; Hodges, D. H.; Avila, J. H.; Kung, R. M.

1980-01-01

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

Nonlinear quasi-static finite element simulations predict in vitro strength of human proximal femora assessed in a dynamic sideways fall setup.

PubMed

Varga, Peter; Schwiedrzik, Jakob; Zysset, Philippe K; Fliri-Hofmann, Ladina; Widmer, Daniel; Gueorguiev, Boyko; Blauth, Michael; Windolf, Markus

2016-04-01

Osteoporotic proximal femur fractures are caused by low energy trauma, typically when falling on the hip from standing height. Finite element simulations, widely used to predict the fracture load of femora in fall, usually include neither mass-related inertial effects, nor the viscous part of bone׳s material behavior. The aim of this study was to elucidate if quasi-static non-linear homogenized finite element analyses can predict in vitro mechanical properties of proximal femora assessed in dynamic drop tower experiments. The case-specific numerical models of 13 femora predicted the strength (R(2)=0.84, SEE=540N, 16.2%), stiffness (R(2)=0.82, SEE=233N/mm, 18.0%) and fracture energy (R(2)=0.72, SEE=3.85J, 39.6%); and provided fair qualitative matches with the fracture patterns. The influence of material anisotropy was negligible for all predictions. These results suggest that quasi-static homogenized finite element analysis may be used to predict mechanical properties of proximal femora in the dynamic sideways fall situation. Copyright © 2015 Elsevier Ltd. All rights reserved.

Damage assessment in reinforced concrete using nonlinear vibration techniques

NASA Astrophysics Data System (ADS)

Van Den Abeele, K.; De Visscher, J.

2000-07-01

Reinforced concrete (RC) structures are subject to microcrack initiation and propagation at load levels far below the actual failure load. In this paper, nonlinear vibration techniques are applied to investigate stages of progressive damage in RC beams induced by static loading tests. At different levels of damage, a modal analysis is carried out, assuming the structure to behave linearly. At the same time, measurement of resonant frequencies and damping ratios as function of vibration amplitude are performed using a frequency domain technique as well as a time domain technique. We compare the results of the linear and nonlinear techniques, and value them against the visual damage evaluation.

Nonlinear aerodynamics of two-dimensional airfoils in severe maneuver

NASA Technical Reports Server (NTRS)

Scott, Matthew T.; Mccune, James E.

1988-01-01

This paper presents a nonlinear theory of forces and moment acting on a two-dimensional airfoil in unsteady potential flow. Results are obtained for cases of both large and small amplitude motion. The analysis, which is based on an extension of Wagner's integral equation to the nonlinear regime, takes full advantage of the trailing wake's tendency to deform under local velocities. Interactive computational results are presented that show examples of wake-induced lift and moment augmentation on the order of 20 percent of quasi-static values. The expandability and flexibility of the present computational method are noted, as well as the relative speed with which solutions are obtained.

The role of flow field structure in determining the aerodynamic response of a delta wing

NASA Astrophysics Data System (ADS)

Addington, Gregory Alan

Delta wings have long been known to exhibit nonlinear aerodynamic responses as a result of the presence of helical leading-edge vortices. This nonlinearity, found under both steady-state and unsteady conditions, is particularly profound in the presence of vortex burst. Modeling such aerodynamic responses with the Nonlinear Indicial Response (NIR) methodology provides a means of simulating these nonlinearities through its inclusion of motion history in addition to superposition. The NIR model also includes provisions for a finite number of discrete locations where the aerodynamic response is discontinuous with response to a state variable. These critical states also separate regions of states where the unsteady aerodynamic responses are potentially of highly-disparate characters. Although these critical states have been found in the past, their relationship with flow field bifurcation is uncertain. The purpose of this dissertation is to explore the relationship between nonlinear aerodynamic responses, critical states and flow field bifurcations from an experimental approach. This task has been accomplished by comparing a comprehensive database of skin-friction line topologies with static and unsteady aerodynamic responses. These data were collected using a 65sp° delta wing which rolled about an inclined longitudinal body axis. In this study, compelling, but not conclusive, evidence was found to suggest that a bifurcation in the skin-friction line topology was a necessary condition for the presence of a critical state. Although the presence of critical states was well predicted through careful observation and analysis of highly-resolved static loading data alone, their precise placement as a function of the independent variable was aided through the consideration of the locations of skin-friction line bifurcations. Furthermore, these static data were found to contain indications of the basic lagged or unlagged behavior of the unsteady aerodynamic response. This indication was found by comparing the relative rate of change seen in the estimated vortical- and potential-rolling-moment components. Through the review of these data in light of current theories on the mechanisms of leading-edge vortex breakdown, the formulation of a hypothesis regarding the relationship between both the static and unsteady aerodynamic response and vorticity dynamics was possible.

Performance evaluation of existing building structure with pushover analysis

NASA Astrophysics Data System (ADS)

Handana, MAP; Karolina, R.; Steven

2018-02-01

In the management of the infrastructure of the building, during the period of buildings common building damage as a result of several reasons, earthquakes are common. The building is planned to work for a certain service life. But during the certain service life, the building vulnerable to damage due to various things. Any damage to cultivate can be detected as early as possible, because the damage could spread, triggering and exacerbating the latest. The newest concept to earthquake engineering is Performance Based Earthquake Engineering (PBEE). PBEE divided into two, namely Performance Based Seismic Design (PBSD) and Performance Based Seismic Evaluation (PBSE). Evaluation on PBSE one of which is the analysis of nonlinear pushover. Pushover analysis is a static analysis of nonlinear where the influence of the earthquake plan on building structure is considered as burdens static catch at the center of mass of each floor, which it was increased gradually until the loading causing the melting (plastic hinge) first within the building structure, then the load increases further changes the shapes of post-elastic large it reached the condition of elastic. Then followed melting (plastic hinge) in the location of the other structured.

The STAGS computer code

NASA Technical Reports Server (NTRS)

Almroth, B. O.; Brogan, F. A.

1978-01-01

Basic information about the computer code STAGS (Structural Analysis of General Shells) is presented to describe to potential users the scope of the code and the solution procedures that are incorporated. Primarily, STAGS is intended for analysis of shell structures, although it has been extended to more complex shell configurations through the inclusion of springs and beam elements. The formulation is based on a variational approach in combination with local two dimensional power series representations of the displacement components. The computer code includes options for analysis of linear or nonlinear static stress, stability, vibrations, and transient response. Material as well as geometric nonlinearities are included. A few examples of applications of the code are presented for further illustration of its scope.

Fully Nonlinear Modeling and Analysis of Precision Membranes

NASA Technical Reports Server (NTRS)

Pai, P. Frank; Young, Leyland G.

2003-01-01

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

A Comparison of the Quasi-static Mechanical and Nonlinear Viscoelastic Properties of the Human Semitendinosus and Gracilis Tendons

PubMed Central

Abramowitch, Steven D.; Zhang, Xiaoyan; Curran, Molly; Kilger, Robert

2010-01-01

Background Over fifty-percent of anterior cruciate ligament reconstructions are performed using semitendinosus and gracilis tendon autografts. Despite their increased use, there remains little quantitative data on their mechanical behavior. Therefore, the objective of this study was to investigate the quasi-static mechanical and nonlinear viscoelastic properties of human semitendinosus and gracilis tendons, as well as the variation of these properties along their length. Methods Specimens were subjected to a series of uniaxial tensile tests: one-hour static stress-relaxation test, 30-cycle cyclic stress-relaxation test and load to failure test. To describe the nonlinear viscoelastic behavior, the quasi-linear viscoelastic theory was utilized to model data from the static stress relaxation experiment. Findings The constants describing the viscoelastic behavior were similar between the proximal and distal halves of the gracilis tendon. The proximal half of the semitendinosus tendon, however, had a greater viscous response than its distal half, which was also significantly higher than the proximal gracilis tendon. In terms of the quasi-static mechanical properties, the properties were similar between the proximal and distal halves of the semitendinosus tendon. However, the distal gracilis tendon showed a significantly higher tangent modulus and ultimate stress compared to its proximal half, which was also significantly higher than the distal semitendinosus tendon. Interpretation The results of this study demonstrate differences between the semitendinosus and gracilis tendons in terms of their quasi-static mechanical and nonlinear viscoelastic properties. These results are important for establishing surgical preconditioning protocols and graft selection. PMID:20092917

A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

NASA Astrophysics Data System (ADS)

Jokhio, G. A.; Izzuddin, B. A.

2015-05-01

This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.

Experimental study of geotextile as plinth beam in a pile group-supported modeled building frame

NASA Astrophysics Data System (ADS)

Ravi Kumar Reddy, C.; Gunneswara Rao, T. D.

2017-12-01

This paper presents the experimental results of static vertical load tests on a model building frame with geotextile as plinth beam supported by pile groups embedded in cohesionless soil (sand). The experimental results have been compared with those obtained from the nonlinear FEA and conventional method of analysis. The results revealed that the conventional method of analysis gives a shear force of about 53%, bending moment at the top of the column about 17% and at the base of the column about 50-98% higher than that by the nonlinear FEA for the frame with geotextile as plinth beam.

Geometrically nonlinear analysis of layered composite plates and shells

NASA Technical Reports Server (NTRS)

Chao, W. C.; Reddy, J. N.

1983-01-01

A degenerated three dimensional finite element, based on the incremental total Lagrangian formulation of a three dimensional layered anisotropic medium was developed. Its use in the geometrically nonlinear, static and dynamic, analysis of layered composite plates and shells is demonstrated. A two dimenisonal finite element based on the Sanders shell theory with the von Karman (nonlinear) strains was developed. It is shown that the deflections obtained by the 2D shell element deviate from those obtained by the more accurate 3D element for deep shells. The 3D degenerated element can be used to model general shells that are not necessarily doubly curved. The 3D degenerated element is computationally more demanding than the 2D shell theory element for a given problem. It is found that the 3D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion.

Respiratory monitoring system based on the nasal pressure technique for the analysis of sleep breathing disorders: Reduction of static and dynamic errors, and comparisons with thermistors and pneumotachographs

NASA Astrophysics Data System (ADS)

Alves de Mesquita, Jayme; Lopes de Melo, Pedro

2004-03-01

Thermally sensitive devices—thermistors—have usually been used to monitor sleep-breathing disorders. However, because of their long time constant, these devices are not able to provide a good characterization of fast events, like hypopneas. Nasal pressure recording technique (NPR) has recently been suggested to quantify airflow during sleep. It is claimed that the short time constants of the devices used to implement this technique would allow an accurate analysis of fast abnormal respiratory events. However, these devices present errors associated with nonlinearities and acoustic resonance that could reduce the diagnostic value of the NPR. Moreover, in spite of the high scientific and clinical potential, there is no detailed description of a complete instrumentation system to implement this promising technique in sleep studies. In this context, the purpose of this work was twofold: (1) describe the development of a flexible NPR device and (2) evaluate the performance of this device when compared to pneumotachographs (PNTs) and thermistors. After the design details are described, the system static accuracy is evaluated by a comparative analysis with a PNT. This analysis revealed a significant reduction (p<0.001) of the static error when system nonlinearities were reduced. The dynamic performance of the NPR system was investigated by frequency response analysis and time constant evaluations and the results showed that the developed device response was as good as PNT and around 100 times faster (τ=5,3 ms) than thermistors (τ=512 ms). Experimental results obtained in simulated clinical conditions and in a patient are presented as examples, and confirmed the good features achieved in engineering tests. These results are in close agreement with physiological fundamentals, supplying substantial evidence that the improved dynamic and static characteristics of this device can contribute to a more accurate implementation of medical research projects and to improve the diagnoses of sleep-breathing disorders.

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Al-Nasra, M.; Zhang, Y.; Baddourah, M. A.; Agarwal, T. K.; Storaasli, O. O.; Carmona, E. A.

1991-01-01

Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

Stability analysis of a reinforced carbon carbon shell

NASA Technical Reports Server (NTRS)

Agan, W. E.; Jordan, B. M.

1977-01-01

This paper presents the development of a stability analysis for the nose cap of the NASA Space Shuttle Orbiter. Stability is evaluated by the differential stiffness analysis of the NASTRAN finite-element computer code, addressing those nonstandard characteristics in the nose cap such as nonuniform curvature, asymmetrical and nonuniform loads, support fixity, and various combinations of membrane and bending stresses. A full-sized nose cap, thinner than production, was statically tested and stability analyzed. The failing load level correlated to within 30%. The region and mode of buckling that occurred during test was accurately predicted by analysis. The criterion for predicting instability is based on the behavior of the nonlinear deflections. The deflections are nonlinear elastic in that the stresses are well within the elastic range of the material, but the geometry-load relationship produces nonlinear deflections. The load-deflection relationship is well defined by differential stiffness analysis up to the zero-slope portion of the curve, the point of neutral stability or where the shell 'snaps through' just prior to general instability.

Acoustic-radiation stress in solids. I - Theory

NASA Technical Reports Server (NTRS)

Cantrell, J. H., Jr.

1984-01-01

The general case of acoustic-radiation stress associated with quasi-compressional and quasi-shear waves propagating in infinite and semiinfinite lossless solids of arbitrary crystalline symmetry is studied. The Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized nonlinearity parameter which characterizes the stress nonlinearity, and the energy density of the propagating wave. Application of the Boltzmann-Ehrenfest principle of adiabatic invariance to a self-constrained system described by the nonlinear equations of motion allows the acoustic-radiation-induced static strain to be identified with a self-constrained variation in the time-averaged product of the internal energy density and displacement gradient. The time-averaged product is scaled by the acoustic nonlinearity parameter and represents the first-order nonlinearity in the virial theorem. Finally, the relationship between the Boussinesq and the Cauchy radiation stress is obtained in a closed three-dimensional form.

LAMPAT and LAMPATNL User’s Manual

DTIC Science & Technology

2012-09-01

nonlinearity. These tools are implemented as subroutines in the finite element software ABAQUS . This user’s manual provides information on the proper...model either through the General tab of the Edit Job dialog box in Abaqus /CAE or the command line with user=( subroutine filename). Table 1...Selection of software product and subroutine . Static Analysis With Abaqus /Standard Dynamic Analysis With Abaqus /Explicit Linear, uncoupled

Nonlinear quasi-static analysis of ultra-deep-water top-tension riser

NASA Astrophysics Data System (ADS)

Gao, Guanghai; Qiu, Xingqi; Wang, Ke; Liu, Jianjun

2017-09-01

In order to analyse the ultra-deep-water top-tension riser deformation in drilling conditions, a nonlinear quasi-static analysis model and equation are established. The riser in this model is regarded as a simply supported beam located in the vertical plane and is subjected to non-uniform axial and lateral forces. The model and the equation are solved by the finite element method. The effects of riser outside diameter, top tension ratio, sea surface current velocity, drag force coefficient, floating system drift distance and water depth on the riser lateral displacement are discussed. Results show that the riser lateral displacement increase with the increase in the sea surface current velocity, drag force coefficient and water depth, whereas decrease with the increase in the riser outside diameter, top tension ratio. The top tension ratio has an important influence on the riser deformation and it should be set reasonably under different circumstances. The drift of the floating system has a complicated influence on the riser deformation and it should avoid a large drift distance in the proceedings of drilling and production.

Development of the Main Wing Structure of a High Altitude Long Endurance UAV

NASA Astrophysics Data System (ADS)

Park, Sang Wook; Shin, Jeong Woo; Kim, Tae-Uk

2018-04-01

To enhance the flight endurance of a HALE UAV, the main wing of the UAV should have a high aspect ratio and low structural weight. Since a main wing constructed with the thin walled and slender components needed for low structural weight can suffer catastrophic failure during flight, it is important to develop a light-weight airframe without sacrificing structural integrity. In this paper, the design of the main wing of the HALE UAV was conducted using spars which were composed of a carbon-epoxy cylindrical tube and bulkheads to achieve both the weight reduction and structural integrity. The spars were sized using numerical analysis considering non-linear deformation under bending moment. Static strength testing of the wing was conducted under the most critical load condition. Then, the experimental results obtained for the wing were compared to the analytical result from the non-linear finite-element analysis. It was found that the developed main wing reduced its structural weight without any failure under the ultimate load condition of the static strength testing.

Transient analysis techniques in performing impact and crash dynamic studies

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Winter, R.

1989-01-01

Because of the emphasis being placed on crashworthiness as a design requirement, increasing demands are being made by various organizations to analyze a wide range of complex structures that must perform safely when subjected to severe impact loads, such as those generated in a crash event. The ultimate goal of crashworthiness design and analysis is to produce vehicles with the ability to reduce the dynamic forces experienced by the occupants to specified levels, while maintaining a survivable envelope around them during a specified crash event. DYCAST is a nonlinear structural dynamic finite element computer code that started from the plans systems of a finite element program for static nonlinear structural analysis. The essential features of DYCAST are outlined.

Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator

PubMed Central

Omar, Mohamed A.

2014-01-01

Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations. PMID:25045732

Static analysis of large-scale multibody system using joint coordinates and spatial algebra operator.

PubMed

Omar, Mohamed A

2014-01-01

Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations.

The static response of a bowed inclined hot wire

NASA Technical Reports Server (NTRS)

Smits, A. J.

1984-01-01

The directional sensitivity of a bowed, inclined hot wire is investigated using a simple model for the convective heat transfer. The static response is analyzed for subsonic and supersonic flows. It is shown that the effects of both end conduction and wire bowing are greater in supersonic flow. Regardless of the Mach number, however, these two phenomena have distinctly different effects; end conduction appears to be responsible for reducing the nonlinearity of the response, whereas bowing increases the directional sensitivity. Comparison with the available data suggests that the analysis is useful for interpreting the experimental results.

Comparison of Seismic Responses for Reinforced Concrete Buildings with Mass and Stiffness Irregularities Using Pushover and Nonlinear Time History Analysis

NASA Astrophysics Data System (ADS)

Teruna, D. R.

2017-03-01

Pushover analysis or also known as nonlinear static procedures (NSP) have been recognized in recent years for practical evaluation of seismic demands and for structural design by estimating a structural building capacities and deformation demands. By comparing these demands and capacities at the performance level interest, the seismic performance of a building can be evaluated. However, the accuracy of NSP for assessment irregular building is not yet a fully satisfactory solution, since irregularities of a building influence the dynamic responses of the building. The objective of the study presented herein is to understand the nonlinear behaviour of six story RC building with mass irregularities at different floors and stiffness irregularity at first story (soft story) using NSP. For the purpose of comparison on the performance level obtained with NSP, nonlinear time history analysis (THA) were also performed under ground motion excitation with compatible to response spectra design. Finally, formation plastic hinges and their progressive development from elastic level to collapse prevention are presented and discussed.

Cocontraction of pairs of antagonistic muscles: analytical solution for planar static nonlinear optimization approaches.

PubMed

Herzog, W; Binding, P

1993-11-01

It has been stated in the literature that static, nonlinear optimization approaches cannot predict coactivation of pairs of antagonistic muscles; however, numerical solutions of such approaches have predicted coactivation of pairs of one-joint and multijoint antagonists. Analytical support for either finding is not available in the literature for systems containing more than one degree of freedom. The purpose of this study was to investigate analytically the possibility of cocontraction of pairs of antagonistic muscles using a static nonlinear optimization approach for a multidegree-of-freedom, two-dimensional system. Analytical solutions were found using the Karush-Kuhn-Tucker conditions, which were necessary and sufficient for optimality in this problem. The results show that cocontraction of pairs of one-joint antagonistic muscles is not possible, whereas cocontraction of pairs of multijoint antagonists is. These findings suggest that cocontraction of pairs of antagonistic muscles may be an "efficient" way to accomplish many movement tasks.

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.

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.

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Applications

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1998-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Application

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1997-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

Application of GRASP (General Rotorcraft Aeromechanical Stability Program) to nonlinear analysis of a cantilever beam

NASA Technical Reports Server (NTRS)

Hinnant, Howard E.; Hodges, Dewey H.

1987-01-01

The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.

Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design

NASA Technical Reports Server (NTRS)

Whiffen, Gregory J.

2006-01-01

Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.

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.

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Kumar, A.; Reddy, S.; Handschuh, R.

1993-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

A Numerical Study of Automated Dynamic Relaxation for Nonlinear Static Tensioned Structures.

DTIC Science & Technology

1987-10-01

sytem f dscree fnit element equations, i.e., an algebraic system. The form of these equa- tions is the same for all nonlinear kinematic structures that...the first phase the solu- tion to the static, prestress configuration is sought. This phase is also referred to as form finding, shape finding, or the...does facilitate stability of the numerical solution. The system of equations, which is the focus of the solution methods presented, is formed by a

Static Flow Characteristics of a Mass Flow Injecting Valve

NASA Technical Reports Server (NTRS)

Mattern, Duane; Paxson, Dan

1995-01-01

A sleeve valve is under development for ground-based forced response testing of air compression systems. This valve will be used to inject air and to impart momentum to the flow inside the first stage of a multi-stage compressor. The valve was designed to deliver a maximum mass flow of 0.22 lbm/s (0.1 kg/s) with a maximum valve throat area of 0.12 sq. in (80 sq. mm), a 100 psid (689 KPA) pressure difference across the valve and a 68 F, (20 C) air supply. It was assumed that the valve mass flow rate would be proportional to the valve orifice area. A static flow calibration revealed a nonlinear valve orifice area to mass flow relationship which limits the maximum flow rate that the valve can deliver. This nonlinearity was found to be caused by multiple choking points in the flow path. A simple model was used to explain this nonlinearity and the model was compared to the static flow calibration data. Only steady flow data is presented here. In this report, the static flow characteristics of a proportionally controlled sleeve valve are modelled and validated against experimental data.

Exact static solutions for discrete phi4 models free of the Peierls-Nabarro barrier: discretized first-integral approach.

PubMed

Dmitriev, S V; Kevrekidis, P G; Yoshikawa, N; Frantzeskakis, D J

2006-10-01

We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Spreight [Nonlinearity 12, 1373 (1999)] and Barashenkov [Phys. Rev. E 72, 035602(R) (2005)], such that they support not only kinks but a one-parameter set of exact static solutions. These solutions can be obtained iteratively from a two-point nonlinear map whose role is played by the discretized first integral of the static Klein-Gordon field, as suggested by Dmitriev [J. Phys. A 38, 7617 (2005)]. We then discuss some discrete phi4 models free of the Peierls-Nabarro barrier and identify for them the full space of available static solutions, including those derived recently by Cooper [Phys. Rev. E 72, 036605 (2005)] but not limited to them. These findings are also relevant to standing wave solutions of discrete nonlinear Schrödinger models. We also study stability of the obtained solutions. As an interesting aside, we derive the list of solutions to the continuum phi4 equation that fill the entire two-dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models.

Development of GENOA Progressive Failure Parallel Processing Software Systems

NASA Technical Reports Server (NTRS)

Abdi, Frank; Minnetyan, Levon

1999-01-01

A capability consisting of software development and experimental techniques has been developed and is described. The capability is integrated into GENOA-PFA to model polymer matrix composite (PMC) structures. The capability considers the physics and mechanics of composite materials and structure by integration of a hierarchical multilevel macro-scale (lamina, laminate, and structure) and micro scale (fiber, matrix, and interface) simulation analyses. The modeling involves (1) ply layering methodology utilizing FEM elements with through-the-thickness representation, (2) simulation of effects of material defects and conditions (e.g., voids, fiber waviness, and residual stress) on global static and cyclic fatigue strengths, (3) including material nonlinearities (by updating properties periodically) and geometrical nonlinearities (by Lagrangian updating), (4) simulating crack initiation. and growth to failure under static, cyclic, creep, and impact loads. (5) progressive fracture analysis to determine durability and damage tolerance. (6) identifying the percent contribution of various possible composite failure modes involved in critical damage events. and (7) determining sensitivities of failure modes to design parameters (e.g., fiber volume fraction, ply thickness, fiber orientation. and adhesive-bond thickness). GENOA-PFA progressive failure analysis is now ready for use to investigate the effects on structural responses to PMC material degradation from damage induced by static, cyclic (fatigue). creep, and impact loading in 2D/3D PMC structures subjected to hygrothermal environments. Its use will significantly facilitate targeting design parameter changes that will be most effective in reducing the probability of a given failure mode occurring.

BEST3D user's manual: Boundary Element Solution Technology, 3-Dimensional Version 3.0

NASA Technical Reports Server (NTRS)

1991-01-01

The theoretical basis and programming strategy utilized in the construction of the computer program BEST3D (boundary element solution technology - three dimensional) and detailed input instructions are provided for the use of the program. An extensive set of test cases and sample problems is included in the manual and is also available for distribution with the program. The BEST3D program was developed under the 3-D Inelastic Analysis Methods for Hot Section Components contract (NAS3-23697). The overall objective of this program was the development of new computer programs allowing more accurate and efficient three-dimensional thermal and stress analysis of hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The BEST3D program allows both linear and nonlinear analysis of static and quasi-static elastic problems and transient dynamic analysis for elastic problems. Calculation of elastic natural frequencies and mode shapes is also provided.

Multibody dynamic simulation of knee contact mechanics

PubMed Central

Bei, Yanhong; Fregly, Benjamin J.

2006-01-01

Multibody dynamic musculoskeletal models capable of predicting muscle forces and joint contact pressures simultaneously would be valuable for studying clinical issues related to knee joint degeneration and restoration. Current three-dimensional multi-body knee models are either quasi-static with deformable contact or dynamic with rigid contact. This study proposes a computationally efficient methodology for combining multibody dynamic simulation methods with a deformable contact knee model. The methodology requires preparation of the articular surface geometry, development of efficient methods to calculate distances between contact surfaces, implementation of an efficient contact solver that accounts for the unique characteristics of human joints, and specification of an application programming interface for integration with any multibody dynamic simulation environment. The current implementation accommodates natural or artificial tibiofemoral joint models, small or large strain contact models, and linear or nonlinear material models. Applications are presented for static analysis (via dynamic simulation) of a natural knee model created from MRI and CT data and dynamic simulation of an artificial knee model produced from manufacturer’s CAD data. Small and large strain natural knee static analyses required 1 min of CPU time and predicted similar contact conditions except for peak pressure, which was higher for the large strain model. Linear and nonlinear artificial knee dynamic simulations required 10 min of CPU time and predicted similar contact force and torque but different contact pressures, which were lower for the nonlinear model due to increased contact area. This methodology provides an important step toward the realization of dynamic musculoskeletal models that can predict in vivo knee joint motion and loading simultaneously. PMID:15564115

A static predictor of seismic demand on frames based on a post-elastic deflected shape

USGS Publications Warehouse

Mori, Y.; Yamanaka, T.; Luco, N.; Cornell, C.A.

2006-01-01

Predictors of seismic structural demands (such as inter-storey drift angles) that are less time-consuming than nonlinear dynamic analysis have proven useful for structural performance assessment and for design. Luco and Cornell previously proposed a simple predictor that extends the idea of modal superposition (of the first two modes) with the square-root-of-sum-of-squares (SRSS) rule by taking a first-mode inelastic spectral displacement into account. This predictor achieved a significant improvement over simply using the response of an elastic oscillator; however, it cannot capture well large displacements caused by local yielding. A possible improvement of Luco's predictor is discussed in this paper, where it is proposed to consider three enhancements: (i) a post-elastic first-mode shape approximated by the deflected shape from a nonlinear static pushover analysis (NSPA) at the step corresponding to the maximum drift of an equivalent inelastic single-degree-of-freedom (SDOF) system, (ii) a trilinear backbone curve for the SDOF system, and (iii) the elastic third-mode response for long-period buildings. Numerical examples demonstrate that the proposed predictor is less biased and results in less dispersion than Luco's original predictor. Copyright ?? 2006 John Wiley & Sons, Ltd.

Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity

NASA Astrophysics Data System (ADS)

Riviere, J.; Guyer, R.; Renaud, G.; TenCate, J. A.; Johnson, P. A.

2012-12-01

In comparison with standard nonlinear ultrasonic methods like frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. This method consists of exciting a sample in Bulk-mode resonance at strains of 10-7 to 10-5 and simultaneously probing with a sequence of high frequency, low amplitude pulses. Time of flight and amplitudes of these pulses, respectively related to nonlinear elastic and dissipative parameters, can be plotted versus vibration strain level. Despite complex nonlinear signatures obtained for most rocks, it can be shown that for low strain amplitude (< 10-6), the nonlinear classical theory issued from a Taylor decomposition can explain the harmonic content. For higher strain, harmonic content becomes richer and the material exhibits more hysteretic behaviors, i.e. strain rate dependencies. Such observations have been made in the past (e.g., Pasqualini et al., JGR 2007), but not with the extreme detail of elasticity provided by DAE. Previous quasi-static measurements made in Berea sandstone (Claytor et al, GRL 2009), show that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate (static limit). Therefore, future work will aim at linking quasi-static and dynamic observations, i.e. the frequency or strain-rate dependence, in order to understand underlying physical phenomena.

PARTICLE FILTERING WITH SEQUENTIAL PARAMETER LEARNING FOR NONLINEAR BOLD fMRI SIGNALS.

PubMed

Xia, Jing; Wang, Michelle Yongmei

Analyzing the blood oxygenation level dependent (BOLD) effect in the functional magnetic resonance imaging (fMRI) is typically based on recent ground-breaking time series analysis techniques. This work represents a significant improvement over existing approaches to system identification using nonlinear hemodynamic models. It is important for three reasons. First, instead of using linearized approximations of the dynamics, we present a nonlinear filtering based on the sequential Monte Carlo method to capture the inherent nonlinearities in the physiological system. Second, we simultaneously estimate the hidden physiological states and the system parameters through particle filtering with sequential parameter learning to fully take advantage of the dynamic information of the BOLD signals. Third, during the unknown static parameter learning, we employ the low-dimensional sufficient statistics for efficiency and avoiding potential degeneration of the parameters. The performance of the proposed method is validated using both the simulated data and real BOLD fMRI data.

The role of nonlinear effects in the propagation of noise from high-power jet aircraft.

PubMed

Gee, Kent L; Sparrow, Victor W; James, Michael M; Downing, J Micah; Hobbs, Christopher M; Gabrielson, Thomas B; Atchley, Anthony A

2008-06-01

To address the question of the role of nonlinear effects in the propagation of noise radiated by high-power jet aircraft, extensive measurements were made of the F-22A Raptor during static engine run-ups. Data were acquired at low-, intermediate-, and high-thrust engine settings with microphones located 23-305 m from the aircraft along several angles. Comparisons between the results of a generalized-Burgers-equation-based nonlinear propagation model and the measurements yield favorable agreement, whereas application of a linear propagation model results in spectral predictions that are much too low at high frequencies. The results and analysis show that significant nonlinear propagation effects occur for even intermediate-thrust engine conditions and at angles well away from the peak radiation angle. This suggests that these effects are likely to be common in the propagation of noise radiated by high-power aircraft.

Analysis of SMA Hybrid Composite Structures in MSC.Nastran and ABAQUS

NASA Technical Reports Server (NTRS)

Turner, Travis L.; Patel, Hemant D.

2005-01-01

A thermoelastic constitutive model for shape memory alloy (SMA) actuators and SMA hybrid composite (SMAHC) structures was recently implemented in the commercial finite element codes MSC.Nastran and ABAQUS. The model may be easily implemented in any code that has the capability for analysis of laminated composite structures with temperature dependent material properties. The model is also relatively easy to use and requires input of only fundamental engineering properties. A brief description of the model is presented, followed by discussion of implementation and usage in the commercial codes. Results are presented from static and dynamic analysis of SMAHC beams of two types; a beam clamped at each end and a cantilever beam. Nonlinear static (post-buckling) and random response analyses are demonstrated for the first specimen. Static deflection (shape) control is demonstrated for the cantilever beam. Approaches for modeling SMAHC material systems with embedded SMA in ribbon and small round wire product forms are demonstrated and compared. The results from the commercial codes are compared to those from a research code as validation of the commercial implementations; excellent correlation is achieved in all cases.

Analysis of SMA Hybrid Composite Structures using Commercial Codes

NASA Technical Reports Server (NTRS)

Turner, Travis L.; Patel, Hemant D.

2004-01-01

A thermomechanical model for shape memory alloy (SMA) actuators and SMA hybrid composite (SMAHC) structures has been recently implemented in the commercial finite element codes MSC.Nastran and ABAQUS. The model may be easily implemented in any code that has the capability for analysis of laminated composite structures with temperature dependent material properties. The model is also relatively easy to use and requires input of only fundamental engineering properties. A brief description of the model is presented, followed by discussion of implementation and usage in the commercial codes. Results are presented from static and dynamic analysis of SMAHC beams of two types; a beam clamped at each end and a cantilevered beam. Nonlinear static (post-buckling) and random response analyses are demonstrated for the first specimen. Static deflection (shape) control is demonstrated for the cantilevered beam. Approaches for modeling SMAHC material systems with embedded SMA in ribbon and small round wire product forms are demonstrated and compared. The results from the commercial codes are compared to those from a research code as validation of the commercial implementations; excellent correlation is achieved in all cases.

Finite Element Analysis of Wrinkled Membrane Structures for Sunshield Applications

NASA Technical Reports Server (NTRS)

Johnston, John D.; Brodeur, Stephen J. (Technical Monitor)

2002-01-01

The deployable sunshield is an example of a gossamer structure envisioned for use on future space telescopes. The basic structure consists of multiple layers of pretensioned, thin-film membranes supported by deployable booms. The prediction and verification of sunshield dynamics has been identified as an area in need of technology development due to the difficulties inherent in predicting nonlinear structural behavior of the membranes and because of the challenges involved. in ground testing of the full-scale structure. This paper describes a finite element analysis of a subscale sunshield that has been subjected to ground testing in support of the Next Generation Space Telescope (NGST) program. The analysis utilizes a nonlinear material model that accounts for wrinkling of the membranes. Results are presented from a nonlinear static preloading analysis and subsequent dynamics analyses to illustrate baseline sunshield structural characteristics. Studies are then described which provide further insight into the effect of membrane. preload on sunshield dynamics and the performance of different membrane modeling techniques. Lastly, a comparison of analytical predictions and ground test results is presented.

Brain signal variability as a window into the bidirectionality between music and language processing: moving from a linear to a nonlinear model

PubMed Central

Hutka, Stefanie; Bidelman, Gavin M.; Moreno, Sylvain

2013-01-01

There is convincing empirical evidence for bidirectional transfer between music and language, such that experience in either domain can improve mental processes required by the other. This music-language relationship has been studied using linear models (e.g., comparing mean neural activity) that conceptualize brain activity as a static entity. The linear approach limits how we can understand the brain’s processing of music and language because the brain is a nonlinear system. Furthermore, there is evidence that the networks supporting music and language processing interact in a nonlinear manner. We therefore posit that the neural processing and transfer between the domains of language and music are best viewed through the lens of a nonlinear framework. Nonlinear analysis of neurophysiological activity may yield new insight into the commonalities, differences, and bidirectionality between these two cognitive domains not measurable in the local output of a cortical patch. We thus propose a novel application of brain signal variability (BSV) analysis, based on mutual information and signal entropy, to better understand the bidirectionality of music-to-language transfer in the context of a nonlinear framework. This approach will extend current methods by offering a nuanced, network-level understanding of the brain complexity involved in music-language transfer. PMID:24454295

Brain signal variability as a window into the bidirectionality between music and language processing: moving from a linear to a nonlinear model.

PubMed

Hutka, Stefanie; Bidelman, Gavin M; Moreno, Sylvain

2013-12-30

There is convincing empirical evidence for bidirectional transfer between music and language, such that experience in either domain can improve mental processes required by the other. This music-language relationship has been studied using linear models (e.g., comparing mean neural activity) that conceptualize brain activity as a static entity. The linear approach limits how we can understand the brain's processing of music and language because the brain is a nonlinear system. Furthermore, there is evidence that the networks supporting music and language processing interact in a nonlinear manner. We therefore posit that the neural processing and transfer between the domains of language and music are best viewed through the lens of a nonlinear framework. Nonlinear analysis of neurophysiological activity may yield new insight into the commonalities, differences, and bidirectionality between these two cognitive domains not measurable in the local output of a cortical patch. We thus propose a novel application of brain signal variability (BSV) analysis, based on mutual information and signal entropy, to better understand the bidirectionality of music-to-language transfer in the context of a nonlinear framework. This approach will extend current methods by offering a nuanced, network-level understanding of the brain complexity involved in music-language transfer.

Non-linear wave interaction in a magnetoplasma column. I - Theory. II Experiment

NASA Technical Reports Server (NTRS)

Larsen, J.-M.; Crawford, F. W.

1979-01-01

The paper presents an analysis of non-linear three-wave interaction for propagation along a cylindrical plasma column surrounded either by a metallic boundary, or by an infinite dielectric, and immersed in an infinite, static, axial magnetic field. An averaged Lagrangian method is used and the results are specialized to parametric amplification and mode conversion, assuming an undepleted pump wave. Computations are presented for a magneto-plasma column surrounded by free space, indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma parameters. In addition, experiments on non-linear mode conversion in a cylindrical magnetoplasma column are described. The results are compared with the theoretical predictions and good qualitative agreement is demonstrated.

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.

Evaluation and Analysis of F-16XL Wind Tunnel Data From Static and Dynamic Tests

NASA Technical Reports Server (NTRS)

Kim, Sungwan; Murphy, Patrick C.; Klein, Vladislav

2004-01-01

A series of wind tunnel tests were conducted in the NASA Langley Research Center as part of an ongoing effort to develop and test mathematical models for aircraft rigid-body aerodynamics in nonlinear unsteady flight regimes. Analysis of measurement accuracy, especially for nonlinear dynamic systems that may exhibit complicated behaviors, is an essential component of this ongoing effort. In this report, tools for harmonic analysis of dynamic data and assessing measurement accuracy are presented. A linear aerodynamic model is assumed that is appropriate for conventional forced-oscillation experiments, although more general models can be used with these tools. Application of the tools to experimental data is demonstrated and results indicate the levels of uncertainty in output measurements that can arise from experimental setup, calibration procedures, mechanical limitations, and input errors.

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.

Hydrostatic Stress Effects Incorporated Into the Analysis of the High-Strain-Rate Deformation of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.

2003-01-01

Procedures for modeling the effect of high strain rate on composite materials are needed for designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and strain rate dependence of the composite response is primarily due to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. An experimental program has been carried out through a university grant with the Ohio State University to obtain tensile and shear deformation data for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. This information has been used at the NASA Glenn Research Center to develop, characterize, and correlate a material model in which the strain rate dependence and nonlinearity (including hydrostatic stress effects) of the polymer are correctly analyzed. To obtain the material data, Glenn s researchers designed and fabricated test specimens of a representative toughened epoxy resin. Quasi-static tests at low strain rates and split Hopkinson bar tests at high strain rates were then conducted at the Ohio State University. The experimental data confirmed the strong effects of strain rate on both the tensile and shear deformation of the polymer. For the analytical model, Glenn researchers modified state variable constitutive equations previously used for the viscoplastic analysis of metals to allow for the analysis of the nonlinear, strain-rate-dependent polymer deformation. Specifically, we accounted for the effects of hydrostatic stresses. An important discovery in the course of this work was that the hydrostatic stress effects varied during the loading process, which needed to be accounted for within the constitutive equations. The model is characterized primarily by shear data, with tensile data used to characterize the hydrostatic stress effects.

Macroscopic Lagrangian description of warm plasmas. II Nonlinear wave interactions

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1983-01-01

A macroscopic Lagrangian is simplified to the adiabatic limit and expanded about equilibrium, to third order in perturbation, for three illustrative cases: one-dimensional compression parallel to the static magnetic field, two-dimensional compression perpendicular to the static magnetic field, and three-dimensional compression. As examples of the averaged-Lagrangian method applied to nonlinear wave interactions, coupling coefficients are derived for interactions between two electron plasma waves and an ion acoustic wave, and between an ordinary wave, an electron plasma wave, and an ion acoustic wave.

Singularity-free solutions for anisotropic charged fluids with Chaplygin equation of state

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

Rahaman, Farook; Ray, Saibal; Jafry, Abdul Kayum

2010-11-15

We extend the Krori-Barua analysis of the static, spherically symmetric, Einstein-Maxwell field equations and consider charged fluid sources with anisotropic stresses. The inclusion of a new variable (tangential pressure) allows the use of a nonlinear, Chaplygin-type equation of state with coefficients fixed by the matching conditions at the boundary of the source. Some physical features are briefly discussed.

Seismic assessment of WSDOT bridges with prestressed hollow core piles : part II.

DOT National Transportation Integrated Search

2009-12-01

This report investigates the seismic performance of a reinforced concrete : bridge with prestressed hollow core piles. Both nonlinear static and nonlinear dynamic : analyses were carried out. A three-dimensional spine model of the bridge was : ...

Protein Aggregation/Folding: The Role of Deterministic Singularities of Sequence Hydrophobicity as Determined by Nonlinear Signal Analysis of Acylphosphatase and Aβ(1–40)

PubMed Central

Zbilut, Joseph P.; Colosimo, Alfredo; Conti, Filippo; Colafranceschi, Mauro; Manetti, Cesare; Valerio, MariaCristina; Webber, Charles L.; Giuliani, Alessandro

2003-01-01

The problem of protein folding vs. aggregation was investigated in acylphosphatase and the amyloid protein Aβ(1–40) by means of nonlinear signal analysis of their chain hydrophobicity. Numerical descriptors of recurrence patterns provided the basis for statistical evaluation of folding/aggregation distinctive features. Static and dynamic approaches were used to elucidate conditions coincident with folding vs. aggregation using comparisons with known protein secondary structure classifications, site-directed mutagenesis studies of acylphosphatase, and molecular dynamics simulations of amyloid protein, Aβ(1–40). The results suggest that a feature derived from principal component space characterized by the smoothness of singular, deterministic hydrophobicity patches plays a significant role in the conditions governing protein aggregation. PMID:14645049

Application of a transonic potential flow code to the static aeroelastic analysis of three-dimensional wings

NASA Technical Reports Server (NTRS)

Whitlow, W., Jr.; Bennett, R. M.

1982-01-01

Since the aerodynamic theory is nonlinear, the method requires the coupling of two iterative processes - an aerodynamic analysis and a structural analysis. A full potential analysis code, FLO22, is combined with a linear structural analysis to yield aerodynamic load distributions on and deflections of elastic wings. This method was used to analyze an aeroelastically-scaled wind tunnel model of a proposed executive-jet transport wing and an aeroelastic research wing. The results are compared with the corresponding rigid-wing analyses, and some effects of elasticity on the aerodynamic loading are noted.

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.

The second– and third– order nonlinear optical properties and electronic transition of a NLO chromophore: A DFT study

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

Altürk, Sümeyye, E-mail: sumeyye-alturk@hotmail.com; Avci, Davut, E-mail: davci@sakarya.edu.tr; Tamer, Ömer, E-mail: omertamer@sakarya.edu.tr

2016-03-25

It is well known that the practical applications of second-order and third-order nonlinear optical (NLO) materials have been reported in modern technology, such as optical data processing, transmission and storage, etc. In this respect, the linear and nonlinear optical parameters (the molecular static polarizability (α), and the first–order static hyperpolarizability (β{sub 0}), the second–order static hyperpolarizability (γ)), UV-vis spectra and HOMO and LUMO energies of 2-(1′-(4’’’-Methoxyphenyl)-5′-(thien-2″-yl)pyrrol-2′-yl)-1,3-benzothiazole were investigated by using the HSEh1PBE/6–311G(d,p) level of density functional theory. The UV–vis spectra were simulated using TD/HSEh1PBE/6– 311G(d,p) level, and the major contributions to the electronic transitions were obtained. The molecular hardness (η)more » and electronegativity (χ) parameters were also obtained by using molecular frontier orbital energies. The NLO parameters of the title compound were calculated, and obtained data were compared with that of para-Nitroaniline (pNA) which is a typical NLO material and the corresponding experimental data. Obtained data of the chromosphere display significant molecular second-and third-nonlinearity.« less

Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

DOE PAGES

Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; ...

2015-09-15

Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinearmore » normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.« less

Piezoelectric control of columns prone to instabilities and nonlinear modal interaction

NASA Astrophysics Data System (ADS)

Sridharan, Srinivasan; Kim, Sunjung

2008-06-01

This paper attempts to unravel the issues of piezoelectric control of structures prone to nonlinear static and dynamic instabilities. A simple yet typical example is considered, namely the problem of a simply supported axially compressed imperfect column on an elastic softening foundation. Here the significant nonlinearity arises from the softening foundation. The column is so designed as to have coincident critical loads for the first two modes of buckling. Piezoelectric actuators/sensors are deemed to be attached to a column in regions of maximum strain at several locations along the length of the column. The issues involved in (i) enhancing the static buckling load, (ii) suppression of vibrations as the column is compressed to a load close to its dynamic instability load and (iii) enhancing the dynamic instability load are investigated and discussed. It is shown that there is a premium price to pay for enhancing the buckling capacity of the column, be it static or dynamic. The paper concludes by alluding to the possibility of a failure of patch control if a higher-order shortwave mode happens to be the governing principal mode of the structure.

Water impact analysis of space shuttle solid rocket motor by the finite element method

NASA Technical Reports Server (NTRS)

Buyukozturk, O.; Hibbitt, H. D.; Sorensen, E. P.

1974-01-01

Preliminary analysis showed that the doubly curved triangular shell elements were too stiff for these shell structures. The doubly curved quadrilateral shell elements were found to give much improved results. A total of six load cases were analyzed in this study. The load cases were either those resulting from a static test using reaction straps to simulate the drop conditions or under assumed hydrodynamic conditions resulting from a drop test. The latter hydrodynamic conditions were obtained through an emperical fit of available data. Results obtained from a linear analysis were found to be consistent with results obtained elsewhere with NASTRAN and BOSOR. The nonlinear analysis showed that the originally assumed loads would result in failure of the shell structures. The nonlinear analysis also showed that it was useful to apply internal pressure as a stabilizing influence on collapse. A final analysis with an updated estimate of load conditions resulted in linear behavior up to full load.

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

DOE PAGES

Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; ...

2016-01-25

We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. Formore » weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.« less

Nonlinear mechanics of non-rigid origami: an efficient computational approach

NASA Astrophysics Data System (ADS)

Liu, K.; Paulino, G. H.

2017-10-01

Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on `bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.

Nonlinear mechanics of non-rigid origami: an efficient computational approach.

PubMed

Liu, K; Paulino, G H

2017-10-01

Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on 'bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.

Effect of nonideal square-law detection on static calibration in noise-injection radiometers

NASA Technical Reports Server (NTRS)

Hearn, C. P.

1984-01-01

The effect of nonideal square-law detection on the static calibration for a class of Dicke radiometers is examined. It is shown that fourth-order curvature in the detection characteristic adds a nonlinear term to the linear calibration relationship normally ascribed to noise-injection, balanced Dicke radiometers. The minimum error, based on an optimum straight-line fit to the calibration curve, is derived in terms of the power series coefficients describing the input-output characteristics of the detector. These coefficients can be determined by simple measurements, and detection nonlinearity is, therefore, quantitatively related to radiometric measurement error.

Frequency, pressure and strain dependence of nonlinear elasticity in Berea Sandstone

DOE PAGES

Riviere, Jacques; Johnson, Paul Allan; Marone, Chris; ...

2016-04-14

Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static ( f → 0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2–3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1fmore » appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. Furthermore, these findings can be used to improve theories relating the macroscopic elastic response to microstructural features.« less

Application of triggered lightning numerical models to the F106B and extension to other aircraft

NASA Technical Reports Server (NTRS)

Ng, Poh H.; Dalke, Roger A.; Horembala, Jim; Rudolph, Terence; Perala, Rodney A.

1988-01-01

The goal of the F106B Thunderstorm Research Program is to characterize the lightning environment for aircraft in flight. This report describes the application of numerical electromagnetic models to this problem. Topics include: (1) Extensive application of linear triggered lightning to F106B data; (2) Electrostatic analysis of F106B field mill data; (3) Application of subgrid modeling to F106B nose region, including both static and nonlinear models; (4) Extension of F106B results to other aircraft of varying sizes and shapes; and (5) Application of nonlinear model to interaction of F106B with lightning leader-return stroke event.

Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations

NASA Astrophysics Data System (ADS)

Sotoudeh, Zahra

2011-07-01

Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.

Characteristic study of head-on collision of dust-ion acoustic solitons of opposite polarity with kappa distributed electrons

NASA Astrophysics Data System (ADS)

Parveen, Shahida; Mahmood, Shahzad; Adnan, Muhammad; Qamar, Anisa

2016-09-01

The head on collision between two dust ion acoustic (DIA) solitary waves, propagating in opposite directions, is studied in an unmagnetized plasma constituting adiabatic ions, static dust charged (positively/negatively) grains, and non-inertial kappa distributed electrons. In the linear limit, the dispersion relation of the dust ion acoustic (DIA) solitary wave is obtained using the Fourier analysis. For studying characteristic head-on collision of DIA solitons, the extended Poincaré-Lighthill-Kuo method is employed to obtain Korteweg-de Vries (KdV) equations with quadratic nonlinearities and investigated the phase shifts in their trajectories after the interaction. It is revealed that only compressive solitary waves can exist for the positive dust charged concentrations while for negative dust charge concentrations both the compressive and rarefactive solitons can propagate in such dusty plasma. It is found that for specific sets of plasma parameters, the coefficient of nonlinearity disappears in the KdV equation for the negative dust charged grains. Therefore, the modified Korteweg-de Vries (mKdV) equations with cubic nonlinearity coefficient, and their corresponding phase shift and trajectories, are also derived for negative dust charged grains plasma at critical composition. The effects of different plasma parameters such as superthermality, concentration of positively/negatively static dust charged grains, and ion to electron temperature ratio on the colliding soliton profiles and their corresponding phase shifts are parametrically examined.

Structural Finite Element Model Updating Using Vibration Tests and Modal Analysis for NPL footbridge - SHM demonstrator

NASA Astrophysics Data System (ADS)

Barton, E.; Middleton, C.; Koo, K.; Crocker, L.; Brownjohn, J.

2011-07-01

This paper presents the results from collaboration between the National Physical Laboratory (NPL) and the University of Sheffield on an ongoing research project at NPL. A 50 year old reinforced concrete footbridge has been converted to a full scale structural health monitoring (SHM) demonstrator. The structure is monitored using a variety of techniques; however, interrelating results and converting data to knowledge are not possible without a reliable numerical model. During the first stage of the project, the work concentrated on static loading and an FE model of the undamaged bridge was created, and updated, under specified static loading and temperature conditions. This model was found to accurately represent the response under static loading and it was used to identify locations for sensor installation. The next stage involves the evaluation of repair/strengthening patches under both static and dynamic loading. Therefore, before deliberately introducing significant damage, the first set of dynamic tests was conducted and modal properties were estimated. The measured modal properties did not match the modal analysis from the statically updated FE model; it was clear that the existing model required updating. This paper introduces the results of the dynamic testing and model updating. It is shown that the structure exhibits large non-linear, amplitude dependant characteristics. This creates a difficult updating process, but we attempt to produce the best linear representation of the structure. A sensitivity analysis is performed to determine the most sensitive locations for planned damage/repair scenarios and is used to decide whether additional sensors will be necessary.

A Stewart isolator with high-static-low-dynamic stiffness struts based on negative stiffness magnetic springs

NASA Astrophysics Data System (ADS)

Zheng, Yisheng; Li, Qingpin; Yan, Bo; Luo, Yajun; Zhang, Xinong

2018-05-01

In order to improve the isolation performance of passive Stewart platforms, the negative stiffness magnetic spring (NSMS) is employed to construct high static low dynamic stiffness (HSLDS) struts. With the NSMS, the resonance frequencies of the platform can be reduced effectively without deteriorating its load bearing capacity. The model of the Stewart isolation platform with HSLDS struts is presented and the stiffness characteristic of its struts is studied firstly. Then the nonlinear dynamic model of the platform including both geometry nonlinearity and stiffness nonlinearity is established; and its simplified dynamic model is derived under the condition of small vibration. The effect of nonlinearity on the isolation performance is also evaluated. Finally, a prototype is built and the isolation performance is tested. Both simulated and experimental results demonstrate that, by using the NSMS, the resonance frequencies of the Stewart isolator are reduced and the isolation performance in all six directions is improved: the isolation frequency band is increased and extended to a lower-frequency level.

Verification of elastic-wave static displacement in solids. [using ultrasonic techniques on Ge single crystals

NASA Technical Reports Server (NTRS)

Cantrell, J. H., Jr.; Winfree, W. P.

1980-01-01

The solution of the nonlinear differential equation which describes an initially sinusoidal finite-amplitude elastic wave propagating in a solid contains a static-displacement term in addition to the harmonic terms. The static-displacement amplitude is theoretically predicted to be proportional to the product of the squares of the driving-wave amplitude and the driving-wave frequency. The first experimental verification of the elastic-wave static displacement in a solid (the 111 direction of single-crystal germanium) is reported, and agreement is found with the theoretical predictions.

Study of solution procedures for nonlinear structural equations

NASA Technical Reports Server (NTRS)

Young, C. T., II; Jones, R. F., Jr.

1980-01-01

A method for the redution of the cost of solution of large nonlinear structural equations was developed. Verification was made using the MARC-STRUC structure finite element program with test cases involving single and multiple degrees of freedom for static geometric nonlinearities. The method developed was designed to exist within the envelope of accuracy and convergence characteristic of the particular finite element methodology used.

Static Methods in the Design of Nonlinear Automatic Control Systems,

DTIC Science & Technology

1984-06-27

227 Chapter VI. Ways of Decrease of the Number of Statistical Nodes During the Research of Nonlinear Systems...at present occupies the central place. This region of research was called the statistical dynamics of nonlinear H automatic control systems...receives further development in the numerous research of Soviet and C foreign scientists. Special role in the development of the statistical dynamics of

Do nonlinear dynamics in economics amount to a Kuhnian paradigm shift?

PubMed

Dore, Mohammed H I; Rosser, J Barkley

2007-01-01

Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity can only increase the Kuhnian anomalies. This crisis can only deepen. However, there is an ideological commitment to general equilibrium that justifies "free enterprise" with only minimal state intervention that may still sustain neoclassical economics despite the growing evidence of Kuhnian anomalies. Thus, orthodox textbook theory continues to ignore this fact and static neoclassical theory remains a dogma with no apparent reformulation to replace it.

The YAV-8B simulation and modeling. Volume 2: Program listing

NASA Technical Reports Server (NTRS)

1983-01-01

Detailed mathematical models of varying complexity representative of the YAV-8B aircraft are defined and documented. These models are used in parameter estimation and in linear analysis computer programs while investigating YAV-8B aircraft handling qualities. Both a six degree of freedom nonlinear model and a linearized three degree of freedom longitudinal and lateral directional model were developed. The nonlinear model is based on the mathematical model used on the MCAIR YAV-8B manned flight simulator. This simulator model has undergone periodic updating based on the results of approximately 360 YAV-8B flights and 8000 hours of wind tunnel testing. Qualified YAV-8B flight test pilots have commented that the handling qualities characteristics of the simulator are quite representative of the real aircraft. These comments are validated herein by comparing data from both static and dynamic flight test maneuvers to the same obtained using the nonlinear program.

Analysis and modeling of a family of two-transistor parallel inverters

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1973-01-01

A family of five static dc-to-square-wave inverters, each employing a square-loop magnetic core in conjunction with two switching transistors, is analyzed using piecewise-linear models for the nonlinear characteristics of the transistors, diodes, and saturable-core devices. Four of the inverters are analyzed in detail for the first time. These analyses show that, by proper choice of a frame of reference, each of the five quite differently appearing inverter circuits can be described by a common equivalent circuit. This equivalent circuit consists of a five-segment nonlinear resistor, a nonlinear saturable reactor, and a linear capacitor. Thus, by proper interpretation and identification of the parameters in the different circuits, the results of a detailed solution for one of the inverter circuits provide similar information and insight into the local and global behavior of each inverter in the family.

Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft

NASA Astrophysics Data System (ADS)

Patil, Mayuresh Jayawant

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

The analysis and large-angle control of a flexible beam using an adaptive truss

NASA Technical Reports Server (NTRS)

Warrington, Thomas J.; Clark, William W.; Robertshaw, Harry H.; Horner, C. Garnett

1991-01-01

This preliminary study of an adaptive truss slewing problem investigates the static positioning of an adaptive truss at slewed orientations and the dynamic vibrations of an attached flexible beam. A nonlinear model of an adaptive truss and flexible beam is derived. Linear control laws are developed and simulated for various truss configurations. Results show the linear control laws developed at a slewed configuration perform best at that configuration.

Analysis of shell type structures subjected to time dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1985-01-01

A general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads is considered. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and ratchetting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model.

Multidirectional In Vivo Characterization of Skin Using Wiener Nonlinear Stochastic System Identification Techniques.

PubMed

Parker, Matthew D; Jones, Lynette A; Hunter, Ian W; Taberner, A J; Nash, M P; Nielsen, P M F

2017-01-01

A triaxial force-sensitive microrobot was developed to dynamically perturb skin in multiple deformation modes, in vivo. Wiener static nonlinear identification was used to extract the linear dynamics and static nonlinearity of the force-displacement behavior of skin. Stochastic input forces were applied to the volar forearm and thenar eminence of the hand, producing probe tip perturbations in indentation and tangential extension. Wiener static nonlinear approaches reproduced the resulting displacements with variances accounted for (VAF) ranging 94-97%, indicating a good fit to the data. These approaches provided VAF improvements of 0.1-3.4% over linear models. Thenar eminence stiffness measures were approximately twice those measured on the forearm. Damping was shown to be significantly higher on the palm, whereas the perturbed mass typically was lower. Coefficients of variation (CVs) for nonlinear parameters were assessed within and across individuals. Individual CVs ranged from 2% to 11% for indentation and from 2% to 19% for extension. Stochastic perturbations with incrementally increasing mean amplitudes were applied to the same test areas. Differences between full-scale and incremental reduced-scale perturbations were investigated. Different incremental preloading schemes were investigated. However, no significant difference in parameters was found between different incremental preloading schemes. Incremental schemes provided depth-dependent estimates of stiffness and damping, ranging from 300 N/m and 2 Ns/m, respectively, at the surface to 5 kN/m and 50 Ns/m at greater depths. The device and techniques used in this research have potential applications in areas, such as evaluating skincare products, assessing skin hydration, or analyzing wound healing.

Tuning diagonal components of static linear and first nonlinear polarizabilities of doped quantum dots by Gaussian white noise

NASA Astrophysics Data System (ADS)

Ganguly, Jayanta; Ghosh, Manas

2015-07-01

We investigate the modulation of diagonal components of static linear (αxx, αyy) and first nonlinear (βxxx, βyyy) polarizabilities of quantum dots by Gaussian white noise. Quantum dot is doped with impurity represented by a Gaussian potential and repulsive in nature. The study reveals the importance of mode of application of noise (additive/multiplicative) on the polarizability components. The doped system is further exposed to a static external electric field of given intensity. As important observation we have found that the strength of additive noise becomes unable to influence the polarizability components. However, the multiplicative noise influences them conspicuously and gives rise to additional interesting features. Multiplicative noise even enhances the magnitude of the polarizability components immensely. The present investigation deems importance in view of the fact that noise seriously affects the optical properties of doped quantum dot devices.

Pushover analysis of reinforced concrete frames considering shear failure at beam-column joints

NASA Astrophysics Data System (ADS)

Sung, Y. C.; Lin, T. K.; Hsiao, C. C.; Lai, M. C.

2013-09-01

Since most current seismic capacity evaluations of reinforced concrete (RC) frame structures are implemented by either static pushover analysis (PA) or dynamic time history analysis, with diverse settings of the plastic hinges (PHs) on such main structural components as columns, beams and walls, the complex behavior of shear failure at beam-column joints (BCJs) during major earthquakes is commonly neglected. This study proposes new nonlinear PA procedures that consider shear failure at BCJs and seek to assess the actual damage to RC structures. Based on the specifications of FEMA-356, a simplified joint model composed of two nonlinear cross struts placed diagonally over the location of the plastic hinge is established, allowing a sophisticated PA to be performed. To verify the validity of this method, the analytical results for the capacity curves and the failure mechanism derived from three different full-size RC frames are compared with the experimental measurements. By considering shear failure at BCJs, the proposed nonlinear analytical procedures can be used to estimate the structural behavior of RC frames, including seismic capacity and the progressive failure sequence of joints, in a precise and effective manner.

Perturbations of the Richardson number field by gravity waves

NASA Technical Reports Server (NTRS)

Wurtele, M. G.; Sharman, R. D.

1985-01-01

An analytic solution is presented for a stratified fluid of arbitrary constant Richardson number. By computer aided analysis the perturbation fields, including that of the Richardson number can be calculated. The results of the linear analytic model were compared with nonlinear simulations, leading to the following conclusions: (1) the perturbations in the Richardson number field, when small, are produced primarily by the perturbations of the shear; (2) perturbations of in the Richardson number field, even when small, are not symmetric, the increase being significantly larger than the decrease (the linear analytic solution and the nonlinear simulations both confirm this result); (3) as the perturbations grow, this asymmetry increases, but more so in the nonlinear simulations than in the linear analysis; (4) for large perturbations of the shear flow, the static stability, as represented by N2, is the dominating mechanism, becoming zero or negative, and producing convective overturning; and (5) the convectional measure of linearity in lee wave theory, NH/U, is no longer the critical parameter (it is suggested that (H/u sub 0) (du sub 0/dz) takes on this role in a shearing flow).

A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics

NASA Technical Reports Server (NTRS)

Ozguven, H. Nevzat

1991-01-01

A six-degree-of-freedom nonlinear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the nonlinear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the 'static transmission error method' developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.

Static Aeroelastic Analysis with an Inviscid Cartesian Method

NASA Technical Reports Server (NTRS)

Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.

2014-01-01

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Investigation of the Finite Element Software Packages at KSC

NASA Technical Reports Server (NTRS)

Lu, Chu-Ho

1991-01-01

The useful and powerful features of NASTRAN and three real world problems for the testing of the capabilities of different NASTRAN versions are discussed. The test problems involve direct transient analysis, nonlinear analysis, and static analysis. The experiences in using graphics software packages are also discussed. It was found that MSC/XL can be more useful if it can be improved to generate picture files of the analysis results and to extend its capabilities to support finite element codes other than MSC/NASTRAN. It was found that the current version of SDRC/I-DEAS (version VI) may have bugs in the module 'Data Loader'.

Aeroelastic optimization methodology for viscous and turbulent flows

NASA Astrophysics Data System (ADS)

Barcelos Junior, Manuel Nascimento Dias

2007-12-01

In recent years, the development of faster computers and parallel processing allowed the application of high-fidelity analysis methods to the aeroelastic design of aircraft. However, these methods are restricted to the final design verification, mainly due to the computational cost involved in iterative design processes. Therefore, this work is concerned with the creation of a robust and efficient aeroelastic optimization methodology for inviscid, viscous and turbulent flows by using high-fidelity analysis and sensitivity analysis techniques. Most of the research in aeroelastic optimization, for practical reasons, treat the aeroelastic system as a quasi-static inviscid problem. In this work, as a first step toward the creation of a more complete aeroelastic optimization methodology for realistic problems, an analytical sensitivity computation technique was developed and tested for quasi-static aeroelastic viscous and turbulent flow configurations. Viscous and turbulent effects are included by using an averaged discretization of the Navier-Stokes equations, coupled with an eddy viscosity turbulence model. For quasi-static aeroelastic problems, the traditional staggered solution strategy has unsatisfactory performance when applied to cases where there is a strong fluid-structure coupling. Consequently, this work also proposes a solution methodology for aeroelastic and sensitivity analyses of quasi-static problems, which is based on the fixed point of an iterative nonlinear block Gauss-Seidel scheme. The methodology can also be interpreted as the solution of the Schur complement of the aeroelastic and sensitivity analyses linearized systems of equations. The methodologies developed in this work are tested and verified by using realistic aeroelastic systems.

Experimental evaluation of four ground-motion scaling methods for dynamic response-history analysis of nonlinear structures

USGS Publications Warehouse

O'Donnell, Andrew P.; Kurama, Yahya C.; Kalkan, Erol; Taflanidis, Alexandros A.

2017-01-01

This paper experimentally evaluates four methods to scale earthquake ground-motions within an ensemble of records to minimize the statistical dispersion and maximize the accuracy in the dynamic peak roof drift demand and peak inter-story drift demand estimates from response-history analyses of nonlinear building structures. The scaling methods that are investigated are based on: (1) ASCE/SEI 7–10 guidelines; (2) spectral acceleration at the fundamental (first mode) period of the structure, Sa(T1); (3) maximum incremental velocity, MIV; and (4) modal pushover analysis. A total of 720 shake-table tests of four small-scale nonlinear building frame specimens with different static and dynamic characteristics are conducted. The peak displacement demands from full suites of 36 near-fault ground-motion records as well as from smaller “unbiased” and “biased” design subsets (bins) of ground-motions are included. Out of the four scaling methods, ground-motions scaled to the median MIV of the ensemble resulted in the smallest dispersion in the peak roof and inter-story drift demands. Scaling based on MIValso provided the most accurate median demands as compared with the “benchmark” demands for structures with greater nonlinearity; however, this accuracy was reduced for structures exhibiting reduced nonlinearity. The modal pushover-based scaling (MPS) procedure was the only method to conservatively overestimate the median drift demands.

A Simple Bimodular Nonlinear Element

NASA Astrophysics Data System (ADS)

Mikhailov, S. G.; Rudenko, O. V.

2018-05-01

We have studied the dynamics of an artificial nonlinear element representing a flexible membrane with oscillation limiters and a static pressing force. Such an element has the property of "bimodularity" and demonstrates "modular" nonlinearity. We have constructed a mathematical model that describes these oscillations. Their shapes have been calculated. We follow the analogy with a classical object—Galileo's pendulum. We demonstrate that for a low-frequency excitation of the membrane, the level of the harmonics in the spectrum is higher than in the vicinity of the resonance frequency. We have established a strong dependence of the level of the harmonics on the magnitude of the pressing force for a weak perturbation. We propose a design scheme for a device in the quasi-static approximation possessing the property of bimodularity. We perform an experiment that confirms its operability. We show a qualitative coincidence of the experimental results and calculations when detecting an amplitude-modulated signal.

A Procedure for 3-D Contact Stress Analysis of Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Kumar, A.; Bibel, G.

1994-01-01

Contact stress distribution of spiral bevel gears using nonlinear finite element static analysis is presented. Procedures have been developed to solve the nonlinear equations that identify the gear and pinion surface coordinates based on the kinematics of the cutting process and orientate the pinion and the gear in space to mesh with each other. Contact is simulated by connecting GAP elements along the intersection of a line from each pinion point (parallel to the normal at the contact point) with the gear surface. A three dimensional model with four gear teeth and three pinion teeth is used to determine the contact stresses at two different contact positions in a spiral bevel gearset. A summary of the elliptical contact stress distribution is given. This information will be helpful to helicopter and aircraft transmission designers who need to minimize weight of the transmission and maximize reliability.

Nonlinear Pressurization and Modal Analysis Procedure for Dynamic Modeling of Inflatable Structures

NASA Technical Reports Server (NTRS)

Smalley, Kurt B.; Tinker, Michael L.; Saxon, Jeff (Technical Monitor)

2002-01-01

An introduction and set of guidelines for finite element dynamic modeling of nonrigidized inflatable structures is provided. A two-step approach is presented, involving 1) nonlinear static pressurization of the structure and updating of the stiffness matrix and 2) hear normal modes analysis using the updated stiffness. Advantages of this approach are that it provides physical realism in modeling of pressure stiffening, and it maintains the analytical convenience of a standard bear eigensolution once the stiffness has been modified. Demonstration of the approach is accomplished through the creation and test verification of an inflated cylinder model using a large commercial finite element code. Good frequency and mode shape comparisons are obtained with test data and previous modeling efforts, verifying the accuracy of the technique. Problems encountered in the application of the approach, as well as their solutions, are discussed in detail.

Static aeroelastic analysis and tailoring of missile control fins

NASA Technical Reports Server (NTRS)

Mcintosh, S. C., Jr.; Dillenius, M. F. E.

1989-01-01

A concept for enhancing the design of control fins for supersonic tactical missiles is described. The concept makes use of aeroelastic tailoring to create fin designs (for given planforms) that limit the variations in hinge moments that can occur during maneuvers involving high load factors and high angles of attack. It combines supersonic nonlinear aerodynamic load calculations with finite-element structural modeling, static and dynamic structural analysis, and optimization. The problem definition is illustrated. The fin is at least partly made up of a composite material. The layup is fixed, and the orientations of the material principal axes are allowed to vary; these are the design variables. The objective is the magnitude of the difference between the chordwise location of the center of pressure and its desired location, calculated for a given flight condition. Three types of constraints can be imposed: upper bounds on static displacements for a given set of load conditions, lower bounds on specified natural frequencies, and upper bounds on the critical flutter damping parameter at a given set of flight speeds and altitudes. The idea is to seek designs that reduce variations in hinge moments that would otherwise occur. The block diagram describes the operation of the computer program that accomplishes these tasks. There is an option for a single analysis in addition to the optimization.

Examination of the Nonlinear Dynamic Systems Associated with Science Student Cognition While Engaging in Science Information Processing

ERIC Educational Resources Information Center

Lamb, Richard; Cavagnetto, Andy; Akmal, Tariq

2016-01-01

A critical problem with the examination of learning in education is that there is an underlying assumption that the dynamic systems associated with student information processing can be measured using static linear assessments. This static linear approach does not provide sufficient ability to characterize learning. Much of the modern research…

Unsteady slip flow of Carreau nanofluid over a wedge with nonlinear radiation and new mass flux condition

NASA Astrophysics Data System (ADS)

Khan, M.; Azam, M.; Alshomrani, A. S.

This article addresses a numerical investigation for the unsteady 2D slip flow of Carreau nanofluid past a static and/or moving wedge with the nonlinear radiation. A zero nanoparticle mass flux and convective boundary conditions are implemented. Further, the most recently devised model for nanofluid is adopted that incorporates the effects of Brownian motion and thermophoresis. A set of suitable transformation is demonstrated to alter the nonlinear partial differential equations into nonlinear ordinary differential equations and then tackled numerically by employing bvp4c in Matlab package. The numerical computations for the wall heat flux (Nusselt number) and wall mass flux (Sherwood number) are also performed. Effects of several controlling parameters on the velocity, temperature and nanoparticles concentration are explored and discussed in detail. Our study reveals that the temperature and the associated thermal boundary layer thickness are enhancing function of the temperature ratio parameter for both shear thickening and shear thinning fluids. Moreover, it is noticed that the velocity in case of moving wedge is higher than static wedge.

Global strength assessment in oblique waves of a large gas carrier ship, based on a non-linear iterative method

NASA Astrophysics Data System (ADS)

Domnisoru, L.; Modiga, A.; Gasparotti, C.

2016-08-01

At the ship's design, the first step of the hull structural assessment is based on the longitudinal strength analysis, with head wave equivalent loads by the ships' classification societies’ rules. This paper presents an enhancement of the longitudinal strength analysis, considering the general case of the oblique quasi-static equivalent waves, based on the own non-linear iterative procedure and in-house program. The numerical approach is developed for the mono-hull ships, without restrictions on 3D-hull offset lines non-linearities, and involves three interlinked iterative cycles on floating, pitch and roll trim equilibrium conditions. Besides the ship-wave equilibrium parameters, the ship's girder wave induced loads are obtained. As numerical study case we have considered a large LPG liquefied petroleum gas carrier. The numerical results of the large LPG are compared with the statistical design values from several ships' classification societies’ rules. This study makes possible to obtain the oblique wave conditions that are inducing the maximum loads into the large LPG ship's girder. The numerical results of this study are pointing out that the non-linear iterative approach is necessary for the computation of the extreme loads induced by the oblique waves, ensuring better accuracy of the large LPG ship's longitudinal strength assessment.

Closed-form solution for static pull-in voltage of electrostatically actuated clamped-clamped micro/nano beams under the effect of fringing field and van der Waals force

NASA Astrophysics Data System (ADS)

Bhojawala, V. M.; Vakharia, D. P.

2017-12-01

This investigation provides an accurate prediction of static pull-in voltage for clamped-clamped micro/nano beams based on distributed model. The Euler-Bernoulli beam theory is used adapting geometric non-linearity of beam, internal (residual) stress, van der Waals force, distributed electrostatic force and fringing field effects for deriving governing differential equation. The Galerkin discretisation method is used to make reduced-order model of the governing differential equation. A regime plot is presented in the current work for determining the number of modes required in reduced-order model to obtain completely converged pull-in voltage for micro/nano beams. A closed-form relation is developed based on the relationship obtained from curve fitting of pull-in instability plots and subsequent non-linear regression for the proposed relation. The output of regression analysis provides Chi-square (χ 2) tolerance value equals to 1  ×  10-9, adjusted R-square value equals to 0.999 29 and P-value equals to zero, these statistical parameters indicate the convergence of non-linear fit, accuracy of fitted data and significance of the proposed model respectively. The closed-form equation is validated using available data of experimental and numerical results. The relative maximum error of 4.08% in comparison to several available experimental and numerical data proves the reliability of the proposed closed-form equation.

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

NASA Technical Reports Server (NTRS)

Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.

1991-01-01

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

Nonlinear Large Deflection Theory with Modified Aeroelastic Lifting Line Aerodynamics for a High Aspect Ratio Flexible Wing

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric; Chaparro, Daniel

2017-01-01

This paper investigates the effect of nonlinear large deflection bending on the aerodynamic performance of a high aspect ratio flexible wing. A set of nonlinear static aeroelastic equations are derived for the large bending deflection of a high aspect ratio wing structure. An analysis is conducted to compare the nonlinear bending theory with the linear bending theory. The results show that the nonlinear bending theory is length-preserving whereas the linear bending theory causes a non-physical effect of lengthening the wing structure under the no axial load condition. A modified lifting line theory is developed to compute the lift and drag coefficients of a wing structure undergoing a large bending deflection. The lift and drag coefficients are more accurately estimated by the nonlinear bending theory due to its length-preserving property. The nonlinear bending theory yields lower lift and span efficiency than the linear bending theory. A coupled aerodynamic-nonlinear finite element model is developed to implement the nonlinear bending theory for a Common Research Model (CRM) flexible wing wind tunnel model to be tested in the University of Washington Aeronautical Laboratory (UWAL). The structural stiffness of the model is designed to give about 10% wing tip deflection which is large enough that could cause the nonlinear deflection effect to become significant. The computational results show that the nonlinear bending theory yields slightly less lift than the linear bending theory for this wind tunnel model. As a result, the linear bending theory is deemed adequate for the CRM wind tunnel model.

Nonlinear Dynamic Characteristics of the Railway Vehicle

NASA Astrophysics Data System (ADS)

Uyulan, Çağlar; Gokasan, Metin

2017-06-01

The nonlinear dynamic characteristics of a railway vehicle are checked into thoroughly by applying two different wheel-rail contact model: a heuristic nonlinear friction creepage model derived by using Kalker 's theory and Polach model including dead-zone clearance. This two models are matched with the quasi-static form of the LuGre model to obtain more realistic wheel-rail contact model. LuGre model parameters are determined using nonlinear optimization method, which it's objective is to minimize the error between the output of the Polach and Kalker model and quasi-static LuGre model for specific operating conditions. The symmetric/asymmetric bifurcation attitude and stable/unstable motion of the railway vehicle in the presence of nonlinearities which are yaw damping forces in the longitudinal suspension system are analyzed in great detail by changing the vehicle speed. Phase portraits of the lateral displacement of the leading wheelset of the railway vehicle are drawn below and on the critical speeds, where sub-critical Hopf bifurcation take place, for two wheel-rail contact model. Asymmetric periodic motions have been observed during the simulation in the lateral displacement of the wheelset under different vehicle speed range. The coexistence of multiple steady states cause bounces in the amplitude of vibrations, resulting instability problems of the railway vehicle. By using Lyapunov's indirect method, the critical hunting speeds are calculated with respect to the radius of the curved track parameter changes. Hunting, which is defined as the oscillation of the lateral displacement of wheelset with a large domain, is described by a limit cycle-type oscillation nature. The evaluated accuracy of the LuGre model adopted from Kalker's model results for prediction of critical speed is higher than the results of the LuGre model adopted from Polach's model. From the results of the analysis, the critical hunting speed must be resolved by investigating the track tests under various kind of excitations.

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.

An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

NASA Astrophysics Data System (ADS)

El-Diasty, Mohammed; El-Rabbany, Ahmed; Pagiatakis, Spiros

2007-12-01

The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been widely used in many applications for positioning and orientation purposes. Traditionally, random walk (RW), Gauss-Markov (GM), and autoregressive (AR) processes have been used to develop the stochastic model in classical Kalman filters. The main disadvantage of classical Kalman filter is the potentially unstable linearization of the nonlinear dynamic system. Consequently, a nonlinear stochastic model is not optimal in derivative-based filters due to the expected linearization error. With a derivativeless-based filter such as the unscented Kalman filter or the divided difference filter, the filtering process of a complicated highly nonlinear dynamic system is possible without linearization error. This paper develops a novel nonlinear stochastic model for inertial sensor error using a wavelet network (WN). A wavelet network is a highly nonlinear model, which has recently been introduced as a powerful tool for modelling and prediction. Static and kinematic data sets are collected using a MEMS-based IMU (DQI-100) to develop the stochastic model in the static mode and then implement it in the kinematic mode. The derivativeless-based filtering method using GM, AR, and the proposed WN-based processes are used to validate the new model. It is shown that the first-order WN-based nonlinear stochastic model gives superior positioning results to the first-order GM and AR models with an overall improvement of 30% when 30 and 60 seconds GPS outages are introduced.

Reflection and diffraction corrections for nonlinear materials characterization by quasi-static pulse measurement

NASA Astrophysics Data System (ADS)

Nagy, Peter B.; Qu, Jianmin; Jacobs, Laurence J.

2014-02-01

A harmonic acoustic tone burst propagating through an elastic solid with quadratic nonlinearity produces not only a parallel burst of second harmonic but also an often neglected quasi-static pulse associated with the acoustic radiation-induced eigenstrain. Although initial analytical and experimental studies by Yost and Cantrell suggested that the pulse might have a right-angled triangular shape with the peak displacement at the leading edge being proportional to the length of the tone burst, more recent theoretical, analytical, numerical, and experimental studies proved that the pulse has a flat-top shape and the peak displacement is proportional to the propagation length. In this paper, analytical and numerical simulation results are presented to illustrate two types of finite-size effects. First, the finite axial dimension of the specimen cannot be simply accounted for by a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. Second, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second harmonic pulses generated by the same transducer. These finite-size effects can make the top of the quasi-static pulse sloped rather than flat and therefore must be taken into consideration in the interpretation of experimental data.

Reflection and diffraction corrections for nonlinear materials characterization by quasi-static pulse measurement

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

Nagy, Peter B.; Qu, Jianmin; Jacobs, Laurence J.

A harmonic acoustic tone burst propagating through an elastic solid with quadratic nonlinearity produces not only a parallel burst of second harmonic but also an often neglected quasi-static pulse associated with the acoustic radiation-induced eigenstrain. Although initial analytical and experimental studies by Yost and Cantrell suggested that the pulse might have a right-angled triangular shape with the peak displacement at the leading edge being proportional to the length of the tone burst, more recent theoretical, analytical, numerical, and experimental studies proved that the pulse has a flat-top shape and the peak displacement is proportional to the propagation length. In thismore » paper, analytical and numerical simulation results are presented to illustrate two types of finite-size effects. First, the finite axial dimension of the specimen cannot be simply accounted for by a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. Second, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second harmonic pulses generated by the same transducer. These finite-size effects can make the top of the quasi-static pulse sloped rather than flat and therefore must be taken into consideration in the interpretation of experimental data.« less

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Riff, R.

1987-01-01

A general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads are developed. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and ratcheting. Thus, geometric as well as material type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1987-01-01

A general mathematical model and solution methodologies are being developed for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads. Among the system responses, which were associated with these load conditions, were thermal buckling, creep buckling, and ratcheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution process.

Numerical Simulation of Earth Pressure on Head Chamber of Shield Machine with FEM

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

Li Shouju; Kang Chengang; Sun, Wei

2010-05-21

Model parameters of conditioned soils in head chamber of shield machine are determined based on tree-axial compression tests in laboratory. The loads acting on tunneling face are estimated according to static earth pressure principle. Based on Duncan-Chang nonlinear elastic constitutive model, the earth pressures on head chamber of shield machine are simulated in different aperture ratio cases for rotating cutterhead of shield machine. Relationship between pressure transportation factor and aperture ratio of shield machine is proposed by using aggression analysis.

Theoretical study on the spectroscopic and third-order nonlinear optical properties of two-dimensional charge-transfer pyrazine derivatives

NASA Astrophysics Data System (ADS)

Li, Haipeng; Zhang, Yi; Bi, Zetong; Xu, Runfeng; Li, Mingxue; Shen, Xiaopeng; Tang, Gang; Han, Kui

2017-12-01

In this paper, density functional theory method was employed to study the electronic absorption spectrum and electronic static second hyperpolarisability of X-shaped pyrazine derivatives with two-dimensional charge-transfer structures. Computational results show that the push-pull electron abilities of the substituent groups and the length of the conjugated chains affect the electronic spectrum and static second hyperpolarisability of the pyrazine derivatives. As the push-pull electron abilities of the substituent groups or the length of the conjugated chains increases, the frontier molecular orbital energy gap decreases, resulting in increased second hyperpolarisability and redshift of the electronic absorption bands. The electronic absorption spectra of the pyrazine derivatives maintain good transparency in the blue light band. The electronic static second hyperpolarisability exhibits a linear relationship to the frontier molecular orbital energy gap. Particularly, increasing/decreasing the push-pull electron abilities of the substituent groups considerably affect the static second hyperpolarisability in long conjugated systems, which is important to the modulation of molecular organic nonlinear optical (NLO) properties. The studied pyrazine derivatives show large third-order NLO response and good transparency in the blue light band and are thus promising candidates as NLO materials for photonics applications.

Nonlinear dynamic analysis of D α signals for type I edge localized modes characterization on JET with a carbon wall

NASA Astrophysics Data System (ADS)

Cannas, Barbara; Fanni, Alessandra; Murari, Andrea; Pisano, Fabio; Contributors, JET

2018-02-01

In this paper, the dynamic characteristics of type-I ELM time-series from the JET tokamak, the world’s largest magnetic confinement plasma physics experiment, have been investigated. The dynamic analysis has been focused on the detection of nonlinear structure in D α radiation time series. Firstly, the method of surrogate data has been applied to evaluate the statistical significance of the null hypothesis of static nonlinear distortion of an underlying Gaussian linear process. Several nonlinear statistics have been evaluated, such us the time delayed mutual information, the correlation dimension and the maximal Lyapunov exponent. The obtained results allow us to reject the null hypothesis, giving evidence of underlying nonlinear dynamics. Moreover, no evidence of low-dimensional chaos has been found; indeed, the analysed time series are better characterized by the power law sensitivity to initial conditions which can suggest a motion at the ‘edge of chaos’, at the border between chaotic and regular non-chaotic dynamics. This uncertainty makes it necessary to further investigate about the nature of the nonlinear dynamics. For this purpose, a second surrogate test to distinguish chaotic orbits from pseudo-periodic orbits has been applied. In this case, we cannot reject the null hypothesis which means that the ELM time series is possibly pseudo-periodic. In order to reproduce pseudo-periodic dynamical properties, a periodic state-of-the-art model, proposed to reproduce the ELM cycle, has been corrupted by a dynamical noise, obtaining time series qualitatively in agreement with experimental time series.

Analytical investigations of seismic responses for reinforced concrete bridge columns subjected to strong near-fault ground motion

NASA Astrophysics Data System (ADS)

Su, Chin-Kuo; Sung, Yu-Chi; Chang, Shuenn-Yih; Huang, Chao-Hsun

2007-09-01

Strong near-fault ground motion, usually caused by the fault-rupture and characterized by a pulse-like velocity-wave form, often causes dramatic instantaneous seismic energy (Jadhav and Jangid 2006). Some reinforced concrete (RC) bridge columns, even those built according to ductile design principles, were damaged in the 1999 Chi-Chi earthquake. Thus, it is very important to evaluate the seismic response of a RC bridge column to improve its seismic design and prevent future damage. Nonlinear time history analysis using step-by-step integration is capable of tracing the dynamic response of a structure during the entire vibration period and is able to accommodate the pulsing wave form. However, the accuracy of the numerical results is very sensitive to the modeling of the nonlinear load-deformation relationship of the structural member. FEMA 273 and ATC-40 provide the modeling parameters for structural nonlinear analyses of RC beams and RC columns. They use three parameters to define the plastic rotation angles and a residual strength ratio to describe the nonlinear load-deformation relationship of an RC member. Structural nonlinear analyses are performed based on these parameters. This method provides a convenient way to obtain the nonlinear seismic responses of RC structures. However, the accuracy of the numerical solutions might be further improved. For this purpose, results from a previous study on modeling of the static pushover analyses for RC bridge columns (Sung et al. 2005) is adopted for the nonlinear time history analysis presented herein to evaluate the structural responses excited by a near-fault ground motion. To ensure the reliability of this approach, the numerical results were compared to experimental results. The results confirm that the proposed approach is valid.

Catenary-induced geometric nonlinearity effects on cable linear vibrations

NASA Astrophysics Data System (ADS)

Mansour, Achref; Mekki, Othman Ben; Montassar, Sami; Rega, Giuseppe

2018-01-01

This paper investigates the free undamped vibrations of cables of arbitrary sag and inclination according to the catenary theory. The proposed approach accounts for the catenary effect on the static profile around which the cable motion is defined. Considering first order geometric nonlinearities, exact expression of the curvature is obtained along with the ensuing correction of the well known Irvine parameter. Taking into account the new characterization, different regions of shallow and non-shallow profiles are identified for various inclinations. In view of such classification, the analysis carried out on cable linear modal properties shows the emergence of new dynamic features such as additional hybrid modes and internal resonances. Analytical and numerical results reduce to those obtained by classic formulations in the cases of both horizontal and inclined shallow/non-shallow cables.

QED multi-dimensional vacuum polarization finite-difference solver

NASA Astrophysics Data System (ADS)

Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo

2015-11-01

The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph

On the acoustic-radiation-induced strain and stress in elastic solids with quadratic nonlinearity (L).

PubMed

Qu, Jianmin; Jacobs, Laurence J; Nagy, Peter B

2011-06-01

This letter demonstrates that an eigenstrain is induced when a wave propagates through an elastic solid with quadratic nonlinearity. It is shown that this eigenstrain is intrinsic to the material, but the mean stress and the total mean strain are not. Instead, the mean stress and total means strain also depend on the boundary conditions, so care must be taken when using the static deformation to measure the acoustic nonlinearity parameter of a solid. © 2011 Acoustical Society of America

Experimental evidence for dynamic friction on rock fractures from frequency-dependent nonlinear hysteresis and harmonic generation

NASA Astrophysics Data System (ADS)

Saltiel, Seth; Bonner, Brian P.; Mittal, Tushar; Delbridge, Brent; Ajo-Franklin, Jonathan B.

2017-07-01

Frictional properties affect the propagation of high-amplitude seismic waves across rock fractures and faults. Laboratory evidence suggests that these properties can be measured in active seismic surveys, potentially offering a route to characterizing friction in situ. We present experimental results from a subresonance torsional modulus and attenuation apparatus that utilizes micron-scale sinusoidal oscillations to probe the nonlinear stress-strain relation at a range of strain amplitudes and rates. Nonlinear effects are further quantified using harmonic distortion; however, time series data best illuminate underlying physical processes. The low-frequency stress-strain hysteretic loops show stiffening at the sinusoid's static ends, but stiffening is reduced above a threshold frequency. This shape is determined by harmonic generation in the strain; the stress signal has no harmonics, confirming that the fractured sample is the source of the nonlinearity. These qualitative observations suggest the presence of rate-dependent friction and are consistent between fractures in three different rock types. We propose that static friction at the low strain rate part of the cycle, when given sufficient "healing" time at low oscillation frequencies, causes this stiffening cusp shape in the hysteresis loop. While rate-and-state friction is commonly used to represent dynamic friction, it cannot capture static friction or negative slip velocities. So we implement another dynamic friction model, based on the work of Dahl, which describes this process and produces similar results. Since the two models have a similar form, parameterizations of field data could constraint fault model inputs, such as specific location velocity strengthening or weakening properties.

Failure analysis of thick composite cylinders under external pressure

NASA Technical Reports Server (NTRS)

Caiazzo, A.; Rosen, B. W.

1992-01-01

Failure of thick section composites due to local compression strength and overall structural instability is treated. Effects of material nonlinearity, imperfect fiber architecture, and structural imperfections upon anticipated failure stresses are determined. Comparisons with experimental data for a series of test cylinders are described. Predicting the failure strength of composite structures requires consideration of stability and material strength modes of failure using linear and nonlinear analysis techniques. Material strength prediction requires the accurate definition of the local multiaxial stress state in the material. An elasticity solution for the linear static analysis of thick anisotropic cylinders and rings is used herein to predict the axisymmetric stress state in the cylinders. Asymmetric nonlinear behavior due to initial cylinder out of roundness and the effects of end closure structure are treated using finite element methods. It is assumed that local fiber or ply waviness is an important factor in the initiation of material failure. An analytical model for the prediction of compression failure of fiber composites, which includes the effects of fiber misalignments, matrix inelasticity, and multiaxial applied stresses is used for material strength calculations. Analytical results are compared to experimental data for a series of glass and carbon fiber reinforced epoxy cylinders subjected to external pressure. Recommendations for pretest characterization and other experimental issues are presented. Implications for material and structural design are discussed.

Computation of maximum gust loads in nonlinear aircraft using a new method based on the matched filter approach and numerical optimization

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S.; Heeg, Jennifer; Perry, Boyd, III

1990-01-01

Time-correlated gust loads are time histories of two or more load quantities due to the same disturbance time history. Time correlation provides knowledge of the value (magnitude and sign) of one load when another is maximum. At least two analysis methods have been identified that are capable of computing maximized time-correlated gust loads for linear aircraft. Both methods solve for the unit-energy gust profile (gust velocity as a function of time) that produces the maximum load at a given location on a linear airplane. Time-correlated gust loads are obtained by re-applying this gust profile to the airplane and computing multiple simultaneous load responses. Such time histories are physically realizable and may be applied to aircraft structures. Within the past several years there has been much interest in obtaining a practical analysis method which is capable of solving the analogous problem for nonlinear aircraft. Such an analysis method has been the focus of an international committee of gust loads specialists formed by the U.S. Federal Aviation Administration and was the topic of a panel discussion at the Gust and Buffet Loads session at the 1989 SDM Conference in Mobile, Alabama. The kinds of nonlinearities common on modern transport aircraft are indicated. The Statical Discrete Gust method is capable of being, but so far has not been, applied to nonlinear aircraft. To make the method practical for nonlinear applications, a search procedure is essential. Another method is based on Matched Filter Theory and, in its current form, is applicable to linear systems only. The purpose here is to present the status of an attempt to extend the matched filter approach to nonlinear systems. The extension uses Matched Filter Theory as a starting point and then employs a constrained optimization algorithm to attack the nonlinear problem.

Front fingering and complex dynamics driven by the interaction of buoyancy and diffusive instabilities.

PubMed

D'Hernoncourt, J; Merkin, J H; De Wit, A

2007-09-01

Traveling fronts can become transversally unstable either because of a diffusive instability arising when the key variables diffuse at sufficiently different rates or because of a buoyancy-driven Rayleigh-Taylor mechanism when the density jump across the front is statically unfavorable. The interaction between such diffusive and buoyancy instabilities of fronts is analyzed theoretically for a simple model system. Linear stability analysis and nonlinear simulations show that their interplay changes considerably the stability properties with regard to the pure Rayleigh-Taylor or diffusive instabilities of fronts. In particular, an instability scenario can arise which triggers convection around statically stable fronts as a result of differential diffusion. Moreover, spatiotemporal chaos can be observed when both buoyancy and diffusive effects cooperate to destabilize the front. Experimental conditions to test our predictions are suggested.

Quadratic Solid⁻Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates.

PubMed

Chalal, Hocine; Abed-Meraim, Farid

2018-06-20

In the current contribution, prismatic and hexahedral quadratic solid⁻shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.

Seismic risk assessment of Trani's Cathedral bell tower in Apulia, Italy

NASA Astrophysics Data System (ADS)

Diaferio, Mariella; Foti, Dora

2017-09-01

The present paper deals with the evaluation of the seismic vulnerability of slender historical buildings; these structures, in fact, may manifest a high risk with respect to seismic actions as usually they have been designed to resist to gravitational loads only, and are characterized by a high flexibility. To evaluate this behavior, the bell tower of the Trani's Cathedral is investigated. The tower is 57 m tall and is characterized by an unusual building typology, i.e., the walls are composed of a concrete core coupled with external masonry stones. The dynamic parameters and the mechanical properties of the tower have been evaluated on the basis of an extensive experimental campaign that made use of ambient vibration tests and ground penetrating radar tests. Such data have been utilized to calibrate a numerical model of the examined tower. A linear static analysis, a dynamic analysis and a nonlinear static analysis have been carried out on such model to evaluate the displacement capacity of the tower and the seismic risk assessment in accordance with the Italian guidelines.

Nonlinear neural control with power systems applications

NASA Astrophysics Data System (ADS)

Chen, Dingguo

1998-12-01

Extensive studies have been undertaken on the transient stability of large interconnected power systems with flexible ac transmission systems (FACTS) devices installed. Varieties of control methodologies have been proposed to stabilize the postfault system which would otherwise eventually lose stability without a proper control. Generally speaking, regular transient stability is well understood, but the mechanism of load-driven voltage instability or voltage collapse has not been well understood. The interaction of generator dynamics and load dynamics makes synthesis of stabilizing controllers even more challenging. There is currently increasing interest in the research of neural networks as identifiers and controllers for dealing with dynamic time-varying nonlinear systems. This study focuses on the development of novel artificial neural network architectures for identification and control with application to dynamic electric power systems so that the stability of the interconnected power systems, following large disturbances, and/or with the inclusion of uncertain loads, can be largely enhanced, and stable operations are guaranteed. The latitudinal neural network architecture is proposed for the purpose of system identification. It may be used for identification of nonlinear static/dynamic loads, which can be further used for static/dynamic voltage stability analysis. The properties associated with this architecture are investigated. A neural network methodology is proposed for dealing with load modeling and voltage stability analysis. Based on the neural network models of loads, voltage stability analysis evolves, and modal analysis is performed. Simulation results are also provided. The transient stability problem is studied with consideration of load effects. The hierarchical neural control scheme is developed. Trajectory-following policy is used so that the hierarchical neural controller performs as almost well for non-nominal cases as they do for the nominal cases. The adaptive hierarchical neural control scheme is also proposed to deal with the time-varying nature of loads. Further, adaptive neural control, which is based on the on-line updating of the weights and biases of the neural networks, is studied. Simulations provided on the faulted power systems with unknown loads suggest that the proposed adaptive hierarchical neural control schemes should be useful for practical power applications.

Challenging the in-vivo assessment of biomechanical properties of the uterine cervix: A critical analysis of ultrasound based quasi-static procedures.

PubMed

Maurer, M M; Badir, S; Pensalfini, M; Bajka, M; Abitabile, P; Zimmermann, R; Mazza, E

2015-06-25

Measuring the stiffness of the uterine cervix might be useful in the prediction of preterm delivery, a still unsolved health issue of global dimensions. Recently, a number of clinical studies have addressed this topic, proposing quantitative methods for the assessment of the mechanical properties of the cervix. Quasi-static elastography, maximum compressibility using ultrasound and aspiration tests have been applied for this purpose. The results obtained with the different methods seem to provide contradictory information about the physiologic development of cervical stiffness during pregnancy. Simulations and experiments were performed in order to rationalize the findings obtained with ultrasound based, quasi-static procedures. The experimental and computational results clearly illustrate that standardization of quasi-static elastography leads to repeatable strain values, but for different loading forces. Since force cannot be controlled, this current approach does not allow the distinction between a globally soft and stiff cervix. It is further shown that introducing a reference elastomer into the elastography measurement might overcome the problem of force standardization, but a careful mechanical analysis is required to obtain reliable stiffness values for cervical tissue. In contrast, the maximum compressibility procedure leads to a repeatable, semi-quantitative assessment of cervical consistency, due to the nonlinear nature of the mechanical behavior of cervical tissue. The evolution of cervical stiffness in pregnancy obtained with this procedure is in line with data from aspiration tests. Copyright © 2015 Elsevier Ltd. All rights reserved.

Characterization of postural control deficit in whiplash patients by means of linear and nonlinear analyses - A pilot study.

PubMed

Madeleine, Pascal; Nielsen, Mogens; Arendt-Nielsen, Lars

2011-04-01

The ability to maintain balance is diminished in patients suffering from a whiplash injury. The aim of this study was to characterize the variability of postural control in patients with chronic whiplash injury. For this purpose, we analyzed static postural recordings from 11 whiplash patients and sex- and age-matched asymptomatic healthy volunteers. Static postural recordings were performed randomly with eyes open, eyes closed, and eyes open and speaking (dual task). Spatial-temporal changes of the center of pressure displacement were analyzed to assess the amplitude and structure of postural variability by computing, respectively, the standard deviation/coefficient of variation and sample entropy/fractal dimension of the time series. The amplitude of variability of the center of pressure was larger among whiplash patients compared with controls (P<0.001) while fractal dimension was lower (P<0.001). The sample entropy increased during both eyes closed and a simple dual task compared with eyes open (P<0.05). The analysis of postural control dynamics revealed increased amplitude of postural variability and decreased signal dimensionality related to the deficit in postural stability found in whiplash patients. Linear and nonlinear analyses can thus be helpful for the quantification of postural control in normal and pathological conditions. Copyright © 2010 Elsevier Ltd. All rights reserved.

Principal Dynamic Mode Analysis of the Hodgkin–Huxley Equations

PubMed Central

Eikenberry, Steffen E.; Marmarelis, Vasilis Z.

2015-01-01

We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin–Huxley (H–H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function. PMID:25630480

Hierarchic Extensions in the Static and Dynamic Analysis of Elastic Beams. Ph.D. Thesis, 1990 Final Report, May 1990

NASA Technical Reports Server (NTRS)

Watson, Robert A.

1991-01-01

Approximate solutions of static and dynamic beam problems by the p-version of the finite element method are investigated. Within a hierarchy of engineering beam idealizations, rigorous formulations of the strain and kinetic energies for straight and circular beam elements are presented. These formulations include rotating coordinate system effects and geometric nonlinearities to allow for the evaluation of vertical axis wind turbines, the motivating problem for this research. Hierarchic finite element spaces, based on extensions of the polynomial orders used to approximate the displacement variables, are constructed. The developed models are implemented into a general purpose computer program for evaluation. Quality control procedures are examined for a diverse set of sample problems. These procedures include estimating discretization errors in energy norm and natural frequencies, performing static and dynamic equilibrium checks, observing convergence for qualities of interest, and comparison with more exacting theories and experimental data. It is demonstrated that p-extensions produce exponential rates of convergence in the approximation of strain energy and natural frequencies for the class of problems investigated.

Suspension system vibration analysis with regard to variable type ability to smooth road irregularities

NASA Astrophysics Data System (ADS)

Rykov, S. P.; Rykova, O. A.; Koval, V. S.; Makhno, D. E.; Fedotov, K. V.

2018-03-01

The paper aims to analyze vibrations of the dynamic system equivalent of the suspension system with regard to tyre ability to smooth road irregularities. The research is based on static dynamics for linear systems of automated control, methods of correlation, spectral and numerical analysis. Input of new data on the smoothing effect of the pneumatic tyre reflecting changes of a contact area between the wheel and road under vibrations of the suspension makes the system non-linear which requires using numerical analysis methods. Taking into account the variable smoothing ability of the tyre when calculating suspension vibrations, one can approximate calculation and experimental results and improve the constant smoothing ability of the tyre.

Reduced-Order Modeling for Flutter/LCO Using Recurrent Artificial Neural Network

NASA Technical Reports Server (NTRS)

Yao, Weigang; Liou, Meng-Sing

2012-01-01

The present study demonstrates the efficacy of a recurrent artificial neural network to provide a high fidelity time-dependent nonlinear reduced-order model (ROM) for flutter/limit-cycle oscillation (LCO) modeling. An artificial neural network is a relatively straightforward nonlinear method for modeling an input-output relationship from a set of known data, for which we use the radial basis function (RBF) with its parameters determined through a training process. The resulting RBF neural network, however, is only static and is not yet adequate for an application to problems of dynamic nature. The recurrent neural network method [1] is applied to construct a reduced order model resulting from a series of high-fidelity time-dependent data of aero-elastic simulations. Once the RBF neural network ROM is constructed properly, an accurate approximate solution can be obtained at a fraction of the cost of a full-order computation. The method derived during the study has been validated for predicting nonlinear aerodynamic forces in transonic flow and is capable of accurate flutter/LCO simulations. The obtained results indicate that the present recurrent RBF neural network is accurate and efficient for nonlinear aero-elastic system analysis

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code. [predicting the response of a lightweight aircraft during a crash

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1980-01-01

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.

Design of robust iterative learning control schemes for systems with polytopic uncertainties and sector-bounded nonlinearities

NASA Astrophysics Data System (ADS)

Boski, Marcin; Paszke, Wojciech

2017-01-01

This paper deals with designing of iterative learning control schemes for uncertain systems with static nonlinearities. More specifically, the nonlinear part is supposed to be sector bounded and system matrices are assumed to range in the polytope of matrices. For systems with such nonlinearities and uncertainties the repetitive process setting is exploited to develop a linear matrix inequality based conditions for computing the feedback and feedforward (learning) controllers. These controllers guarantee acceptable dynamics along the trials and ensure convergence of the trial-to-trial error dynamics, respectively. Numerical examples illustrate the theoretical results and confirm effectiveness of the designed control scheme.

Perception of static orientation in a constant gravitoinertial environment

NASA Technical Reports Server (NTRS)

Ormsby, C. C.; Young, L. R.

1976-01-01

The illusions associated with the perception of static tilt in various specific force environments have been reviewed and then classified in such a way that a simple perceptual model could be developed to account for the experimental data. The fundamental conclusion to be drawn from this model is that these illusions can be accounted for by a simple nonlinear transformation of the information primarily from the saccule.

Mathematical model of the SH-3G helicopter

NASA Technical Reports Server (NTRS)

Phillips, J. D.

1982-01-01

A mathematical model of the Sikorsky SH-3G helicopter based on classical nonlinear, quasi-steady rotor theory was developed. The model was validated statically and dynamically by comparison with Navy flight-test data. The model incorporates ad hoc revisions which address the ideal assumptions of classical rotor theory and improve the static trim characteristics to provide a more realistic simulation, while retaining the simplicity of the classical model.

Propagation of short stress pulses in discrete strongly nonlinear tunable metamaterials.

PubMed

Xu, Yichao; Nesterenko, Vitali F

2014-08-28

The propagation of short pulses with wavelength comparable to the size of a unit cell has been studied in a one-dimensional discrete metamaterial composed of steel discs alternating with toroidal nitrile O-rings under different levels of precompression using experiments, numerical simulations and theoretical analysis. This strongly nonlinear metamaterial is more tunable than granular chains composed of linear elastic spherical particles and has better potential for attenuation of dynamic loads. A double power-law relationship for compressed O-rings was found to describe adequately their quasi-static and dynamic behaviour with significantly different elastic moduli. It is demonstrated that the double power-law metamaterial investigated allows a dramatic increase in sound speed and acoustic impedance of three to four times using a moderate force. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Effects of static tensile load on the thermal expansion of Gr/PI composite material

NASA Technical Reports Server (NTRS)

Farley, G. L.

1981-01-01

The effect of static tensile load on the thermal expansion of Gr/PI composite material was measured for seven different laminate configurations. A computer program was developed which implements laminate theory in a piecewise linear fashion to predict the coupled nonlinear thermomechanical behavior. Static tensile load significantly affected the thermal expansion characteristics of the laminates tested. This effect is attributed to a fiber instability micromechanical behavior of the constituent materials. Analytical results correlated reasonably well with free thermal expansion tests (no load applied to the specimen). However, correlation was poor for tests with an applied load.

Flutter Sensitivity to Boundary Layer Thickness, Structural Damping, and Static Pressure Differential for a Shuttle Tile Overlay Repair Concept

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Bartels, Robert E.

2009-01-01

This paper examines the aeroelastic stability of an on-orbit installable Space Shuttle patch panel. CFD flutter solutions were obtained for thick and thin boundary layers at a free stream Mach number of 2.0 and several Mach numbers near sonic speed. The effect of structural damping on these flutter solutions was also examined, and the effect of structural nonlinearities associated with in-plane forces in the panel was considered on the worst case linear flutter solution. The results of the study indicated that adequate flutter margins exist for the panel at the Mach numbers examined. The addition of structural damping improved flutter margins as did the inclusion of nonlinear effects associated with a static pressure difference across the panel.

State of charge estimation in Ni-MH rechargeable batteries

NASA Astrophysics Data System (ADS)

Milocco, R. H.; Castro, B. E.

In this work we estimate the state of charge (SOC) of Ni-MH rechargeable batteries using the Kalman filter based on a simplified electrochemical model. First, we derive the complete electrochemical model of the battery which includes diffusional processes and kinetic reactions in both Ni and MH electrodes. The full model is further reduced in a cascade of two parts, a linear time invariant dynamical sub-model followed by a static nonlinearity. Both parts are identified using the current and potential measured at the terminals of the battery with a simple 1-D minimization procedure. The inverse of the static nonlinearity together with a Kalman filter provide the SOC estimation as a linear estimation problem. Experimental results with commercial batteries are provided to illustrate the estimation procedure and to show the performance.

Non-linear programming in shakedown analysis with plasticity and friction

NASA Astrophysics Data System (ADS)

Spagnoli, A.; Terzano, M.; Barber, J. R.; Klarbring, A.

2017-07-01

Complete frictional contacts, when subjected to cyclic loading, may sometimes develop a favourable situation where slip ceases after a few cycles, an occurrence commonly known as frictional shakedown. Its resemblance to shakedown in plasticity has prompted scholars to apply direct methods, derived from the classical theorems of limit analysis, in order to assess a safe limit to the external loads applied on the system. In circumstances where zones of plastic deformation develop in the material (e.g., because of the large stress concentrations near the sharp edges of a complete contact), it is reasonable to expect an effect of mutual interaction of frictional slip and plastic strains on the load limit below which the global behaviour is non dissipative, i.e., both slip and plastic strains go to zero after some dissipative load cycles. In this paper, shakedown of general two-dimensional discrete systems, involving both friction and plasticity, is discussed and the shakedown limit load is calculated using a non-linear programming algorithm based on the static theorem of limit analysis. An illustrative example related to an elastic-plastic solid containing a frictional crack is provided.

Nonlinear acoustic propagation of launch vehicle and military jet aircraft noise

NASA Astrophysics Data System (ADS)

Gee, Kent L.

2010-10-01

The noise from launch vehicles and high-performance military jet aircraft has been shown to travel nonlinearly as a result of an amplitude-dependent speed of sound. Because acoustic pressure compressions travel faster than rarefactions, the waveform steepens and shocks form. This process results in a very different (and readily audible) noise signature and spectrum than predicted by linear models. On-going efforts to characterize the nonlinearity using statistical and spectral measures are described with examples from recent static tests of solid rocket boosters and the F-22 Raptor.

Thermodynamic potentials in anisotropic and nonlinear dielectrics

NASA Astrophysics Data System (ADS)

Parravicini, Jacopo

2018-07-01

The variation of total energy, entropy, Helmoltz free energy due to the application of a static electric field is calculated and discussed, under suitable conditions, in the case of a dielectric with either anisotropic or nonlinear response. The proposed approach starts from Fröhlich's theory of dielectric thermodynamics and, by analyzing its assumptions, provides a method to generalize it. The obtained relationships can be employed for describing the thermodynamics of different classes of dielectric materials, also in experimental investigations. Specifically, the anisotropy and nonlinearity conditions are considered and relative examples are indicated and discussed.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Riff, R.

1988-01-01

This research is performed to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling, and ratcheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, George J.

1990-01-01

The development of a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-like structures under dynamic and/or static thermomechanical loads is examined. In the mathematical model, geometric as well as material-type of nonlinearities are considered. Traditional as well as novel approaches are reported and detailed applications are presented in the appendices. The emphasis for the mathematical model, the related solution schemes, and the applications, is on thermal viscoelastic and viscoplastic phenomena, which can predict creep and ratchetting.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.

1991-01-01

This report deals with the development of a general mathematical model and solution methodology for analyzing the structural response of thin, metallic shell-like structures under dynamic and/or static thermomechanical loads. In the mathematical model, geometric as well as the material-type of nonlinearities are considered. Traditional as well as novel approaches are reported and detailed applications are presented in the appendices. The emphasis for the mathematical model, the related solution schemes, and the applications, is on thermal viscoelastic and viscoplastic phenomena, which can predict creep and ratchetting.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.

1989-01-01

The objective is to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling, and racheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Riff, R.

1988-01-01

The objective of this research is to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and racheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Parametric analysis of swept-wing geometry with sheared wing tips

NASA Technical Reports Server (NTRS)

Fremaux, C. M.; Vijgen, P. M. H. W.; Van Dam, C. P.

1990-01-01

A computational parameter study is presented of potential reductions in induced drag and increases in lateral-directional stability due to sheared wing tips attached to an untwisted wing of moderate sweep and aspect ratio. Sheared tips are swept and tapered wing-tip devices mounted in the plane of the wing. The induced-drag results are obtained using an inviscid, incompressible surface-panel method that models the nonlinear effects due to the deflected and rolled-up wake behind the lifting surface. The induced-drag results with planar sheared tips are compared to straight-tapered tip extensions and nonplanar winglet geometries. The lateral-directional static-stability characteristics of the wing with sheared tips are estimated using a quasi-vortex-lattice method. For certain combinations of sheared-tip sweep and taper, both the induced efficiency of the wing and the relevant static-stability derivatives are predicted to increase compared to the wing with a straight-tapered tip modification.

Static non-reciprocity in mechanical metamaterials.

PubMed

Coulais, Corentin; Sounas, Dimitrios; Alù, Andrea

2017-02-23

Reciprocity is a general, fundamental principle governing various physical systems, which ensures that the transfer function-the transmission of a physical quantity, say light intensity-between any two points in space is identical, regardless of geometrical or material asymmetries. Breaking this transmission symmetry offers enhanced control over signal transport, isolation and source protection. So far, devices that break reciprocity (and therefore show non-reciprocity) have been mostly considered in dynamic systems involving electromagnetic, acoustic and mechanical wave propagation associated with fields varying in space and time. Here we show that it is possible to break reciprocity in static systems, realizing mechanical metamaterials that exhibit vastly different output displacements under excitation from different sides, as well as one-way displacement amplification. This is achieved by combining large nonlinearities with suitable geometrical asymmetries and/or topological features. In addition to extending non-reciprocity and isolation to statics, our work sheds light on energy propagation in nonlinear materials with asymmetric crystalline structures and topological properties. We anticipate that breaking reciprocity will open avenues for energy absorption, conversion and harvesting, soft robotics, prosthetics and optomechanics.

MATLAB Stability and Control Toolbox Trim and Static Stability Module

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Crespo, Luis

2012-01-01

MATLAB Stability and Control Toolbox (MASCOT) utilizes geometric, aerodynamic, and inertial inputs to calculate air vehicle stability in a variety of critical flight conditions. The code is based on fundamental, non-linear equations of motion and is able to translate results into a qualitative, graphical scale useful to the non-expert. MASCOT was created to provide the conceptual aircraft designer accurate predictions of air vehicle stability and control characteristics. The code takes as input mass property data in the form of an inertia tensor, aerodynamic loading data, and propulsion (i.e. thrust) loading data. Using fundamental nonlinear equations of motion, MASCOT then calculates vehicle trim and static stability data for the desired flight condition(s). Available flight conditions include six horizontal and six landing rotation conditions with varying options for engine out, crosswind, and sideslip, plus three take-off rotation conditions. Results are displayed through a unique graphical interface developed to provide the non-stability and control expert conceptual design engineer a qualitative scale indicating whether the vehicle has acceptable, marginal, or unacceptable static stability characteristics. If desired, the user can also examine the detailed, quantitative results.

Field measurements of the linear and nonlinear shear moduli of cemented alluvium using dynamically loaded surface footings

NASA Astrophysics Data System (ADS)

Park, Kwangsoo

In this dissertation, a research effort aimed at development and implementation of a direct field test method to evaluate the linear and nonlinear shear modulus of soil is presented. The field method utilizes a surface footing that is dynamically loaded horizontally. The test procedure involves applying static and dynamic loads to the surface footing and measuring the soil response beneath the loaded area using embedded geophones. A wide range in dynamic loads under a constant static load permits measurements of linear and nonlinear shear wave propagation from which shear moduli and associated shearing strains are evaluated. Shear wave velocities in the linear and nonlinear strain ranges are calculated from time delays in waveforms monitored by geophone pairs. Shear moduli are then obtained using the shear wave velocities and the mass density of a soil. Shear strains are determined using particle displacements calculated from particle velocities measured at the geophones by assuming a linear variation between geophone pairs. The field test method was validated by conducting an initial field experiment at sandy site in Austin, Texas. Then, field experiments were performed on cemented alluvium, a complex, hard-to-sample material. Three separate locations at Yucca Mountain, Nevada were tested. The tests successfully measured: (1) the effect of confining pressure on shear and compression moduli in the linear strain range and (2) the effect of strain on shear moduli at various states of stress in the field. The field measurements were first compared with empirical relationships for uncemented gravel. This comparison showed that the alluvium was clearly cemented. The field measurements were then compared to other independent measurements including laboratory resonant column tests and field seismic tests using the spectral-analysis-of-surface-waves method. The results from the field tests were generally in good agreement with the other independent test results, indicating that the proposed method has the ability to directly evaluate complex material like cemented alluvium in the field.

The role of ensemble-based statistics in variational assimilation of cloud-affected observations from infrared imagers

NASA Astrophysics Data System (ADS)

Hacker, Joshua; Vandenberghe, Francois; Jung, Byoung-Jo; Snyder, Chris

2017-04-01

Effective assimilation of cloud-affected radiance observations from space-borne imagers, with the aim of improving cloud analysis and forecasting, has proven to be difficult. Large observation biases, nonlinear observation operators, and non-Gaussian innovation statistics present many challenges. Ensemble-variational data assimilation (EnVar) systems offer the benefits of flow-dependent background error statistics from an ensemble, and the ability of variational minimization to handle nonlinearity. The specific benefits of ensemble statistics, relative to static background errors more commonly used in variational systems, have not been quantified for the problem of assimilating cloudy radiances. A simple experiment framework is constructed with a regional NWP model and operational variational data assimilation system, to provide the basis understanding the importance of ensemble statistics in cloudy radiance assimilation. Restricting the observations to those corresponding to clouds in the background forecast leads to innovations that are more Gaussian. The number of large innovations is reduced compared to the more general case of all observations, but not eliminated. The Huber norm is investigated to handle the fat tails of the distributions, and allow more observations to be assimilated without the need for strict background checks that eliminate them. Comparing assimilation using only ensemble background error statistics with assimilation using only static background error statistics elucidates the importance of the ensemble statistics. Although the cost functions in both experiments converge to similar values after sufficient outer-loop iterations, the resulting cloud water, ice, and snow content are greater in the ensemble-based analysis. The subsequent forecasts from the ensemble-based analysis also retain more condensed water species, indicating that the local environment is more supportive of clouds. In this presentation we provide details that explain the apparent benefit from using ensembles for cloudy radiance assimilation in an EnVar context.

Integrated multidisciplinary design optimization using discrete sensitivity analysis for geometrically complex aeroelastic configurations

NASA Astrophysics Data System (ADS)

Newman, James Charles, III

1997-10-01

The first two steps in the development of an integrated multidisciplinary design optimization procedure capable of analyzing the nonlinear fluid flow about geometrically complex aeroelastic configurations have been accomplished in the present work. For the first step, a three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed. The advantage of unstructured grids, when compared with a structured-grid approach, is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited for geometrically complex configurations of practical interest. In this work the time-dependent, nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional cases and a Gauss-Seidel algorithm for the three-dimensional; at steady-state, similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Various surface parameterization techniques have been employed in the current study to control the shape of the design surface. Once this surface has been deformed, the interior volume of the unstructured grid is adapted by considering the mesh as a system of interconnected tension springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR, an advanced automatic-differentiation software tool. To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for several two- and three-dimensional cases. In twodimensions, an initially symmetric NACA-0012 airfoil and a high-lift multielement airfoil were examined. For the three-dimensional configurations, an initially rectangular wing with uniform NACA-0012 cross-sections was optimized; in addition, a complete Boeing 747-200 aircraft was studied. Furthermore, the current study also examines the effect of inconsistency in the order of spatial accuracy between the nonlinear fluid and linear shape sensitivity equations. The second step was to develop a computationally efficient, high-fidelity, integrated static aeroelastic analysis procedure. To accomplish this, a structural analysis code was coupled with the aforementioned unstructured grid aerodynamic analysis solver. The use of an unstructured grid scheme for the aerodynamic analysis enhances the interaction compatibility with the wing structure. The structural analysis utilizes finite elements to model the wing so that accurate structural deflections may be obtained. In the current work, parameters have been introduced to control the interaction of the computational fluid dynamics and structural analyses; these control parameters permit extremely efficient static aeroelastic computations. To demonstrate and evaluate this procedure, static aeroelastic analysis results for a flexible wing in low subsonic, high subsonic (subcritical), transonic (supercritical), and supersonic flow conditions are presented.

Parameter design and experimental study of a bifunctional isolator for optical payload protection and stabilization

NASA Astrophysics Data System (ADS)

Wang, Guang-yuan; Guan, Xin; Cao, Dong-jing; Tang, Shao-fan; Chen, Xiang; Liang, Lu; Zheng, Gang-tie

2017-11-01

With the raise of resolution, optical payloads are becoming increasingly sensitive to satellite jitter. An approach where the entire spacecraft is pointed with great accuracy requires sophisticated and expensive bus design. In an effort to lower the overall cost of space missions that require highly stable line-of-sight pointing, a method of separating the bus and the payload with low frequency isolators is proposed. This isolation system can block the transmission of disturbance and allow relatively large bus motion. However, if the isolator is linear then there is a trade-off between isolation and static deflection as the launch and the on-orbit stage have difference requirements on the isolation frequency. Otherwise, an extra locking system should be appended to protect the payload before getting into orbit, as the STABLE isolation system[1] and the MIM isolation system[2] did. To overcome this limitation, an alternative approach is to design a nonlinear isolator with high-static stiffness during launch and low dynamic stiffness on orbit. Several specially designed nonlinear isolators have achieved low dynamic stiffness with large static load capacity. Virgin[3] considered a structure made from a highly deformed elastic element to achieve a softening spring. Platus[4] exploited the buckling of beams under axial load in a specific configuration to achieve a negative stiffness in combination with a positive stiffness, and hence low-dynamic stiffness. Others have achieved the same by connecting linear springs with positive stiffness in parallel with elements of negative stiffness[5] [7]. In the present study, a bifunctional isolator has been developed for optical payloads. The isolator have good performance both during launch and on orbit because of its specially designed nonlinear stiffness and damping. The isolator works in a linear part with low stiffness and small damping ratio under the micro-vibration and microgravity on orbit. The transmissibility requirement and the displacement restriction during launch are satisfied by tuning the nonlinear stiffness and damping parameters. A group of sample isolators are designed tested both statically and dynamically.

Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

NASA Technical Reports Server (NTRS)

Ahmad, Shahid

1991-01-01

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Nonlinear dynamics of the human lumbar intervertebral disc.

PubMed

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

2015-02-05

Systems with a quasi-static response similar to the axial response of the intervertebral disc (i.e. progressive stiffening) often present complex dynamics, characterized by peculiar nonlinearities in the frequency response. However, such characteristics have not been reported for the dynamic response of the disc. The accurate understanding of disc dynamics is essential to investigate the unclear correlation between whole body vibration and low back pain. The present study investigated the dynamic response of the disc, including its potential nonlinear response, over a range of loading conditions. Human lumbar discs were tested by applying a static preload to the top and a sinusoidal displacement at the bottom of the disc. The frequency of the stimuli was set to increase linearly from a low frequency to a high frequency limit and back down. In general, the response showed nonlinear and asymmetric characteristics. For each test, the disc had different response in the frequency-increasing compared to the frequency-decreasing sweep. In particular, the system presented abrupt changes of the oscillation amplitude at specific frequencies, which differed between the two sweeps. This behaviour indicates that the system oscillation has a different equilibrium condition depending on the path followed by the stimuli. Preload and amplitude of the oscillation directly influenced the disc response by changing the nonlinear dynamics and frequency of the jump-phenomenon. These results show that the characterization of the dynamic response of physiological systems should be readdressed to determine potential nonlinearities. Their direct effect on the system function should be further investigated. Copyright © 2014 Elsevier Ltd. All rights reserved.

Limit Cycle Analysis Applied to the Oscillations of Decelerating Blunt-Body Entry Vehicles

NASA Technical Reports Server (NTRS)

Schoenenberger, Mark; Queen, Eric M.

2008-01-01

Many blunt-body entry vehicles have nonlinear dynamic stability characteristics that produce self-limiting oscillations in flight. Several different test techniques can be used to extract dynamic aerodynamic coefficients to predict this oscillatory behavior for planetary entry mission design and analysis. Most of these test techniques impose boundary conditions that alter the oscillatory behavior from that seen in flight. Three sets of test conditions, representing three commonly used test techniques, are presented to highlight these effects. Analytical solutions to the constant-coefficient planar equations-of-motion for each case are developed to show how the same blunt body behaves differently depending on the imposed test conditions. The energy equation is applied to further illustrate the governing dynamics. Then, the mean value theorem is applied to the energy rate equation to find the effective damping for an example blunt body with nonlinear, self-limiting dynamic characteristics. This approach is used to predict constant-energy oscillatory behavior and the equilibrium oscillation amplitudes for the various test conditions. These predictions are verified with planar simulations. The analysis presented provides an overview of dynamic stability test techniques and illustrates the effects of dynamic stability, static aerodynamics and test conditions on observed dynamic motions. It is proposed that these effects may be leveraged to develop new test techniques and refine test matrices in future tests to better define the nonlinear functional forms of blunt body dynamic stability curves.

Nonlinear Dynamics of a Magnetically Driven Duffing-Type Spring-Magnet Oscillator in the Static Magnetic Field of a Coil

ERIC Educational Resources Information Center

Donoso, Guillermo; Ladera, Celso L.

2012-01-01

We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the…

A class of stabilizing controllers for flexible multibody systems

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.; Kelkar, Atul G.; Maghami, Peiman G.

1995-01-01

The problem of controlling a class of nonlinear multibody flexible space systems consisting of a flexible central body to which a number of articulated appendages are attached is considered. Collocated actuators and sensors are assumed, and global asymptotic stability of such systems is established under a nonlinear dissipative control law. The stability is shown to be robust to unmodeled dynamics and parametric uncertainties. For a special case in which the attitude motion of the central body is small, the system, although still nonlinear, is shown to be stabilized by linear dissipative control laws. Two types of linear controllers are considered: static dissipative (constant gain) and dynamic dissipative. The static dissipative control law is also shown to provide robust stability in the presence of certain classes of actuator and sensor nonlinearities and actuator dynamics. The results obtained for this special case can also be readily applied for controlling single-body linear flexible space structures. For this case, a synthesis technique for the design of a suboptimal dynamic dissipative controller is also presented. The results obtained in this paper are applicable to a broad class of multibody and single-body systems such as flexible multilink manipulators, multipayload space platforms, and space antennas. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems.

Punchets: nonlinear transport in Hamiltonian pump-ratchet hybrids

NASA Astrophysics Data System (ADS)

Dittrich, Thomas; Medina Sánchez, Nicolás

2018-02-01

‘Punchets’ are hybrids between ratchets and pumps, combining a spatially periodic static potential, typically asymmetric under space inversion, with a local driving that breaks time-reversal invariance, and are intended to model metal or semiconductor surfaces irradiated by a collimated laser beam. Their crucial feature is irregular driven scattering between asymptotic regions supporting periodic (as opposed to free) motion. With all binary spatio-temporal symmetries broken, scattering in punchets typically generates directed currents. We here study the underlying nonlinear transport mechanisms, from chaotic scattering to the parameter dependence of the currents, in three types of Hamiltonian models, (i) with spatially periodic potentials where only in the driven scattering region, spatial and temporal symmetries are broken, and (ii), spatially asymmetric (ratchet) potentials with a driving that only breaks time-reversal invariance. As more realistic models of laser-irradiated surfaces, we consider (iii), a driving in the form of a running wave confined to a compact region by a static envelope. In this case, the induced current can even run against the direction of wave propagation, drastically evidencing its nonlinear nature. Quantizing punchets is indicated as a viable research perspective.

Nonlinear Contact Effects in Staggered Thin-Film Transistors

NASA Astrophysics Data System (ADS)

Fischer, Axel; Zündorf, Hilke; Kaschura, Felix; Widmer, Johannes; Leo, Karl; Kraft, Ulrike; Klauk, Hagen

2017-11-01

The static and dynamic electrical characteristics of thin-film transistors (TFTs) are often limited by the parasitic contact resistances, especially for TFTs with a small channel length. For the smallest possible contact resistance, the staggered device architecture has a general advantage over the coplanar architecture of a larger injection area. Since the charge transport occurs over an extended area, it is inherently more difficult to develop an accurate analytical device model for staggered TFTs. Most analytical models for staggered TFTs, therefore, assume that the contact resistance is linear, even though this is commonly accepted not to be the case. Here, we introduce a semiphenomenological approach to accurately fit experimental data based on a highly discretized equivalent network circuit explicitly taking into account the inherent nonlinearity of the contact resistance. The model allows us to investigate the influence of nonlinear contact resistances on the static and dynamic performance of staggered TFTs for different contact layouts with a relatively short computation time. The precise extraction of device parameters enables us to calculate the transistor behavior as well as the potential for optimization in real circuits.

Develop advanced nonlinear signal analysis topographical mapping system

NASA Technical Reports Server (NTRS)

1994-01-01

The Space Shuttle Main Engine (SSME) has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature, pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system; (2) develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amount of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. High compression ratio can be achieved to allow minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities; and (3) integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of malfunction, and indicate feasible engineering solutions. The final result of this program will yield an ATMS system of nonlinear and nonstationary spectral analysis software package integrated with the Compressed SSME TOPO Data Base (CSTDB) on the same platform. This system will allow NASA engineers to retrieve any unique defect signatures and trends associated with different failure modes and anomalous phenomena over the entire SSME test history across turbo pump families.

Develop advanced nonlinear signal analysis topographical mapping system

NASA Technical Reports Server (NTRS)

Jong, Jen-Yi

1993-01-01

The SSME has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) Develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system. (2) Develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amounts of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. A high compression ratio can be achieved to allow the minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities. (3) Integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for a quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of malfunction, and indicate feasible engineering solutions. The final result of this program will yield an ATMS system of nonlinear and nonstationary spectral analysis software package integrated with the Compressed SSME TOPO Data Base (CSTDB) on the same platform. This system will allow NASA engineers to retrieve any unique defect signatures and trends associated with different failure modes and anomalous phenomena over the entire SSME test history across turbo pump families.

On the construction of a direct numerical simulation of a breaking inertia-gravity wave in the upper mesosphere

NASA Astrophysics Data System (ADS)

Fruman, Mark D.; Remmler, Sebastian; Achatz, Ulrich; Hickel, Stefan

2014-10-01

A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and structure of the primary instability and to initialize nonlinear "2.5-D" simulations (with three-dimensional velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave, a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of the wave and generation of turbulence is faster in three dimensions, but the results are otherwise qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the domain and initial condition are chosen properly.

Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study.

PubMed

Li, Nianqiang; Susanto, H; Cemlyn, B R; Henning, I D; Adams, M J

2018-02-19

We study the nonlinear dynamics of solitary and optically injected two-element laser arrays with a range of waveguide structures. The analysis is performed with a detailed direct numerical simulation, where high-resolution dynamic maps are generated to identify regions of dynamic instability in the parameter space of interest. Our combined one- and two-parameter bifurcation analysis uncovers globally diverse dynamical regimes (steady-state, oscillation, and chaos) in the solitary laser arrays, which are greatly influenced by static design waveguiding structures, the amplitude-phase coupling factor of the electric field, i.e. the linewidth-enhancement factor, as well as the control parameter, e.g. the pump rate. When external optical injection is introduced to one element of the arrays, we show that the whole system can be either injection-locked simultaneously or display rich, different dynamics outside the locking region. The effect of optical injection is to significantly modify the nature and the regions of nonlinear dynamics from those found in the solitary case. We also show similarities and differences (asymmetry) between the oscillation amplitude of the two elements of the array in specific well-defined regions, which hold for all the waveguiding structures considered. Our findings pave the way to a better understanding of dynamic instability in large arrays of lasers.

A square wave is the most efficient and reliable waveform for resonant actuation of micro switches

NASA Astrophysics Data System (ADS)

Ben Sassi, S.; Khater, M. E.; Najar, F.; Abdel-Rahman, E. M.

2018-05-01

This paper investigates efficient actuation methods of shunt MEMS switches and other parallel-plate actuators. We start by formulating a multi-physics model of the micro switch, coupling the nonlinear Euler-Bernoulli beam theory with the nonlinear Reynolds equation to describe the structural and fluidic domains, respectively. The model takes into account fringing field effects as well as mid-plane stretching and squeeze film damping nonlinearities. Static analysis is undertaken using the differential quadrature method (DQM) to obtain the pull-in voltage, which is verified by means of the finite element model and validated experimentally. We develop a reduced order model employing the Galerkin method for the structural domain and DQM for the fluidic domain. The proposed waveforms are intended to be more suitable for integrated circuit standards. The dynamic response of the micro switch to harmonic, square and triangular waveforms are evaluated and compared experimentally and analytically. Low voltage actuation is obtained using dynamic pull-in with the proposed waveforms. In addition, global stability analysis carried out for the three signals shows advantages of employing the square signal as the actuation method in enhancing the performance of the micro switch in terms of actuation voltage, switching time, and sensitivity to initial conditions.

Heterogeneous mechanics of the mouse pulmonary arterial network.

PubMed

Lee, Pilhwa; Carlson, Brian E; Chesler, Naomi; Olufsen, Mette S; Qureshi, M Umar; Smith, Nicolas P; Sochi, Taha; Beard, Daniel A

2016-10-01

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure-radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.

Vibration of mechanically-assembled 3D microstructures formed by compressive buckling

NASA Astrophysics Data System (ADS)

Wang, Heling; Ning, Xin; Li, Haibo; Luan, Haiwen; Xue, Yeguang; Yu, Xinge; Fan, Zhichao; Li, Luming; Rogers, John A.; Zhang, Yihui; Huang, Yonggang

2018-03-01

Micro-electromechanical systems (MEMS) that rely on structural vibrations have many important applications, ranging from oscillators and actuators, to energy harvesters and vehicles for measurement of mechanical properties. Conventional MEMS, however, mostly utilize two-dimensional (2D) vibrational modes, thereby imposing certain limitations that are not present in 3D designs (e.g., multi-directional energy harvesting). 3D vibrational micro-platforms assembled through the techniques of controlled compressive buckling are promising because of their complex 3D architectures and the ability to tune their vibrational behavior (e.g., natural frequencies and modes) by reversibly changing their dimensions by deforming their soft, elastomeric substrates. A clear understanding of such strain-dependent vibration behavior is essential for their practical applications. Here, we present a study on the linear and nonlinear vibration of such 3D mesostructures through analytical modeling, finite element analysis (FEA) and experiment. An analytical solution is obtained for the vibration mode and linear natural frequency of a buckled ribbon, indicating a mode change as the static deflection amplitude increases. The model also yields a scaling law for linear natural frequency that can be extended to general, complex 3D geometries, as validated by FEA and experiment. In the regime of nonlinear vibration, FEA suggests that an increase of amplitude of external loading represents an effective means to enhance the bandwidth. The results also uncover a reduced nonlinearity of vibration as the static deflection amplitude of the 3D structures increases. The developed analytical model can be used in the development of new 3D vibrational micro-platforms, for example, to enable simultaneous measurement of diverse mechanical properties (density, modulus, viscosity etc.) of thin films and biomaterials.

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.

1999-01-01

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Nonlinear effective theory of dark energy

NASA Astrophysics Data System (ADS)

Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo

2018-04-01

We develop an approach to parametrize cosmological perturbations beyond linear order for general dark energy and modified gravity models characterized by a single scalar degree of freedom. We derive the full nonlinear action, focusing on Horndeski theories. In the quasi-static, non-relativistic limit, there are a total of six independent relevant operators, three of which start at nonlinear order. The new nonlinear couplings modify, beyond linear order, the generalized Poisson equation relating the Newtonian potential to the matter density contrast. We derive this equation up to cubic order in perturbations and, in a companion article [1], we apply it to compute the one-loop matter power spectrum. Within this approach, we also discuss the Vainshtein regime around spherical sources and the relation between the Vainshtein scale and the nonlinear scale for structure formation.

Analysis of the stability of nonlinear suspension system with slow-varying sprung mass under dual-excitation

NASA Astrophysics Data System (ADS)

Yao, Jun; Zhang, Jinqiu; Zhao, Mingmei; Li, Xin

2018-07-01

This study investigated the stability of vibration in a nonlinear suspension system with slow-varying sprung mass under dual-excitation. A mathematical model of the system was first established and then solved using the multi-scale method. Finally, the amplitude-frequency curve of vehicle vibration, the solution's stable region and time-domain curve in Hopf bifurcation were derived. The obtained results revealed that an increase in the lower excitation would reduce the system's stability while an increase in the upper excitation can make the system more stable. The slow-varying sprung mass will change the system's damping from negative to positive, leading to the appearance of limit cycle and Hopf bifurcation. As a result, the vehicle's vibration state is forced to change. The stability of this system is extremely fragile under the effect of dynamic Hopf bifurcation as well as static bifurcation.

Nonlinear Thermoelastic Model for SMAs and SMA Hybrid Composites

NASA Technical Reports Server (NTRS)

Turner, Travis L.

2004-01-01

A constitutive mathematical model has been developed that predicts the nonlinear thermomechanical behaviors of shape-memory-alloys (SMAs) and of shape-memory-alloy hybrid composite (SMAHC) structures, which are composite-material structures that contain embedded SMA actuators. SMAHC structures have been investigated for their potential utility in a variety of applications in which there are requirements for static or dynamic control of the shapes of structures, control of the thermoelastic responses of structures, or control of noise and vibrations. The present model overcomes deficiencies of prior, overly simplistic or qualitative models that have proven ineffective or intractable for engineering of SMAHC structures. The model is sophisticated enough to capture the essential features of the mechanics of SMAHC structures yet simple enough to accommodate input from fundamental engineering measurements and is in a form that is amenable to implementation in general-purpose structural analysis environments.

Dynamics near the threshold for blowup in the one-dimensional focusing nonlinear Klein-Gordon equation

NASA Astrophysics Data System (ADS)

Bizoń, Piotr; Chmaj, Tadeusz; Szpak, Nikodem

2011-10-01

We study dynamics near the threshold for blowup in the focusing nonlinear Klein-Gordon equation utt - uxx + u - |u|2αu = 0 on the line. Using mixed numerical and analytical methods we find that solutions starting from even initial data, fine-tuned to the threshold, are trapped by the static solution S for intermediate times. The details of trapping are shown to depend on the power α, namely, we observe fast convergence to S for α > 1, slow convergence for α = 1, and very slow (if any) convergence for 0 < α < 1. Our findings are complementary with respect to the recent rigorous analysis of the same problem (for α > 2) by Krieger, Nakanishi, and Schlag ["Global dynamics above from the ground state energy for the one-dimensional NLKG equation," preprint arXiv:1011.1776 [math.AP

Transient dynamics of a nonlinear magneto-optical rotation

NASA Astrophysics Data System (ADS)

Grewal, Raghwinder Singh; Pustelny, S.; Rybak, A.; Florkowski, M.

2018-04-01

We analyze nonlinear magneto-optical rotation (NMOR) in rubidium vapor subjected to a continuously scanned magnetic field. By varying the magnetic-field sweep rate, a transition from traditionally observed dispersivelike NMOR signals (low sweep rate) to oscillating signals (higher sweep rates) is demonstrated. The transient oscillatory behavior is studied versus light and magnetic-field parameters, revealing a strong dependence of the signals on magnetic sweep rate and light intensity. The experimental results are supported with density-matrix calculations, which enable quantitative analysis of the effect. Fitting of the signals simulated versus different parameters with a theoretically motivated curve reveals the presence of oscillatory and static components in the signals. The components depend differently on the system parameters, which suggests their distinct nature. The investigations provide insight into the dynamics of ground-state coherence generation and enable application of NMOR in detection of transient spin couplings.

The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model.

PubMed

Gras, Laure-Lise; Mitton, David; Crevier-Denoix, Nathalie; Laporte, Sébastien

2012-01-01

Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Young's modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.

An Optimization Code for Nonlinear Transient Problems of a Large Scale Multidisciplinary Mathematical Model

NASA Astrophysics Data System (ADS)

Takasaki, Koichi

This paper presents a program for the multidisciplinary optimization and identification problem of the nonlinear model of large aerospace vehicle structures. The program constructs the global matrix of the dynamic system in the time direction by the p-version finite element method (pFEM), and the basic matrix for each pFEM node in the time direction is described by a sparse matrix similarly to the static finite element problem. The algorithm used by the program does not require the Hessian matrix of the objective function and so has low memory requirements. It also has a relatively low computational cost, and is suited to parallel computation. The program was integrated as a solver module of the multidisciplinary analysis system CUMuLOUS (Computational Utility for Multidisciplinary Large scale Optimization of Undense System) which is under development by the Aerospace Research and Development Directorate (ARD) of the Japan Aerospace Exploration Agency (JAXA).

VALIDATION OF ANSYS FINITE ELEMENT ANALYSIS SOFTWARE

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

HAMM, E.R.

2003-06-27

This document provides a record of the verification and Validation of the ANSYS Version 7.0 software that is installed on selected CH2M HILL computers. The issues addressed include: Software verification, installation, validation, configuration management and error reporting. The ANSYS{reg_sign} computer program is a large scale multi-purpose finite element program which may be used for solving several classes of engineering analysis. The analysis capabilities of ANSYS Full Mechanical Version 7.0 installed on selected CH2M Hill Hanford Group (CH2M HILL) Intel processor based computers include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency andmore » buckling eigenvalue problems, static or time-varying magnetic analyses and various types of field and coupled-field applications. The program contains many special features which allow nonlinearities or secondary effects to be included in the solution, such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and thermal radiation. The ANSYS program has been in commercial use since 1970, and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil and steel industries.« less

The mechanisms of the effects of magnetic fields on cells

NASA Astrophysics Data System (ADS)

Kondrachuk, A.

The evolution of organisms in conditions of the Earth magnetism results in close dependence of their functioning on the properties of the Earth magnetic field. The magnetic conditions in space flight differ from those on the Earth (e.g. much smaller values of magnetic filed) that effect various processes in living organisms. Meanwhile the mechanisms of interaction of magnetic fields with cell structures are poorly understood and systemized. The goal of the present work is to analyze and estimate the main established mechanisms of "magnetic fields - cell" interaction. Due to variety and complexity of the effects the analysis is mainly restricted to biological effects of the static magnetic field at a cellular level. 1) Magnetic induction. Static magnetic fields exert forces on moving ions in solution (e.g., electrolytes), giving rise to induced electric fields and currents. This effect may be especially important when the currents changed due to the magnetic field application are participating in some receptor functions of cells (e.g. plant cells). 2) Magneto-mechanical effect of reorientation. Uniform static magnetic fields produce torques on certain molecules with anisotropic magnetic properties, which results in their reorientation and spatial ordering. Since the structures of biological cells are magnetically and mechanically inhomogeneous, the application of a homogeneous magnetic field may cause redistribution of stresses within cells, deformation of intracellular structures, change of membrane permeability, etc. 3) Ponderomotive effects. Spatially non-uniform magnetic field exerts ponderomotive force on magnetically non-uniform cell structures. This force is proportional to the gradient of the square of magnetic field and the difference of magnetic susceptibilities of the component of the cell and its environment. 4) Biomagnetic effects. Magnetic fields can exert torques and translational forces on ferromagnetic structures, such as magnetite and ferritins presented in the cells. 5) Electronic interactions. Static magnetic fields can alter energy levels and spin orientation of electrons. Similar interactions can also occur with nuclear spins, but these are very weak compared to electron interactions. 6) Free radicals. Magnetic fields alter the spin states of the radicals, which, in turn, changes the relative probabilities of recombination and other interactions, possibly with biological consequences. 7) Non-linear effects. A number of non-linear mechanisms of magnetic effects on cells were recently proposed to explain how the cell could extract a weak magnetic signal from noise (e.g. stochastic non-linear resonance, self-tuned Hopf bifurcations). These new models need further experimental testing.

Nonlinear generation of sum and difference frequency waves by two helicon waves in a semiconductor

NASA Astrophysics Data System (ADS)

Salimullah, M.; Ferdous, T.

1984-05-01

This paper presents a theoretical investigation of the nonlinear generation of electrostatic waves at the sum and the difference frequency when two high amplitude elliptically polarized helicon waves propagate along the direction of the externally applied static magnetic field in an n-type semiconductor. The nonlinearity arises through the ponderomotive force on electrons. It is noticed that the power conversion efficiency of the difference frequency generation is much larger than that of the sum frequency generation. The power conversion efficiency may be easily increased by increasing the density of electrons in the semiconductor.

Time series with tailored nonlinearities

NASA Astrophysics Data System (ADS)

Räth, C.; Laut, I.

2015-10-01

It is demonstrated how to generate time series with tailored nonlinearities by inducing well-defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncorrelated Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for, e.g., turbulence and financial data can thus be explained in terms of phase correlations.

System design optimization for a Mars-roving vehicle and perturbed-optimal solutions in nonlinear programming

NASA Technical Reports Server (NTRS)

Pavarini, C.

1974-01-01

Work in two somewhat distinct areas is presented. First, the optimal system design problem for a Mars-roving vehicle is attacked by creating static system models and a system evaluation function and optimizing via nonlinear programming techniques. The second area concerns the problem of perturbed-optimal solutions. Given an initial perturbation in an element of the solution to a nonlinear programming problem, a linear method is determined to approximate the optimal readjustments of the other elements of the solution. Then, the sensitivity of the Mars rover designs is described by application of this method.

Improved operation of magnetic bearings for flywheel energy storage system

NASA Technical Reports Server (NTRS)

Zmood, R. B.; Pang, D.; Anand, D. K.; Kirk, J. A.

1990-01-01

Analysis and operation of prototype 500-Wh flywheel at low speeds have shown that many factors affect the correct functioning of the magnetic bearings. An examination is made of a number of these, including magnetic bearing control system nonlinearities and displacement transducer positioning, and their effects upon the successful operation of the suspension system. It is observed that the bearing control system is extremely sensitive to actuator parameters such as coil inductance. As a consequence of the analysis of bearing relaxation oscillations, the bearing actuator design methodology which has previously been used, where coil parameter selection is based upon static considerations, has been revised. Displacement transducer sensors which overcome the collocation problem are discussed.

Neural Network Based Modeling and Analysis of LP Control Surface Allocation

NASA Technical Reports Server (NTRS)

Langari, Reza; Krishnakumar, Kalmanje; Gundy-Burlet, Karen

2003-01-01

This paper presents an approach to interpretive modeling of LP based control allocation in intelligent flight control. The emphasis is placed on a nonlinear interpretation of the LP allocation process as a static map to support analytical study of the resulting closed loop system, albeit in approximate form. The approach makes use of a bi-layer neural network to capture the essential functioning of the LP allocation process. It is further shown via Lyapunov based analysis that under certain relatively mild conditions the resulting closed loop system is stable. Some preliminary conclusions from a study at Ames are stated and directions for further research are given at the conclusion of the paper.

Origin of the Absorption Band of Bromophenol Blue in Acidic and Basic pH: Insight from a Combined Molecular Dynamics and TD-DFT/MM Study.

PubMed

Chattopadhyaya, M; Murugan, N Arul; Rinkevicius, Zilvinas

2016-09-15

We study the linear and nonlinear optical properties of a well-known acid-base indicator, bromophenol blue (BPB), in aqueous solution by employing static and integrated approaches. In the static approach, optical properties have been calculated using time-dependent density functional theory (TD-DFT) on the fully relaxed geometries of the neutral and different unprotonated forms of BPB. Moreover, both closed and open forms of BPB were considered. In the integrated approach, the optical properties have been computed over many snapshots extracted from molecular dynamics simulation using a hybrid time-dependent density functional theory/molecular mechanics approach. The static approach suggests closed neutral ⇒ anionic interconversion as the dominant mechanism for the red shift in the absorption spectra of BPB due to a change from acidic to basic pH. It is found by employing an integrated approach that the two interconversions, namely open neutral ⇒ anionic and open neutral ⇒ dianionic, can contribute to the pH-dependent shift in the absorption spectra of BPB. Even though both static and integrated approaches reproduce the pH-dependent red shift in the absorption spectra of BPB, the latter one is suitable to determine both the spectra and spectral broadening. Finally, the computed static first hyperpolarizability for various protonated and deprotonated forms of BPB reveals that this molecule can be used as a nonlinear optical probe for pH sensing in addition to its highly exploited use as an optical probe.

Thermomechanical Response of Shape Memory Alloy Hybrid Composites. Degree awarded by Virginia Polytechnic Inst. and State Univ., Blackburg, Virginia, Nov. 2000.

NASA Technical Reports Server (NTRS)

Turner, Travis L.

2001-01-01

This study examines the use of embedded shape memory alloy (SMA) actuators for adaptive control of the thermomechanical response of composite structures. A nonlinear thermomechanical model is presented for analyzing shape memory alloy hybrid composite (SMAHC) structures exposed to steady-state thermal and dynamic mechanical loads. Also presented are (1) fabrication procedures for SMAHC specimens, (2) characterization of the constituent materials for model quantification, (3) development of the test apparatus for conducting static and dynamic experiments on specimens with and without SMA, (4) discussion of the experimental results, and (5) validation of the analytical and numerical tools developed in the study. Excellent agreement is achieved between the predicted and measured SAMHC responses including thermal buckling, thermal post-buckling and dynamic response due to inertial loading. The validated model and thermomechanical analysis tools are used to demonstrate a variety of static and dynamic response behaviors including control of static (thermal buckling and post-buckling) and dynamic responses (vibration, sonic fatigue, and acoustic transmission). and SMAHC design considerations for these applications. SMAHCs are shown to have significant advantages over conventional response abatement approaches for vibration, sonic fatigue, and noise control.

A Nonlinear Modal Aeroelastic Solver for FUN3D

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.

2016-01-01

A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.

Finite element analyses for seismic shear wall international standard problem

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

Park, Y.J.; Hofmayer, C.H.

Two identical reinforced concrete (RC) shear walls, which consist of web, flanges and massive top and bottom slabs, were tested up to ultimate failure under earthquake motions at the Nuclear Power Engineering Corporation`s (NUPEC) Tadotsu Engineering Laboratory, Japan. NUPEC provided the dynamic test results to the OECD (Organization for Economic Cooperation and Development), Nuclear Energy Agency (NEA) for use as an International Standard Problem (ISP). The shear walls were intended to be part of a typical reactor building. One of the major objectives of the Seismic Shear Wall ISP (SSWISP) was to evaluate various seismic analysis methods for concrete structuresmore » used for design and seismic margin assessment. It also offered a unique opportunity to assess the state-of-the-art in nonlinear dynamic analysis of reinforced concrete shear wall structures under severe earthquake loadings. As a participant of the SSWISP workshops, Brookhaven National Laboratory (BNL) performed finite element analyses under the sponsorship of the U.S. Nuclear Regulatory Commission (USNRC). Three types of analysis were performed, i.e., monotonic static (push-over), cyclic static and dynamic analyses. Additional monotonic static analyses were performed by two consultants, F. Vecchio of the University of Toronto (UT) and F. Filippou of the University of California at Berkeley (UCB). The analysis results by BNL and the consultants were presented during the second workshop in Yokohama, Japan in 1996. A total of 55 analyses were presented during the workshop by 30 participants from 11 different countries. The major findings on the presented analysis methods, as well as engineering insights regarding the applicability and reliability of the FEM codes are described in detail in this report. 16 refs., 60 figs., 16 tabs.« less

Self-similar perturbations of a Friedmann universe

NASA Technical Reports Server (NTRS)

Carr, Bernard J.; Yahil, Amos

1990-01-01

The present analysis of spherically symmetric self-similar solutions to the Einstein equations gives attention to those solutions that are asymptotically k = 0 Friedmann at large z values, and possess finite but perturbed density at the origin. Such solutions represent nonlinear density fluctuations which grow at the same rate as the universe's particle horizon. The overdense solutions span only a narrow range of parameters, and resemble static isothermal gas spheres just within the sonic point; the underdense solutions may have arbitrarily low density at the origin while exhibiting a unique relationship between amplitude and scale. Their relevance to large-scale void formation is considered.

An Ultrasonic Technique to Determine the Residual Strength of Adhesive Bonds

NASA Technical Reports Server (NTRS)

Achenbach, J. D.; Tang, Z.

1999-01-01

In this work, ultrasonic techniques to nondestructively evaluate adhesive bond degradation have been studied. The key to the present approach is the introduction of an external factor which pulls the adhesive bond in the nonlinear range, simultaneously with the application of an ultrasonic technique. With the aid of an external static tensile loading, a superimposed longitudinal wave has.been used to obtain the slopes of the stress-strain curve of an adhesive bond at a series of load levels. The critical load, at which a reduction of the slope is detected by the superimposed longitudinal wave, is an indication of the onset of nonlinear behavior of the adhesive bond, and therefore of bond degradation. This approach has been applied to the detection of adhesive bond degradation induced by cyclic fatigue loading. Analogously to the longitudinal wave case, a superimposed shear wave has been used to obtain the effective shear modulus of adhesive layers at different shear load levels. The onset of the nonlinear behavior of an adhesive bond under shear loading has been detected by the use of a superimposed shear wave. Experiments show that a longitudinal wave can also detect the nonlinear behavior when an adhesive bond is subjected to shear loading. An optimal combination of ultrasonic testing and mechanical loading methods for the detection of degradation related nonlinear behavior of adhesive bonds has been discussed. For the purpose of a practical application, an ultrasonic technique that uses a temperature increase as an alternative to static loading has also been investigated. A general strain-temperature correspondence principle that relates a mechanical strain to a temperature has been presented. Explicit strain-temperature correspondence relations for both the tension and shear cases have been derived. An important parameter which quantifies the relation between the wave velocity and temperature has been defined. This parameter, which is indicative of adhesive bond nonlinearity and which can be conveniently obtained by an ultrasonic measurement, has been used as an indication of adhesive bond degradation. Experimental results have shown that the temperature increase method is a convenient and productive alternative to static loading. A technique which uses the reflected waveform data to obtain the fundamental ultrasonic parameters (transit time, reflection coefficient and attenuation coefficient) of an adhesive bond has also been presented.

Contribution a la caracterisation des betons endommages par des methodes de l'acoustique non lineaire. Application a la reaction alcalis-silice

NASA Astrophysics Data System (ADS)

Kodjo, Apedovi

The aim of this thesis is to contribute to the non-destructive characterization of concrete materials damaged by alkali-silica reaction (ASR). For this purpose, some nonlinear characterization techniques have been developed, as well as a nonlinear resonance test device. In order to optimize the sensitivity of the test device, the excitation module and signal processing have been improved. The nonlinear tests were conducted on seven samples of concrete damaged by ASR, three samples of concrete damaged by heat, three concrete samples damaged mechanically and three sound concrete samples. Since, nonlinear behaviour of the material is often attribute to its micro-defects hysteretic behaviour, it was shown at first that concrete damaged by ASR exhibits an hysteresis behaviour. To conduct this study, an acoustoelastic test was set, and then nonlinear resonance test device was used for characterizing sound concrete and concrete damaged by ASR. It was shown that the nonlinear technique can be used for characterizing the material without knowing its initial state, and also for detecting early damage in the reactive material. Studies were also carried out on the effect of moisture regarding the nonlinear parameters; they allowed understanding the low values of nonlinear parameters measured on concrete samples that were kept in high moisture conditions. In order to find a specific characteristic of damage caused by ASR, the viscosity of ASR gel was used. An approach, based on static creep analysis, performed on the material, while applying the nonlinear resonance technique. The spring-damping model of Maxwell was used for the interpretation of the results. Then, the creep time was analysed on samples damaged by ASR. It appears that the ASR gel increases the creep time. Finally, the limitations of the nonlinear resonance technique for in situ application have been explained and a new applicable nonlinear technique was initiated. This technique use an external source such as a mass for making non-linearity behaviour in the material, while an ultrasound wave is investigating the medium. Keywords. Concrete, Alkali-silica reaction, Nonlinear acoustics, Nonlinearity, Hysteresis, Damage diagnostics.

Experimental Investigation of Stiffness Characteristics and Damping Properties of a Metallic Rubber Material

NASA Astrophysics Data System (ADS)

Lu, Ch. Zh.; Li, Jingyuan; Zhou, Bangyang; Li, Shuang

2017-09-01

The static stiffness and dynamic damping properties of a metallic rubber material (MR) were investigated, which exhibited a nonlinear deformation behavior. Its static stiffness is analyzed and discussed. The effects of structural parameters of MR and experimental conditions on its shock absorption capacity were examined by dynamic tests. Results revealed excellent elastic and damping properties of the material. Its stiffness increased with density, but decreased with thickness. The damping property of MR varied with its density, thickness, loading frequency, and amplitude.

Turbine Engine Control Synthesis. Volume 1. Optimal Controller Synthesis and Demonstration

DTIC Science & Technology

1975-03-01

Nomenclature (Continued) Symbol Deseription M Matrix (of Table 12) M Mach number N Rotational speed, rpm N ’ Nonlinear rotational speed, rpm P Power lever... P Pressure, N /m 2; bfh/ft 2 PLA Power lever angle PR = PT3/PT2 Pressure ratio ( P Power, ft-lbf/sec Q Matrix (of Table 30) R Universal gas constant, 53...function, i = 1, 2, 3, ... in Inlet n Stage number designation out Outlet p Variable associated with particle s Static condition _se Static condition

Acoustic radiation stress measurement

NASA Technical Reports Server (NTRS)

Cantrell, John H., Jr.; Yost, William T.

1987-01-01

Ultrasonic radio frequency tone-bursts are launched into a sample of material tested. The amplitude of the tone-bursts and the slope of the resulting static displacement pulses are measured. These measurements are used to calculate the nonlinearities of the materials.

Solution procedure of dynamical contact problems with friction

NASA Astrophysics Data System (ADS)

Abdelhakim, Lotfi

2017-07-01

Dynamical contact is one of the common research topics because of its wide applications in the engineering field. The main goal of this work is to develop a time-stepping algorithm for dynamic contact problems. We propose a finite element approach for elastodynamics contact problems [1]. Sticking, sliding and frictional contact can be taken into account. Lagrange multipliers are used to enforce non-penetration condition. For the time discretization, we propose a scheme equivalent to the explicit Newmark scheme. Each time step requires solving a nonlinear problem similar to a static friction problem. The nonlinearity of the system of equation needs an iterative solution procedure based on Uzawa's algorithm [2][3]. The applicability of the algorithm is illustrated by selected sample numerical solutions to static and dynamic contact problems. Results obtained with the model have been compared and verified with results from an independent numerical method.

A k-Vector Approach to Sampling, Interpolation, and Approximation

NASA Astrophysics Data System (ADS)

Mortari, Daniele; Rogers, Jonathan

2013-12-01

The k-vector search technique is a method designed to perform extremely fast range searching of large databases at computational cost independent of the size of the database. k-vector search algorithms have historically found application in satellite star-tracker navigation systems which index very large star catalogues repeatedly in the process of attitude estimation. Recently, the k-vector search algorithm has been applied to numerous other problem areas including non-uniform random variate sampling, interpolation of 1-D or 2-D tables, nonlinear function inversion, and solution of systems of nonlinear equations. This paper presents algorithms in which the k-vector search technique is used to solve each of these problems in a computationally-efficient manner. In instances where these tasks must be performed repeatedly on a static (or nearly-static) data set, the proposed k-vector-based algorithms offer an extremely fast solution technique that outperforms standard methods.

Dynamic analysis of clamp band joint system subjected to axial vibration

NASA Astrophysics Data System (ADS)

Qin, Z. Y.; Yan, S. Z.; Chu, F. L.

2010-10-01

Clamp band joints are commonly used for connecting circular components together in industry. Some of the systems jointed by clamp band are subjected to dynamic load. However, very little research on the dynamic characteristics for this kind of joint can be found in the literature. In this paper, a dynamic model for clamp band joint system is developed. Contact and frictional slip between the components are accommodated in this model. Nonlinear finite element analysis is conducted to identify the model parameters. Then static experiments are carried out on a scaled model of the clamp band joint to validate the joint model. Finally, the model is adopted to study the dynamic characteristics of the clamp band joint system subjected to axial harmonic excitation and the effects of the wedge angle of the clamp band joint and the preload on the response. The model proposed in this paper can represent the nonlinearity of the clamp band joint and be used conveniently to investigate the effects of the structural and loading parameters on the dynamic characteristics of this type of joint system.

Conformational, spectroscopic and nonlinear optical investigations on 1-(4-chlorophenyl)-3-(4-chlorophenyl)-2-propen-1-one: a DFT study

NASA Astrophysics Data System (ADS)

Altürk, Sümeyye; Boukabcha, Nourdine; Benhalima, Nadia; Tamer, Ömer; Chouaih, Abdelkader; Avcı, Davut; Atalay, Yusuf; Hamzaoui, Fodil

2017-05-01

The density functional theory calculations on 1-(4-chlorophenyl)-3-(4-chlorophenyl)-2-propen-1-one (CPCPP) are performed by using B3LYP and HSEh1PBE levels. These methods along with 6-311++G(d,p) basis set have been used to determine optimized molecular geometries, vibrational frequencies, electronic absorption wavelengths and bonding features of CPCPP. The solvent effect on the electronic absorption properties of CPCPP is examined at polar (ethanol and water) and nonpolar (toluene and n-hexane) solvents. In order to find the most stable conformers, conformational analysis is carried out by using B3LYP level. The computed small energy gaps between HOMO and LUMO energies show that the charge transfers occur within CPCPP. DFT calculations have been also performed to investigate the dipole moment (μ), mean polarizability (α), anisotropy of polarizability (Δα), first order static hyperpolarizability (β) for CPCPP. The obtained values show that CPCPP is an excellent candidate to nonlinear optical materials. NBO analysis has been used to investigate the bond strengths, molecular stability, hyperconjugative interactions and intramolecular charge transfer (ICT).

Finite Elements Analysis of a Composite Semi-Span Test Article With and Without Discrete Damage

NASA Technical Reports Server (NTRS)

Lovejoy, Andrew E.; Jegley, Dawn C. (Technical Monitor)

2000-01-01

AS&M Inc. performed finite element analysis, with and without discrete damage, of a composite semi-span test article that represents the Boeing 220-passenger transport aircraft composite semi-span test article. A NASTRAN bulk data file and drawings of the test mount fixtures and semi-span components were utilized to generate the baseline finite element model. In this model, the stringer blades are represented by shell elements, and the stringer flanges are combined with the skin. Numerous modeling modifications and discrete source damage scenarios were applied to the test article model throughout the course of the study. This report details the analysis method and results obtained from the composite semi-span study. Analyses were carried out for three load cases: Braked Roll, LOG Down-Bending and 2.5G Up-Bending. These analyses included linear and nonlinear static response, as well as linear and nonlinear buckling response. Results are presented in the form of stress and strain plots. factors of safety for failed elements, buckling loads and modes, deflection prediction tables and plots, and strainage prediction tables and plots. The collected results are presented within this report for comparison to test results.

Advanced analysis technique for the evaluation of linear alternators and linear motors

NASA Technical Reports Server (NTRS)

Holliday, Jeffrey C.

1995-01-01

A method for the mathematical analysis of linear alternator and linear motor devices and designs is described, and an example of its use is included. The technique seeks to surpass other methods of analysis by including more rigorous treatment of phenomena normally omitted or coarsely approximated such as eddy braking, non-linear material properties, and power losses generated within structures surrounding the device. The technique is broadly applicable to linear alternators and linear motors involving iron yoke structures and moving permanent magnets. The technique involves the application of Amperian current equivalents to the modeling of the moving permanent magnet components within a finite element formulation. The resulting steady state and transient mode field solutions can simultaneously account for the moving and static field sources within and around the device.

A Four-Dimensional Computed Tomography Comparison of Healthy vs. Asthmatic Human Lungs

PubMed Central

Jahani, Nariman; Choi, Sanghun; Choi, Jiwoong; Haghighi, Babak; Hoffman, Eric A.; Comellas, Alejandro P.; Kline, Joel N.; Lin, Ching-Long

2017-01-01

The purpose of this study was to explore new insights in non-linearity, hysteresis and ventilation heterogeneity of asthmatic human lungs using four-dimensional computed tomography (4D-CT) image data acquired during tidal breathing. Volumetric image data were acquired for 5 non-severe and one severe asthmatic volunteers. Besides 4D-CT image data, function residual capacity and total lung capacity image data during breath-hold were acquired for comparison with dynamic scans. Quantitative results were compared with the previously reported analysis of five healthy human lungs. Using an image registration technique, local variables such as regional ventilation and anisotropic deformation index (ADI) were estimated. Regional ventilation characteristics of non-severe asthmatic subjects were similar to those of healthy subjects, but different from the severe asthmatic subject. Lobar airflow fractions were also well correlated between static and dynamic scans (R2 > 0.84). However, local ventilation heterogeneity significantly increased during tidal breathing in both healthy and asthmatic subjects relative to that of breath-hold perhaps because of airway resistance present only in dynamic breathing. ADI was used to quantify non-linearity and hysteresis of lung motion during tidal breathing. Nonlinearity was greater on inhalation than exhalation among all subjects. However, exhalation nonlinearity among asthmatic subjects was greater than healthy subjects and the difference diminished during inhalation. An increase of non-linearity during exhalation in asthmatic subjects accounted for lower hysteresis relative to that of healthy ones. Thus, assessment of nonlinearity differences between healthy and asthmatic lungs during exhalation may provide quantitative metrics for subject identification and outcome assessment of new interventions. PMID:28372795

Finite element analysis (FEA) analysis of the preflex beam

NASA Astrophysics Data System (ADS)

Wan, Lijuan; Gao, Qilang

2017-10-01

The development of finite element analysis (FEA) has been relatively mature, and is one of the important means of structural analysis. This method changes the problem that the research of complex structure in the past needs to be done by a large number of experiments. Through the finite element method, the numerical simulation of the structure can be used to achieve a variety of static and dynamic simulation analysis of the mechanical problems, it is also convenient to study the parameters of the structural parameters. Combined with a certain number of experiments to verify the simulation model can be completed in the past all the needs of experimental research. The nonlinear finite element method is used to simulate the flexural behavior of the prestressed composite beams with corrugated steel webs. The finite element analysis is used to understand the mechanical properties of the structure under the action of bending load.

Key functions analysis of a novel nonlinear optical D-π-A bridge type (2E)-3-(4-Methylphenyl)-1-(3-nitrophenyl) prop-2-en-1-one chalcone: An experimental and theoretical approach

NASA Astrophysics Data System (ADS)

Patil, Parutagouda Shankaragouda; Shkir, Mohd; Maidur, Shivaraj R.; AlFaify, S.; Arora, M.; Rao, S. Venugopal; Abbas, Haider; Ganesh, V.

2017-10-01

In the current work a new third-order nonlinear optical organic single crystal of (2E)-3-(4-Methylphenyl)-1-(3-nitrophenyl) prop-2-en-1-one (ML3NC) has been grown with well-defined morphology using the slow evaporation solution growth technique. X-ray diffraction technique was used to confirm the crystal system. The presence of functional groups in the molecular structure was identified by robust FT-IR and FT-Raman spectra by experimental and theoretical analysis. The ultraviolet-visible-near infrared and photoluminescence studies shows that the grown crystals possess excellent transparency window and green emission band (∼560 nm) confirms their use in green OLEDs. The third-order nonlinear and optical limiting studies have been performed using femtosecond (fs) Z-scan technique. The third-order nonlinear optical susceptibility (χ(3)), second-order hyperpolarizability (γ), nonlinear refractive index (n2) and limiting threshold values are found to be 4.03 × 10-12 esu, 14.2 × 10-32 esu, -4.33 × 10-14 cm2/W and 2.41 mJ/cm2, respectively. Furthermore, the quantum chemical studies were carried out to achieve the ground state molecular geometry and correlate with experimental results. The experimental value of absorption wavelength (λabs = 328 nm) is found to be in excellent accord with the theoretical value (λabs = 328 nm) at TD-DFT/B3LYP/6-31G* level of theory. To understand the static and dynamic NLO behavior, the polarizability (α) and second hyperpolarizability (γ) values were determined using TD-HF method. The computed second hyperpolarizability γ(-3ω; ω,ω,ω) at 800 nm wavelength was found to be 0.499 × 10-32 esu which is in good agreement with experimental value at the same wavelength. These results confirms the applied nature of title molecule in optoelectronic and nonlinear optical devices.

Static response of coated microbubbles compressed between rigid plates: Simulations and asymptotic analysis including elastic and adhesive forces

NASA Astrophysics Data System (ADS)

Lytra, A.; Pelekasis, N.

2018-03-01

The static response of coated microbubbles is investigated with a novel approach employed for modeling contact between a microbubble and the cantilever of an atomic force microscope. Elastic tensions and moments are described via appropriate constitutive laws. The encapsulated gas is assumed to undergo isothermal variations. Due to the hydrophilic nature of the cantilever, an ultrathin aqueous film is formed, which transfers the force onto the shell. An interaction potential describes the local pressure applied on the shell. The problem is solved in axisymmetric form with the finite element method. The response is governed by the dimensionless bending, k^ b=kb/(χ R02 ), pressure, P^ A=(PAR0 )/χ , and interaction potential, W ^ =w0/χ . Hard polymeric shells have negligible resistance to gas compression, while for the softer lipid shells gas compressibility is comparable with shell elasticity. As the external force increases, numerical simulations reveal that the force versus deformation (f vs d) curve of polymeric shells exhibits a transition from the linear O(d) (Reissner) regime, marked by flattened shapes around the contact region, to a non-linear O(d1/2) (Pogorelov) regime dominated by shapes exhibiting crater formation due to buckling. When lipid shells are tested, buckling is bypassed as the external force increases and flattened shapes prevail in an initially linear f vs d curve. Transition to a curved upwards regime is observed as the force increases, where gas compression and area dilatation form the dominant balance providing a nonlinear regime with an O(d3) dependence. Asymptotic analysis recovers the above patterns and facilitates estimation of the shell mechanical properties.

Hilbert-Schmidt and Sobol sensitivity indices for static and time series Wnt signaling measurements in colorectal cancer - part A.

PubMed

Sinha, Shriprakash

2017-12-04

Ever since the accidental discovery of Wingless [Sharma R.P., Drosophila information service, 1973, 50, p 134], research in the field of Wnt signaling pathway has taken significant strides in wet lab experiments and various cancer clinical trials, augmented by recent developments in advanced computational modeling of the pathway. Information rich gene expression profiles reveal various aspects of the signaling pathway and help in studying different issues simultaneously. Hitherto, not many computational studies exist which incorporate the simultaneous study of these issues. This manuscript ∙ explores the strength of contributing factors in the signaling pathway, ∙ analyzes the existing causal relations among the inter/extracellular factors effecting the pathway based on prior biological knowledge and ∙ investigates the deviations in fold changes in the recently found prevalence of psychophysical laws working in the pathway. To achieve this goal, local and global sensitivity analysis is conducted on the (non)linear responses between the factors obtained from static and time series expression profiles using the density (Hilbert-Schmidt Information Criterion) and variance (Sobol) based sensitivity indices. The results show the advantage of using density based indices over variance based indices mainly due to the former's employment of distance measures & the kernel trick via Reproducing kernel Hilbert space (RKHS) that capture nonlinear relations among various intra/extracellular factors of the pathway in a higher dimensional space. In time series data, using these indices it is now possible to observe where in time, which factors get influenced & contribute to the pathway, as changes in concentration of the other factors are made. This synergy of prior biological knowledge, sensitivity analysis & representations in higher dimensional spaces can facilitate in time based administration of target therapeutic drugs & reveal hidden biological information within colorectal cancer samples.

Use Of Adaptive Optics Element For Wavefront Error Correction In The Gemini CO2 Laser Fusion System

NASA Astrophysics Data System (ADS)

Viswanathan, V. K.; Parker, J. V.; Nussmier, T. A.; Swigert, C. J.; King, W.; Lau, A. S.; Price, K.

1980-11-01

The Gemini two beam CO2 laser fusion system incorporates a complex optical system with nearly 100 surfaces per beam, associated with the generation, transport and focusing of CO2 laser beams for irradiating laser fusion targets. Even though the system is nominally diffraction limited, in practice the departure from the ideal situation drops the Strehl ratio to 0.24. This departure is caused mostly by the imperfections in the large (34 cm optical clear aperture diameter) state-of-the-art components like the sodium chloride windows and micromachined mirrors. While the smaller optical components also contribute to this degradation, the various possible misalignments and nonlinear effects are considered to contribute very little to it. Analysis indicates that removing the static or quasi-static errors can dramatically improve the Strehl ratio. A deformable mirror which can comfortably achieve the design goal Strehl ratio of >= 0.7 is described, along with the various system trade-offs in the design of the mirror and the control system.

Modeling and Analysis of the Static Characteristics and Dynamic Responses of Herringbone-grooved Thrust Bearings

NASA Astrophysics Data System (ADS)

Yu, Yunluo; Pu, Guang; Jiang, Kyle

2017-12-01

This paper describes a theoretical investigation of static and dynamic characteristics of herringbone-grooved air thrust bearings. Firstly, Finite Difference Method (FDM) and Finite Volume Method (FVM) are used in combination to solve the non-linear Reynolds equation and to find the pressure distribution of the film and the total loading capacity of the bearing. The influence of design parameters on air film gap characteristics, including the air film thickness, depth of the groove and rotating speed, are analyzed based on the FDM model. The simulation results show that hydrostatic thrust bearings can achieve a better load capacity with less air consumption than herringbone grooved thrust bearings at low compressibility number; herringbone grooved thrust bearings can achieve a higher load capacity but with more air consumption than hydrostatic thrust bearing at high compressibility number; herringbone grooved thrust bearings would lose stability at high rotating speeds, and the stability increases with the depth of the grooves.

Finite element analyses of continuous filament ties for masonry applications : final report for the Arquin Corporation.

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

Quinones, Armando, Sr.; Bibeau, Tiffany A.; Ho, Clifford Kuofei

2008-08-01

Finite-element analyses were performed to simulate the response of a hypothetical vertical masonry wall subject to different lateral loads with and without continuous horizontal filament ties laid between rows of concrete blocks. A static loading analysis and cost comparison were also performed to evaluate optimal materials and designs for the spacers affixed to the filaments. Results showed that polypropylene, ABS, and polyethylene (high density) were suitable materials for the spacers based on performance and cost, and the short T-spacer design was optimal based on its performance and functionality. Simulations of vertical walls subject to static loads representing 100 mph windsmore » (0.2 psi) and a seismic event (0.66 psi) showed that the simulated walls performed similarly and adequately when subject to these loads with and without the ties. Additional simulations and tests are required to assess the performance of actual walls with and without the ties under greater loads and more realistic conditions (e.g., cracks, non-linear response).« less

Investigating Strategies to Increase Persistence and Success Rates among Anatomy & Physiology Students: A Case Study at Austin Community College District

NASA Astrophysics Data System (ADS)

Vedartham, Padmaja B.

Snap-through buckling provides an intricate force-displacement relationship for study. With the possibility for multiple limit points and pitchfork bifurcations and large regions of instability, experimental validation of numerical analysis can become difficult. This requires stabilization of unstable static equilibria, for which limited prior research exists. For all but the simplest cases, more than one actuator is needed, increasing the complexity of the experiment to the point of intractability without a control system. In this thesis, the necessary conditions for stabilization of a buckled beam with pinned boundaries under transverse loading were determined. By combining various nonlinear solution methods, a control system was created that could stabilize any branch of the force-displacement response. Experimental traversal of an unstable branch are presented along with other unstable static equilibrium configurations. The control system had numerical limitations, losing convergence near singular points. The groundwork for experimental stabilization was validated and demonstrated.

Liquidity crises on different time scales

NASA Astrophysics Data System (ADS)

Corradi, Francesco; Zaccaria, Andrea; Pietronero, Luciano

2015-12-01

We present an empirical analysis of the microstructure of financial markets and, in particular, of the static and dynamic properties of liquidity. We find that on relatively large time scales (15 min) large price fluctuations are connected to the failure of the subtle mechanism of compensation between the flows of market and limit orders: in other words, the missed revelation of the latent order book breaks the dynamical equilibrium between the flows, triggering the large price jumps. On smaller time scales (30 s), instead, the static depletion of the limit order book is an indicator of an intrinsic fragility of the system, which is related to a strongly nonlinear enhancement of the response. In order to quantify this phenomenon we introduce a measure of the liquidity imbalance present in the book and we show that it is correlated to both the sign and the magnitude of the next price movement. These findings provide a quantitative definition of the effective liquidity, which proves to be strongly dependent on the considered time scales.

Liquidity crises on different time scales.

PubMed

Corradi, Francesco; Zaccaria, Andrea; Pietronero, Luciano

2015-12-01

We present an empirical analysis of the microstructure of financial markets and, in particular, of the static and dynamic properties of liquidity. We find that on relatively large time scales (15 min) large price fluctuations are connected to the failure of the subtle mechanism of compensation between the flows of market and limit orders: in other words, the missed revelation of the latent order book breaks the dynamical equilibrium between the flows, triggering the large price jumps. On smaller time scales (30 s), instead, the static depletion of the limit order book is an indicator of an intrinsic fragility of the system, which is related to a strongly nonlinear enhancement of the response. In order to quantify this phenomenon we introduce a measure of the liquidity imbalance present in the book and we show that it is correlated to both the sign and the magnitude of the next price movement. These findings provide a quantitative definition of the effective liquidity, which proves to be strongly dependent on the considered time scales.

Structure design and characteristic analysis of micro-nano probe based on six dimensional micro-force measuring principle

NASA Astrophysics Data System (ADS)

Yang, Hong-tao; Cai, Chun-mei; Fang, Chuan-zhi; Wu, Tian-feng

2013-10-01

In order to develop micro-nano probe having error self-correcting function and good rigidity structure, a new micro-nano probe system was developed based on six-dimensional micro-force measuring principle. The structure and working principle of the probe was introduced in detail. The static nonlinear decoupling method was established with BP neural network to do the static decoupling for the dimension coupling existing in each direction force measurements. The optimal parameters of BP neural network were selected and the decoupling simulation experiments were done. The maximum probe coupling rate after decoupling is 0.039% in X direction, 0.025% in Y direction and 0.027% in Z direction. The static measurement sensitivity of the probe can reach 10.76μɛ / mN in Z direction and 14.55μɛ / mN in X and Y direction. The modal analysis and harmonic response analysis under three dimensional harmonic load of the probe were done by using finite element method. The natural frequencies under different vibration modes were obtained and the working frequency of the probe was determined, which is higher than 10000 Hz . The transient response analysis of the probe was done, which indicates that the response time of the probe can reach 0.4 ms. From the above results, it is shown that the developed micro-nano probe meets triggering requirements of micro-nano probe. Three dimension measuring force can be measured precisely by the developed probe, which can be used to predict and correct the force deformation error and the touch error of the measuring ball and the measuring rod.

Shake, Rattle, and Roll: Nonlinear Dynamics in Mechanical Engineering

NASA Astrophysics Data System (ADS)

Shaw, Steven

1997-03-01

This presentation will focus on three mechanical engineering applications in which methods from nonlinear dynamics have been applied with success. Each topic will be briefly surveyed by outlining the development of a mathematical model, providing a description of the analysis tools employed, and showing the main results obtained. The applications are: vibration reduction in internal combustion engines, impact dynamics of mechanical components, and the dynamics of ship capsize. The first topic demonstrates a novel arrangement of dynamic absorbers that can be used for attenuating torsional vibrations in rotating machinery. The operation of this device takes advantage of a purely nonlinear system response that results from a period doubling bifurcation. This configuration is more effective than existing absorbers and it cannot be imagined by using naive extensions of linear vibration theory. The second topic deals with the dynamics of mechanical systems in which components make intermittent contact with each another. Such dynamics are often the source of undesirable noise and wear in machinery and can be extremely complicated. Results obtained from simple predictive models and some application areas will be presented for these impacting systems. The final topic deals with the gross motions of seagoing vessels and their stability against capsize. Existing safety regulations for ship stability are based on purely static measures, whereas capsize is an inherently nonlinear dynamic event. An overview will be given that considers some basic modeling issues, dynamic analysis techniques (based on the concept of chaotic phase-space transport), and the resulting predictive tools that have been developed for this class of problems.

Theoretical transient analysis of a hearing aid feedback canceller with a saturation type nonlinearity in the direct path.

PubMed

Costa, Márcio Holsbach

2017-12-01

Feedback cancellation in a hearing aid is essential for achieving high maximum stable gain to compensate for the losses in severe to profound hearing impaired people. The performance of adaptive feedback cancellers has been studied by assuming that the feedback path can be modeled as a linear system. However, limited dynamic range, low-cost loudspeakers, and nonlinear power amplifiers may distort the hearing aid output signal. In this way, linear-based predictions of the canceller performance may lead to significant deviations from its actual behavior. This work presents a theoretical performance analysis of a Least Mean Square based shadow filter that is applied to set up the coefficients of a feedback canceller, which is subject to a static saturation type nonlinearity at the output of the direct path. Deterministic recursive equations are derived to predict the mean square feedback error and the mean coefficient vector evolution between updates of the feedback canceller. These models are defined as functions of the canceller parameters and input signal statistics. Comparisons with Monte Carlo simulations show the provided models are highly accurate under the considered assumptions. The developed models allow inferences about the potential impact of an overdriven loudspeaker over the transient performance of the direct method feedback canceller, serving as insightful tools for understanding the involved mechanisms. Copyright © 2017 Elsevier Ltd. All rights reserved.

Development of a nonlinear switching function and its application to static lift characteristics of straight wings

NASA Technical Reports Server (NTRS)

Hewes, D. E.

1978-01-01

A mathematical modeling technique was developed for the lift characteristics of straight wings throughout a very wide angle of attack range. The technique employs a mathematical switching function that facilitates the representation of the nonlinear aerodynamic characteristics in the partially and fully stalled regions and permits matching empirical data within + or - 4 percent of maximum values. Although specifically developed for use in modeling the lift characteristics, the technique appears to have other applications in both aerodynamic and nonaerodynamic fields.

A two-step FEM-SEM approach for wave propagation analysis in cable structures

NASA Astrophysics Data System (ADS)

Zhang, Songhan; Shen, Ruili; Wang, Tao; De Roeck, Guido; Lombaert, Geert

2018-02-01

Vibration-based methods are among the most widely studied in structural health monitoring (SHM). It is well known, however, that the low-order modes, characterizing the global dynamic behaviour of structures, are relatively insensitive to local damage. Such local damage may be easier to detect by methods based on wave propagation which involve local high frequency behaviour. The present work considers the numerical analysis of wave propagation in cables. A two-step approach is proposed which allows taking into account the cable sag and the distribution of the axial forces in the wave propagation analysis. In the first step, the static deformation and internal forces are obtained by the finite element method (FEM), taking into account geometric nonlinear effects. In the second step, the results from the static analysis are used to define the initial state of the dynamic analysis which is performed by means of the spectral element method (SEM). The use of the SEM in the second step of the analysis allows for a significant reduction in computational costs as compared to a FE analysis. This methodology is first verified by means of a full FE analysis for a single stretched cable. Next, simulations are made to study the effects of damage in a single stretched cable and a cable-supported truss. The results of the simulations show how damage significantly affects the high frequency response, confirming the potential of wave propagation based methods for SHM.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

PubMed

Fonseca, P Z G; Aranas, E B; Millen, J; Monteiro, T S; Barker, P F

2016-10-21

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

NASA Astrophysics Data System (ADS)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-10-01

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Mobility analysis, simulation, and scale model testing for the design of wheeled planetary rovers

NASA Technical Reports Server (NTRS)

Lindemann, Randel A.; Eisen, Howard J.

1993-01-01

The use of computer based techniques to model and simulate wheeled rovers on rough natural terrains is considered. Physical models of a prototype vehicle can be used to test the correlation of the simulations in scaled testing. The computer approaches include a quasi-static planar or two dimensional analysis and design tool based on the traction necessary for the vehicle to have imminent mobility. The computer program modeled a six by six wheel drive vehicle of original kinematic configuration, called the Rocker Bogie. The Rocker Bogie was optimized using the quasi-static software with respect to its articulation parameters prior to fabrication of a prototype. In another approach used, the dynamics of the Rocker Bogie vehicle in 3-D space was modeled on an engineering workstation using commercial software. The model included the complex and nonlinear interaction of the tire and terrain. The results of the investigation yielded numerical and graphical results of the rover traversing rough terrain on the earth, moon, and Mars. In addition, animations of the rover excursions were also generated. A prototype vehicle was then used in a series of testbed and field experiments. Correspondence was then established between the computer models and the physical model. The results indicated the utility of the quasi-static tool for configurational design, as well as the predictive ability of the 3-D simulation to model the dynamic behavior of the vehicle over short traverses.

Seismological Field Observation of Mesoscopic Nonlinearity

NASA Astrophysics Data System (ADS)

Sens-Schönfelder, Christoph; Gassenmeier, Martina; Eulenfeld, Tom; Tilmann, Frederik; Korn, Michael; Niederleithinger, Ernst

2016-04-01

Noise based observations of seismic velocity changes have been made in various environments. We know of seasonal changes of velocities related to ground water or temperature changes, co-seismic changes originating from shaking or stress redistribution and changes related to volcanic activity. Is is often argued that a decrease of velocity is related to the opening of cracks while the closure of cracks leads to a velocity increase if permanent stress changes are invoked. In contrast shaking induced changes are often related to "damage" and subsequent "healing" of the material. The co-seismic decrease and transient recovery of seismic velocities can thus be explained with both - static stress changes or damage/healing processes. This results in ambiguous interpretations of the observations. Here we present the analysis of one particular seismic station in northern Chile that shows very strong and clear velocity changes associated with several earthquakes ranging from Mw=5.3 to Mw=8.1. The fact that we can observe the response to several events of various magnitudes from different directions offers the unique possibility to discern the two possible causative processes. We test the hypothesis, that the velocity changes are related to shaking rather than stress changes by developing an empirical model that is based on the local ground acceleration at the sensor site. The eight year of almost continuous observations of velocity changes are well modeled by a daily drop of the velocity followed by an exponential recovery. Both, the amplitude of the drop as well as the recovery time are proportional to the integrated acceleration at the seismic station. Effects of consecutive days are independent and superimposed resulting in strong changes after earthquakes and constantly increasing velocities during quiet days thereafter. This model describes the continuous observations of the velocity changes solely based on the acceleration time series without individually defined dates of events associated with separately inverted parameters. As the local ground acceleration is not correlated to static stress changes we can exclude static stress changes as causative process. The shaking sensitivity and healing process is well known from laboratory experiments in composite materials as mesoscopic nonlinearity. The sensitive behavior at this station is related to the particular near surface material that is a conglomerate cemented with gypsum - so called gypcrete. However, mesoscopic nonlinearity with different parameters might be a key to understand velocity changes also at other sites.

Cyclic tensile response of a pre-tensioned polyurethane

NASA Astrophysics Data System (ADS)

Nie, Yizhou; Liao, Hangjie; Chen, Weinong W.

2018-05-01

In the research reported in this paper, we subject a polyurethane to uniaxial tensile loading at a quasi-static strain rate, a high strain rate and a jumping strain rate where the specimen is under quasi-static pre-tension and is further subjected to a dynamic cyclic loading using a modified Kolsky tension bar. The results obtained at the quasi-static and high strain rate clearly show that the mechanical response of this material is significantly rate sensitive. The rate-jumping experimental results show that the response of the material behavior is consistent before jumping. After jumping the stress-strain response of the material does not jump to the corresponding high-rate curve. Rather it approaches the high-rate curve asymptotically. A non-linear hyper-viscoelastic (NLHV) model, after having been calibrated by monotonic quasi-static and high-rate experimental results, was found to be capable of describing the material tensile behavior under such rate jumping conditions.

Estimation of dynamic stability parameters from drop model flight tests

NASA Technical Reports Server (NTRS)

Chambers, J. R.; Iliff, K. W.

1981-01-01

A recent NASA application of a remotely-piloted drop model to studies of the high angle-of-attack and spinning characteristics of a fighter configuration has provided an opportunity to evaluate and develop parameter estimation methods for the complex aerodynamic environment associated with high angles of attack. The paper discusses the overall drop model operation including descriptions of the model, instrumentation, launch and recovery operations, piloting concept, and parameter identification methods used. Static and dynamic stability derivatives were obtained for an angle-of-attack range from -20 deg to 53 deg. The results of the study indicated that the variations of the estimates with angle of attack were consistent for most of the static derivatives, and the effects of configuration modifications to the model (such as nose strakes) were apparent in the static derivative estimates. The dynamic derivatives exhibited greater uncertainty levels than the static derivatives, possibly due to nonlinear aerodynamics, model response characteristics, or additional derivatives.

Variable camber wing based on pneumatic artificial muscles

NASA Astrophysics Data System (ADS)

Yin, Weilong; Liu, Libo; Chen, Yijin; Leng, Jinsong

2009-07-01

As a novel bionic actuator, pneumatic artificial muscle has high power to weight ratio. In this paper, a variable camber wing with the pneumatic artificial muscle is developed. Firstly, the experimental setup to measure the static output force of pneumatic artificial muscle is designed. The relationship between the static output force and the air pressure is investigated. Experimental result shows the static output force of pneumatic artificial muscle decreases nonlinearly with increasing contraction ratio. Secondly, the finite element model of the variable camber wing is developed. Numerical results show that the tip displacement of the trailing-edge increases linearly with increasing external load and limited with the maximum static output force of pneumatic artificial muscles. Finally, the variable camber wing model is manufactured to validate the variable camber concept. Experimental result shows that the wing camber increases with increasing air pressure and that it compare very well with the FEM result.

Aerodynamic characteristics at high angles of attack

NASA Technical Reports Server (NTRS)

Chambers, J. R.

1977-01-01

An overview is presented of the aerodynamic inputs required for analysis of flight dynamics in the high-angle-of-attack regime wherein large-disturbance, nonlinear effects predominate. An outline of the presentation is presented. The discussion includes: (1) some important fundamental phenomena which determine to a large extent the aerodynamic characteristics of airplanes at high angles of attack; (2) static and dynamic aerodynamic characteristics near the stall; (3) aerodynamics of the spin; (4) test techniques used in stall/spin studies; (5) applications of aerodynamic data to problems in flight dynamics in the stall/spin area; and (6) the outlook for future research in the area.

Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum

NASA Astrophysics Data System (ADS)

Sander, Oliver; Schiela, Anton

2014-12-01

We formulate the static mechanical coupling of a geometrically exact Cosserat rod to a nonlinearly elastic continuum. In this setting, appropriate coupling conditions have to connect a one-dimensional model with director variables to a three-dimensional model without directors. Two alternative coupling conditions are proposed, which correspond to two different configuration trace spaces. For both, we show existence of solutions of the coupled problems, using the direct method of the calculus of variations. From the first-order optimality conditions, we also derive the corresponding conditions for the dual variables. These are then interpreted in mechanical terms.

Nonlinear dynamics of the cellular-automaton ``game of Life''

NASA Astrophysics Data System (ADS)

Garcia, J. B. C.; Gomes, M. A. F.; Jyh, T. I.; Ren, T. I.; Sales, T. R. M.

1993-11-01

A statistical analysis of the ``game of Life'' due to Conway [Berlekamp, Conway, and Guy, Winning Ways for Your Mathematical Plays (Academic, New York, 1982), Vol. 2] is reported. The results are based on extensive computer simulations starting with uncorrelated distributions of live sites at t=0. The number n(s,t) of clusters of s live sites at time t, the mean cluster size s¯(t), and the diversity of sizes among other statistical functions are obtained. The dependence of the statistical functions with the initial density of live sites is examined. Several scaling relations as well as static and dynamic critical exponents are found.

Nonlinear bleaching, absorption, and scattering of 532-nm-irradiated plasmonic nanoparticles

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

Liberman, V.; Sworin, M.; Kingsborough, R. P.

2013-02-07

Single-pulse irradiation of Au and Ag suspensions of nanospheres and nanodisks with 532-nm 4-ns pulses has identified complex optical nonlinearities while minimizing material damage. For all materials tested, we observe competition between saturable absorption (SA) and reverse SA (RSA), with RSA behavior dominating for intensities above {approx}50 MW/cm{sup 2}. Due to reduced laser damage in single-pulse experiments, the observed intrinsic nonlinear absorption coefficients are the highest reported to date for Au nanoparticles. We find size dependence to the nonlinear absorption enhancement for Au nanoparticles, peaking in magnitude for 80-nm nanospheres and falling off at larger sizes. The nonlinear absorption coefficientsmore » for Au and Ag spheres are comparable in magnitude. On the other hand, the nonlinear absorption for Ag disks, when corrected for volume fraction, is several times higher. These trends in nonlinear absorption are correlated to local electric field enhancement through quasi-static mean-field theory. Through variable size aperture measurements, we also separate nonlinear scattering from nonlinear absorption. For all materials tested, we find that nonlinear scattering is highly directional and that its magnitude is comparable to that of nonlinear absorption. These results indicate methods to improve the efficacy of plasmonic nanoparticles as optical limiters in pulsed laser systems.« less

Dielectric relaxation studies of binary mixture of β-picoline and methanol using time domain reflectometry at different temperatures

NASA Astrophysics Data System (ADS)

Trivedi, C. M.; Rana, V. A.; Hudge, P. G.; Kumbharkhane, A. C.

2016-08-01

Complex permittivity spectra of binary mixtures of varying concentrations of β-picoline and Methanol (MeOH) have been obtained using time domain reflectometry (TDR) technique over frequency range 10 MHz to 25 GHz at 283.15, 288.15, 293.15 and 298.15 K temperatures. The dielectric relaxation parameters namely static permittivity (ɛ0), high frequency limit permittivity (ɛ∞1) and the relaxation time (τ) were determined by fitting complex permittivity data to the single Debye/Cole-Davidson model. Complex nonlinear least square (CNLS) fitting procedure was carried out using LEVMW software. The excess permittivity (ɛ0E) and the excess inverse relaxation time (1/τ)E which contain information regarding molecular structure and interaction between polar-polar liquids were also determined. From the experimental data, parameters such as effective Kirkwood correlation factor (geff), Bruggeman factor (fB) and some thermo dynamical parameters have been calculated. Excess parameters were fitted to the Redlich-Kister polynomial equation. The values of static permittivity and relaxation time increase nonlinearly with increase in the mol-fraction of MeOH at all temperatures. The values of excess static permittivity (ɛ0E) and the excess inverse relaxation time (1/τ)E are negative for the studied β-picoline — MeOH system at all temperatures.

A cobalt (II) complex with 6-methylpicolinate: Synthesis, characterization, second- and third-order nonlinear optical properties, and DFT calculations

NASA Astrophysics Data System (ADS)

Altürk, Sümeyye; Avcı, Davut; Tamer, Ömer; Atalay, Yusuf; Şahin, Onur

2016-11-01

A cobalt(II) complex of 6-methylpicolinic acid, [Co(6-Mepic)2(H2O)2]·2H2O, was prepared and fully determined by single crystal X-ray crystal structure analysis as well as FT-IR, FT-Raman. UV-vis spectra were recorded within different solvents, to illustrate electronic transitions and molecular charge transfer within complex 1. The coordination sphere of complex 1 is a distorted octahedron according to single crystal X-ray results. Moreover, DFT (density functional theory) calculations with HSEH1PBE/6-311 G(d,p) level were carried out to back up the experimental results, and form base for future work in advanced level. Hyperconjugative interactions, intramolecular charge transfer (ICT), molecular stability and bond strength were researched by the using natural bond orbital (NBO) analysis. X-ray and NBO analysis results demonsrate that O-H···O hydrogen bonds between the water molecules and carboxylate oxygen atoms form a 2D supramolecular network, and also adjacent 2D networks connected by C-H···π and π···π interactions to form a 3D supramolecular network. Additionally, the second- and third-order nonlinear optical parameters of complex 1 were computed at DFT/HSEH1PBE/6-311 G(d,p) level. The refractive index (n) was calculated by using the Lorentz-Lorenz equation in order to investigate polarization behavior of complex 1 in different solvent polarities. The first-order static hyperpolarizability (β) value is found to be lower than pNA value because of the inversion symmetry around Co (II). But the second-order static hyperpolarizability (γ) value is 2.45 times greater than pNA value (15×10-30 esu). According to these results, Co(II) complex can be considered as a candidate to NLO material. Lastly molecular electrostatic potential (MEP), frontier molecular orbital energies and related molecular parameters for complex 1 were evaluated.

The Use of Non-Standard Devices in Finite Element Analysis

NASA Technical Reports Server (NTRS)

Schur, Willi W.; Broduer, Steve (Technical Monitor)

2001-01-01

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

A technique using a nonlinear helicopter model for determining trims and derivatives

NASA Technical Reports Server (NTRS)

Ostroff, A. J.; Downing, D. R.; Rood, W. J.

1976-01-01

A technique is described for determining the trims and quasi-static derivatives of a flight vehicle for use in a linear perturbation model; both the coupled and uncoupled forms of the linear perturbation model are included. Since this technique requires a nonlinear vehicle model, detailed equations with constants and nonlinear functions for the CH-47B tandem rotor helicopter are presented. Tables of trims and derivatives are included for airspeeds between -40 and 160 knots and rates of descent between + or - 10.16 m/sec (+ or - 200 ft/min). As a verification, the calculated and referenced values of comparable trims, derivatives, and linear model poles are shown to have acceptable agreement.

Imitative and best response behaviors in a nonlinear Cournotian setting

NASA Astrophysics Data System (ADS)

Cerboni Baiardi, Lorenzo; Naimzada, Ahmad K.

2018-05-01

We consider the competition among quantity setting players in a deterministic nonlinear oligopoly framework characterized by an isoelastic demand curve. Players are characterized by having heterogeneous decisional mechanisms to set their outputs: some players are imitators, while the remaining others adopt a rational-like rule according to which their past decisions are adjusted towards their static expectation best response. The Cournot-Nash production level is a stationary state of our model together with a further production level that can be interpreted as the competitive outcome in case only imitators are present. We found that both the number of players and the relative fraction of imitators influence stability of the Cournot-Nash equilibrium with an ambiguous role, and double instability thresholds may be observed. Global analysis shows that a wide variety of complex dynamic scenarios emerge. Chaotic trajectories as well as multi-stabilities, where different attractors coexist, are robust phenomena that can be observed for a wide spectrum of parameter sets.

Leading-edge flow reattachment and the lateral static stability of low-aspect-ratio rectangular wings

NASA Astrophysics Data System (ADS)

Linehan, Thomas; Mohseni, Kamran

2017-11-01

The relationship between lateral static stability derivative, Clβ,lift coefficient, CL, and angle of attack was investigated for rectangular wings of aspect ratio A R =0.75 ,1 ,1.5 , and 3 using Stereo-Digital Particle Image Velocimetry (S-DPIV) and direct force and moment measurements. When the product Cl βA R is plotted with respect to CL, the lateral stability curves of each wing collapse to a single line for CL<0.7 . For CL>0.7 , the linearity and scaling of Clβwith respect to CL is lost. S-DPIV is used to elucidate the flow physics in this nonlinear regime. At α =10∘ , the leading-edge separation region emerges on the leeward portion of the sideslipped wing by means of vortex shedding. For the A R ≤1.5 wings at α >15∘ , the tip vortex downwash is sufficient to restrict the shedding of leading-edge vorticity thereby sustaining the lift of the leading-edge separation region at high angles of attack. Concurrently, the windward tip vortex grows in size and strength with increasing angle of attack, displacing the leading-edge separation region further toward the leeward wing. This reorganization of lift-generating vorticity results in the initial nonlinearities between Cl β and CL at angles of attack for which CL is still increasing. At angles of attack near that of maximum lift for the A R ≤1 wings, the windward tip vortex lifts off the wing, decreasing the lateral static stability of the wing prior to lift stall. For the A R =3 wing at α >10∘ , nonlinear trends in Cl β versus CL occur due to the spanwise evolution of stalled flow.

Three-dimensional nonlinear responses to impact loads on free-span pipeline: Torsional coupling and load steps

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

Chung, J.S.; Huttelmaier, H.P.; Cheng, B.R.

1995-12-31

For a heavy object falling on a free-span pipeline, this study assesses three-dimensional (3-D) pipe-span responses with the torsional ({theta}x-) coupling of a pipeline through the biaxial (y) bending responses. The static pipe-span equilibrium is achieved with its self-weight and buoyancy and the external torsional moment induced by the cross-flow (y-directional) current on the sagged pipe span. Load steps taken for 2 different sequences of applying static loads induced different pipe deformations, and the pipe twists in entirely different pattern. The two types of impact loads are applied in the vertical (z-) direction to excite the pipe span in itsmore » static equilibrium: (1) triangular impulse loading and (2) ramp loading. Boundary condition of the span supports is ``fixed-fixed`` at both ends in both displacement and rotation. 3-D coupled axial (x-), bending (y- and z-) and torsional ({theta}x-) responses, both state and dynamic, to the z-directional impact loadings, are modeled and analyzed by a nonlinear FEM method for a 16-in pipeline. The 3-D responses are compared with 2-D responses. The comparison shows significant torsional vibrations caused by the cross-flow current, especially for longer spans. The torsional ({theta}x-) coupling is very sensitive to the time-step size in achieving numerical stability and accuracy, particularly for the ramp loading and for a shorter span. For very large impact loads, the response frequencies differ from the fundamental frequencies of the span, exhibiting beatings and strong bending-to-axial and to-twist couplings. Also, the eigenvalues for the linear system are not necessarily the resonance frequencies for these nonlinear coupled responses.« less

Demonstration of a Balloon Borne Arc-second Pointer Design

NASA Astrophysics Data System (ADS)

Deweese, K.; Ward, P.

Many designs for utilizing stratospheric balloons as low-cost platforms on which to conduct space science experiments have been proposed throughout the years A major hurdle in extending the range of experiments for which these vehicles are useful has been the imposition of the gondola dynamics on the accuracy with which an instrument can be kept pointed at a celestial target A significant number of scientists have sought the ability to point their instruments with jitter in the arc-second range This paper presents the design and analysis of a stratospheric balloon borne pointing system that is able to meet this requirement The test results of a demonstration prototype of the design with similar ability are also presented Discussion of a high fidelity controller simulation for design analysis is presented The flexibility of the flight train is represented through generalized modal analysis A multiple controller scheme is utilized for coarse and fine pointing Coarse azimuth pointing is accomplished by an established pointing system with extensive flight history residing above the gondola structure A pitch-yaw gimbal mount is used for fine pointing providing orthogonal axes when nominally on target Fine pointing actuation is from direct drive dc motors eliminating backlash problems An analysis of friction nonlinearities and a demonstration of the necessity in eliminating static friction are provided A unique bearing hub design is introduced that eliminates static friction from the system dynamics A control scheme involving linear

Static aeroelastic analysis of wings using Euler/Navier-Stokes equations coupled with improved wing-box finite element structures

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; MacMurdy, Dale E.; Kapania, Rakesh K.

1994-01-01

Strong interactions between flow about an aircraft wing and the wing structure can result in aeroelastic phenomena which significantly impact aircraft performance. Time-accurate methods for solving the unsteady Navier-Stokes equations have matured to the point where reliable results can be obtained with reasonable computational costs for complex non-linear flows with shock waves, vortices and separations. The ability to combine such a flow solver with a general finite element structural model is key to an aeroelastic analysis in these flows. Earlier work involved time-accurate integration of modal structural models based on plate elements. A finite element model was developed to handle three-dimensional wing boxes, and incorporated into the flow solver without the need for modal analysis. Static condensation is performed on the structural model to reduce the structural degrees of freedom for the aeroelastic analysis. Direct incorporation of the finite element wing-box structural model with the flow solver requires finding adequate methods for transferring aerodynamic pressures to the structural grid and returning deflections to the aerodynamic grid. Several schemes were explored for handling the grid-to-grid transfer of information. The complex, built-up nature of the wing-box complicated this transfer. Aeroelastic calculations for a sample wing in transonic flow comparing various simple transfer schemes are presented and discussed.

A CFD/CSD Interaction Methodology for Aircraft Wings

NASA Technical Reports Server (NTRS)

Bhardwaj, Manoj K.

1997-01-01

With advanced subsonic transports and military aircraft operating in the transonic regime, it is becoming important to determine the effects of the coupling between aerodynamic loads and elastic forces. Since aeroelastic effects can contribute significantly to the design of these aircraft, there is a strong need in the aerospace industry to predict these aero-structure interactions computationally. To perform static aeroelastic analysis in the transonic regime, high fidelity computational fluid dynamics (CFD) analysis tools must be used in conjunction with high fidelity computational structural fluid dynamics (CSD) analysis tools due to the nonlinear behavior of the aerodynamics in the transonic regime. There is also a need to be able to use a wide variety of CFD and CSD tools to predict these aeroelastic effects in the transonic regime. Because source codes are not always available, it is necessary to couple the CFD and CSD codes without alteration of the source codes. In this study, an aeroelastic coupling procedure is developed which will perform static aeroelastic analysis using any CFD and CSD code with little code integration. The aeroelastic coupling procedure is demonstrated on an F/A-18 Stabilator using NASTD (an in-house McDonnell Douglas CFD code) and NASTRAN. In addition, the Aeroelastic Research Wing (ARW-2) is used for demonstration of the aeroelastic coupling procedure by using ENSAERO (NASA Ames Research Center CFD code) and a finite element wing-box code (developed as part of this research).

Experimental Nonlinear Dynamics and Snap-Through of Post-Buckled Thin Laminated Composite Plates

NASA Astrophysics Data System (ADS)

Kim, Han-Gyu

Modern aerospace systems are increasingly being designed with composite panels and plates to achieve light weight and high specific strength and stiffness. For constrained panels, thermally-induced axial loading may cause buckling of the structure, which can lead to nonlinear and potentially chaotic behavior. When post-buckled composite plates experience snap-through, they are subjected to large-amplitude deformations and in-plane compressive loading. These phenomena pose a potential threat to the structural integrity of composite structures. In this work, the nonlinear dynamic behavior of post-buckled composite plates was investigated experimentally and computationally. For the experimental work, an electrodynamic shaker was used to apply harmonic loads and the dynamic response of plate specimens was measured using a single-point displacement-sensing laser, a double-point laser vibrometer (velocity-sensing), and a set of digital image correlation cameras. Both chaotic and periodic steady-state snap-through behaviors were investigated. The experimental data were used to characterize snap-through behaviors of the post-buckled specimens and their boundaries in the harmonic forcing parameter space. The nonlinear behavior of post-buckled plates was modeled using the classical laminated plate theory (CLPT) and the von Karman strain-displacement relations. The static equilibrium paths of the post-buckled plates were analyzed using an arc-length method with a branch-switching technique. For the dynamic analysis, the nonlinear equations of motion were derived based on CLPT and the nonlinear finite element model of the equations was constructed using the Hermite cubic interpolation functions for both conforming and nonconforming elements. The numerical analyses were conducted using the model and were compared with the experimental data.

Comparison of Damage Path Predictions for Composite Laminates by Explicit and Standard Finite Element Analysis Tools

NASA Technical Reports Server (NTRS)

Bogert, Philip B.; Satyanarayana, Arunkumar; Chunchu, Prasad B.

2006-01-01

Splitting, ultimate failure load and the damage path in center notched composite specimens subjected to in-plane tension loading are predicted using progressive failure analysis methodology. A 2-D Hashin-Rotem failure criterion is used in determining intra-laminar fiber and matrix failures. This progressive failure methodology has been implemented in the Abaqus/Explicit and Abaqus/Standard finite element codes through user written subroutines "VUMAT" and "USDFLD" respectively. A 2-D finite element model is used for predicting the intra-laminar damages. Analysis results obtained from the Abaqus/Explicit and Abaqus/Standard code show good agreement with experimental results. The importance of modeling delamination in progressive failure analysis methodology is recognized for future studies. The use of an explicit integration dynamics code for simple specimen geometry and static loading establishes a foundation for future analyses where complex loading and nonlinear dynamic interactions of damage and structure will necessitate it.

Nonlinear dynamics induced in a structure by seismic and environmental loading

DOE PAGES

Gueguen, Philippe; Johnson, Paul Allan; Roux, Philippe

2016-07-26

In this study,we show that under very weak dynamic and quasi-static deformation, that is orders of magnitude below the yield deformation of the equivalent stress strain curve (around 10 -3), the elastic parameters of a civil engineering structure (resonance frequency and damping) exhibit nonlinear softening and recovery. These observations bridge the gap between laboratory and seismic scales where elastic nonlinear behavior has been previously observed. Under weak seismic or atmospheric loading, modal frequencies are modified by around 1% and damping by more than 100% for strain levels between 10 -7 and 10 -4. These observations support the concept of universalmore » behavior of nonlinear elastic behavior in diverse systems, including granular materials and damaged solids that scale from millimeter dimensions to the scale of structures to fault dimensions in the Earth.« less

Nonlinear dynamics induced in a structure by seismic and environmental loading

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

Gueguen, Philippe; Johnson, Paul Allan; Roux, Philippe

In this study,we show that under very weak dynamic and quasi-static deformation, that is orders of magnitude below the yield deformation of the equivalent stress strain curve (around 10 -3), the elastic parameters of a civil engineering structure (resonance frequency and damping) exhibit nonlinear softening and recovery. These observations bridge the gap between laboratory and seismic scales where elastic nonlinear behavior has been previously observed. Under weak seismic or atmospheric loading, modal frequencies are modified by around 1% and damping by more than 100% for strain levels between 10 -7 and 10 -4. These observations support the concept of universalmore » behavior of nonlinear elastic behavior in diverse systems, including granular materials and damaged solids that scale from millimeter dimensions to the scale of structures to fault dimensions in the Earth.« less

Multiphoton microscopy of ECM proteins in baboon aortic leaflet

NASA Astrophysics Data System (ADS)

Gonzalez, Mariacarla; Saytashev, Ilyas; Luna, Camila; Gonzalez, Brittany; Pinero, Alejandro; Perez, Manuel; Ramaswamy, Sharan; Ramella-Roman, Jessica

2018-02-01

The extracellular matrix (ECM) plays crucial role in defining mechanical properties of a heart valve yet the mechanobiological role of the ECM proteins - collagen and elastin - in living heart valve leaflets is still poorly understood. In this study, non-linear microscopy was used to obtain three dimensional images of collagen and elastin arrangement in aortic leaflets under combined steady flow (850 ml/min) and cyclic flexure (1 Hz) mechanical (dynamic) training. A novel bioreactor capable of mimicking the flow conditions in a living heart was used in this study and was optimized for microscopic imagery. A custom made non-linear microscope was used in this study to provide Second Harmonic Generation (SHG) imaging of collagen arrangement and two-photon imaging of elastin. Two control and three trained leaflet samples from static and dynamic tissue culture were imaged to observe protein changes in the tissue for a period of seven days. Dynamic training led to a decrease in alignment index of the protein fibers compared to the static treatment.

Nonlinear optical properties of curcumin: solvatochromism-based approach and computational study

NASA Astrophysics Data System (ADS)

Margar, Sachin N.; Sekar, Nagaiyan

2016-06-01

Nonlinear optical (NLO) properties of curcumin were studied using solvatochromic method and density functional theory (DFT). DFT calculations were performed to determine the static first hyperpolarisability (βο) and its related properties (μ, α0,Δα, β, ?) for curcumin, using B3LYP functional with 6-31G (d), 6-311+G (d) and 6-311+G (d,p) basis sets at the ground-state and excited-state geometries and with CAM-B3LYP using 6-311+G (d,p) basis sets at the ground-state geometry in different solvent environments. In polar solvent environment, the values are slightly lower as compared to the non-polar solvent environments. The results obtained are correlated with the polarisability parameter αCT, first hyperpolarisability parameter βCT and the solvatochromic descriptor of γSDobtained by the solvatochromic method. The static first hyperpolarisability (βο) and its related properties were compared with urea and dibenzoylmethane (β-diketonate) and it is observed that curcumin shows very large values for first hyperpolarisability and its components.

Quasi-Static Viscoelastic Finite Element Model of an Aircraft Tire

NASA Technical Reports Server (NTRS)

Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

1999-01-01

An elastic large displacement thick-shell mixed finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at the element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses is included in the mixed variational functional. The nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the nonlinear elastic equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to computationally simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.

Brain tissue deforms similarly to filled elastomers and follows consolidation theory

NASA Astrophysics Data System (ADS)

Franceschini, G.; Bigoni, D.; Regitnig, P.; Holzapfel, G. A.

2006-12-01

Slow, large deformations of human brain tissue—accompanying cranial vault deformation induced by positional plagiocephaly, occurring during hydrocephalus, and in the convolutional development—has surprisingly received scarce mechanical investigation. Since the effects of these deformations may be important, we performed a systematic series of in vitro experiments on human brain tissue, revealing the following features. (i) Under uniaxial (quasi-static), cyclic loading, brain tissue exhibits a peculiar nonlinear mechanical behaviour, exhibiting hysteresis, Mullins effect and residual strain, qualitatively similar to that observed in filled elastomers. As a consequence, the loading and unloading uniaxial curves have been found to follow the Ogden nonlinear elastic theory of rubber (and its variants to include Mullins effect and permanent strain). (ii) Loaded up to failure, the "shape" of the stress/strain curve qualitatively changes, evidencing softening related to local failure. (iii) Uniaxial (quasi-static) strain experiments under controlled drainage conditions provide the first direct evidence that the tissue obeys consolidation theory involving fluid migration, with properties similar to fine soils, but having much smaller volumetric compressibility. (iv) Our experimental findings also support the existence of a viscous component of the solid phase deformation. Brain tissue should, therefore, be modelled as a porous, fluid-saturated, nonlinear solid with very small volumetric (drained) compressibility.

Nonlinear Structural Analysis Methodology and Dynamics Scaling of Inflatable Parabolic Reflector Antenna Concepts

NASA Technical Reports Server (NTRS)

Sreekantamurthy, Tham; Gaspar, James L.; Mann, Troy; Behun, Vaughn; Pearson, James C., Jr.; Scarborough, Stephen

2007-01-01

Ultra-light weight and ultra-thin membrane inflatable antenna concepts are fast evolving to become the state-of-the-art antenna concepts for deep-space applications. NASA Langley Research Center has been involved in the structural dynamics research on antenna structures. One of the goals of the research is to develop structural analysis methodology for prediction of the static and dynamic response characteristics of the inflatable antenna concepts. This research is focused on the computational studies to use nonlinear large deformation finite element analysis to characterize the ultra-thin membrane responses of the antennas. Recently, structural analyses have been performed on a few parabolic reflector antennas of varying size and shape, which are referred in the paper as 0.3 meters subscale, 2 meters half-scale, and 4 meters full-scale antenna. The various aspects studied included nonlinear analysis methodology and solution techniques, ways to speed convergence in iterative methods, the sensitivities of responses with respect to structural loads, such as inflation pressure, gravity, and pretension loads in the ground and in-space conditions, and the ultra-thin membrane wrinkling characteristics. Several such intrinsic aspects studied have provided valuable insight into evaluation of structural characteristics of such antennas. While analyzing these structural characteristics, a quick study was also made to assess the applicability of dynamics scaling of the half-scale antenna. This paper presents the details of the nonlinear structural analysis results, and discusses the insight gained from the studies on the various intrinsic aspects of the analysis methodology. The predicted reflector surface characteristics of the three inflatable ultra-thin membrane parabolic reflector antenna concepts are presented as easily observable displacement fringe patterns with associated maximum values, and normal mode shapes and associated frequencies. Wrinkling patterns are presented to show how surface wrinkle progress with increasing tension loads. Antenna reflector surface accuracies were found to be very much dependent on the type and size of the antenna, the reflector surface curvature, reflector membrane supports in terms of spacing of catenaries, as well as the amount of applied load.

Effectiveness of modified pushover analysis procedure for the estimation of seismic demands of buildings subjected to near-fault ground motions having fling step

NASA Astrophysics Data System (ADS)

Mortezaei, A.; Ronagh, H. R.

2013-06-01

Near-fault ground motions with long-period pulses have been identified as being critical in the design of structures. These motions, which have caused severe damage in recent disastrous earthquakes, are characterized by a short-duration impulsive motion that transmits large amounts of energy into the structures at the beginning of the earthquake. In nearly all of the past near-fault earthquakes, significant higher mode contributions have been evident in building structures near the fault rupture, resulting in the migration of dynamic demands (i.e. drifts) from the lower to the upper stories. Due to this, the static nonlinear pushover analysis (which utilizes a load pattern proportional to the shape of the fundamental mode of vibration) may not produce accurate results when used in the analysis of structures subjected to near-fault ground motions. The objective of this paper is to improve the accuracy of the pushover method in these situations by introducing a new load pattern into the common pushover procedure. Several pushover analyses are performed for six existing reinforced concrete buildings that possess a variety of natural periods. Then, a comparison is made between the pushover analyses' results (with four new load patterns) and those of FEMA (Federal Emergency Management Agency)-356 with reference to nonlinear dynamic time-history analyses. The comparison shows that, generally, the proposed pushover method yields better results than all FEMA-356 pushover analysis procedures for all investigated response quantities and is a closer match to the nonlinear time-history responses. In general, the method is able to reproduce the essential response features providing a reasonable measure of the likely contribution of higher modes in all phases of the response.

Airfoil stall interpreted through linear stability analysis

NASA Astrophysics Data System (ADS)

Busquet, Denis; Juniper, Matthew; Richez, Francois; Marquet, Olivier; Sipp, Denis

2017-11-01

Although airfoil stall has been widely investigated, the origin of this phenomenon, which manifests as a sudden drop of lift, is still not clearly understood. In the specific case of static stall, multiple steady solutions have been identified experimentally and numerically around the stall angle. We are interested here in investigating the stability of these steady solutions so as to first model and then control the dynamics. The study is performed on a 2D helicopter blade airfoil OA209 at low Mach number, M 0.2 and high Reynolds number, Re 1.8 ×106 . Steady RANS computation using a Spalart-Allmaras model is coupled with continuation methods (pseudo-arclength and Newton's method) to obtain steady states for several angles of incidence. The results show one upper branch (high lift), one lower branch (low lift) connected by a middle branch, characterizing an hysteresis phenomenon. A linear stability analysis performed around these equilibrium states highlights a mode responsible for stall, which starts with a low frequency oscillation. A bifurcation scenario is deduced from the behaviour of this mode. To shed light on the nonlinear behavior, a low order nonlinear model is created with the same linear stability behavior as that observed for that airfoil.

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.

Fabrication and characterization of anthracene thin films for wide-scale organic optoelectronic applications based on linear/nonlinear analyzed optical dispersion parameters

NASA Astrophysics Data System (ADS)

Nawar, Ahmed M.; Yahia, I. S.

2017-08-01

This research work is devoted to studying the linear and nonlinear optical properties of anthracene thin films. For the first time, the fabrication of nanocrystalline anthracene films is presented by using the thermal evaporation conventional technique. All the studied anthracene films exhibit monoclinic crystal structure with dominant preferred orientation along the (001) plane in accordance with X-ray diffraction analysis. The average crystalline size and the strain parameter were calculated and found to be ≈ 14 nm and 42 lines2. nm, respectively. The transparency of the fabricated anthracene films is high (>80%) from the end of the visible to the near-infrared region at 1500 nm, after that; it reaches to 87%. The characteristic behavior, analysis of refractive index and absorption coefficient based on the measured spectrophotometric data of the transmittance and reflectance spectra. The transition is allowed one and the evaluated optical band gap ∼3.1 eV with energy tail ∼105 meV. The dispersion curves of the refractive index were found to follow the Wemple-DiDomenico model. The static optical dielectric constant was found to be 2.592. The molecular polarizability of anthracene thin films presented and its value ∼56.58 (Å)3. A simple spectroscopic method is used to characterize and estimate the nonlinear optical susceptibilities. Thermal evaporation technology could be useful to fabricate blue OLED and window film in photodetector devices based-anthracene films.

Nonlinear Modeling of Joint Dominated Structures

NASA Technical Reports Server (NTRS)

Chapman, J. M.

1990-01-01

The development and verification of an accurate structural model of the nonlinear joint-dominated NASA Langley Mini-Mast truss are described. The approach is to characterize the structural behavior of the Mini-Mast joints and struts using a test configuration that can directly measure the struts' overall stiffness and damping properties, incorporate this data into the structural model using the residual force technique, and then compare the predicted response with empirical data taken by NASA/LaRC during the modal survey tests of the Mini-Mast. A new testing technique, referred to as 'link' testing, was developed and used to test prototype struts of the Mini-Masts. Appreciable nonlinearities including the free-play and hysteresis were demonstrated. Since static and dynamic tests performed on the Mini-Mast also exhibited behavior consistent with joints having free-play and hysteresis, nonlinear models of the Mini-Mast were constructed and analyzed. The Residual Force Technique was used to analyze the nonlinear model of the Mini-Mast having joint free-play and hysteresis.

Quasi-static axisymmetric eversion hemispherical domes made of elastomers

NASA Astrophysics Data System (ADS)

Kabrits, Sergey A.; Kolpak, Eugeny P.

2016-06-01

The paper considers numerical solution for the problem of quasi-static axisymmetric eversion of a spherical shell (hemisphere) under action of external pressure. Results based on the general nonlinear theory of shells made of elastomers, proposed by K. F. Chernykh. It is used two models of shells based on the hypotheses of the Kirchhoff and Timoshenko, modified K.F. Chernykh for the case of hyperelastic rubber-like material. The article presents diagrams of equilibrium states of eversion hemispheres for both models as well as the shape of the shell at different points in the diagram.

Exact Solutions in Three-Dimensional Gravity

NASA Astrophysics Data System (ADS)

García-Díaz, Alberto A.

2017-09-01

Preface; 1. Introduction; 2. Point particles; 3. Dust solutions; 4. AdS cyclic symmetric stationary solutions; 5. Perfect fluid static stars; 6. Static perfect fluid stars with Λ; 7. Hydrodynamic equilibrium; 8. Stationary perfect fluid with Λ; 9. Friedmann–Robertson–Walker cosmologies; 10. Dilaton-inflaton FRW cosmologies; 11. Einstein–Maxwell solutions; 12. Nonlinear electrodynamics black hole; 13. Dilaton minimally coupled to gravity; 14. Dilaton non-minimally coupled to gravity; 15. Low energy 2+1 string gravity; 16. Topologically massive gravity; 17. Bianchi type spacetimes in TMG; 18. Petrov type N wave metrics; 19. Kundt spacetimes in TMG; 20. Cotton tensor in Riemannian spacetimes; References; Index.

Pretest predictions for the response of a 1:8-scale steel LWR containment building model to static overpressurization

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

Clauss, D.B.

The analyses used to predict the behavior of a 1:8-scale model of a steel LWR containment building to static overpressurization are described and results are presented. Finite strain, large displacement, and nonlinear material properties were accounted for using finite element methods. Three-dimensional models were needed to analyze the penetrations, which included operable equipment hatches, personnel lock representations, and a constrained pipe. It was concluded that the scale model would fail due to leakage caused by large deformations of the equipment hatch sleeves. 13 refs., 34 figs., 1 tab.

On vibrational imperfection sensitivity of Augusti's model structure in the vicinity of a non-linear static state

NASA Technical Reports Server (NTRS)

Elishakoff, Isaac; Marcus, S.; Starnes, J. H., JR.

1998-01-01

In this paper we present a closed-form solution for vibrational imperfection sensitivity the effect of small imperfections on the vibrational frequencies of perturbed motion around the static equilibrium state of Augusti's model Structure (a rigid link, pinned at one end to a rigid foundation and supported at the other by a linear extensional spring that retains its horizontality, as the system deflects). We also treat a modified version of that model with attendant slightly different dynamics. It is demonstrated that the vibrational frequencies decreases as the initial imperfections increase.

Dynamic Modeling and Very Short-term Prediction of Wind Power Output Using Box-Cox Transformation

NASA Astrophysics Data System (ADS)

Urata, Kengo; Inoue, Masaki; Murayama, Dai; Adachi, Shuichi

2016-09-01

We propose a statistical modeling method of wind power output for very short-term prediction. The modeling method with a nonlinear model has cascade structure composed of two parts. One is a linear dynamic part that is driven by a Gaussian white noise and described by an autoregressive model. The other is a nonlinear static part that is driven by the output of the linear part. This nonlinear part is designed for output distribution matching: we shape the distribution of the model output to match with that of the wind power output. The constructed model is utilized for one-step ahead prediction of the wind power output. Furthermore, we study the relation between the prediction accuracy and the prediction horizon.

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

NASA Technical Reports Server (NTRS)

Wang, P. K. C.; Hadaegh, F. Y.

1996-01-01

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

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.

Nonlinear dynamics of a magnetically driven Duffing-type spring-magnet oscillator in the static magnetic field of a coil

NASA Astrophysics Data System (ADS)

Donoso, Guillermo; Ladera, Celso L.

2012-11-01

We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the first, excited with an ac current, provides the oscillating magnetic driving force on the system. From the magnet-coil interactions, we obtain, analytically, the nonlinear motion equation of the system, found to be a forced and damped cubic Duffing oscillator moving in a quartic potential. The relative strengths of the coefficients of the motion equation can be easily set by varying the coils’ dc and ac currents. We demonstrate, theoretically and experimentally, the nonlinear behaviour of this oscillator, including its oscillation modes and nonlinear resonances, the fold-over effect, the hysteresis and amplitude jumps, and its chaotic behaviour. It is an oscillating system suitable for teaching an advanced experiment in nonlinear dynamics both at senior undergraduate and graduate levels.

Dynamics of coupled mode solitons in bursting neural networks

NASA Astrophysics Data System (ADS)

Nfor, N. Oma; Ghomsi, P. Guemkam; Moukam Kakmeni, F. M.

2018-02-01

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

Development and validation of a low-frequency modeling code for high-moment transmitter rod antennas

NASA Astrophysics Data System (ADS)

Jordan, Jared Williams; Sternberg, Ben K.; Dvorak, Steven L.

2009-12-01

The goal of this research is to develop and validate a low-frequency modeling code for high-moment transmitter rod antennas to aid in the design of future low-frequency TX antennas with high magnetic moments. To accomplish this goal, a quasi-static modeling algorithm was developed to simulate finite-length, permeable-core, rod antennas. This quasi-static analysis is applicable for low frequencies where eddy currents are negligible, and it can handle solid or hollow cores with winding insulation thickness between the antenna's windings and its core. The theory was programmed in Matlab, and the modeling code has the ability to predict the TX antenna's gain, maximum magnetic moment, saturation current, series inductance, and core series loss resistance, provided the user enters the corresponding complex permeability for the desired core magnetic flux density. In order to utilize the linear modeling code to model the effects of nonlinear core materials, it is necessary to use the correct complex permeability for a specific core magnetic flux density. In order to test the modeling code, we demonstrated that it can accurately predict changes in the electrical parameters associated with variations in the rod length and the core thickness for antennas made out of low carbon steel wire. These tests demonstrate that the modeling code was successful in predicting the changes in the rod antenna characteristics under high-current nonlinear conditions due to changes in the physical dimensions of the rod provided that the flux density in the core was held constant in order to keep the complex permeability from changing.

Elastic interaction of hydrogen atoms on graphene: A multiscale approach from first principles to continuum elasticity

NASA Astrophysics Data System (ADS)

Branicio, Paulo S.; Vastola, Guglielmo; Jhon, Mark H.; Sullivan, Michael B.; Shenoy, Vivek B.; Srolovitz, David J.

2016-10-01

The deformation of graphene due to the chemisorption of hydrogen atoms on its surface and the long-range elastic interaction between hydrogen atoms induced by these deformations are investigated using a multiscale approach based on first principles, empirical interactions, and continuum modeling. Focus is given to the intrinsic low-temperature structure and interactions. Therefore, all calculations are performed at T =0 , neglecting possible temperature or thermal fluctuation effects. Results from different methods agree well and consistently describe the local deformation of graphene on multiple length scales reaching 500 Å . The results indicate that the elastic interaction mediated by this deformation is significant and depends on the deformation of the graphene sheet both in and out of plane. Surprisingly, despite the isotropic elasticity of graphene, within the linear elastic regime, atoms elastically attract or repel each other depending on (i) the specific site they are chemisorbed; (ii) the relative position of the sites; (iii) and if they are on the same or on opposite surface sides. The interaction energy sign and power-law decay calculated from molecular statics agree well with theoretical predictions from linear elasticity theory, considering in-plane or out-of-plane deformations as a superposition or in a coupled nonlinear approach. Deviations on the exact power law between molecular statics and the linear elastic analysis are evidence of the importance of nonlinear effects on the elasticity of monolayer graphene. These results have implications for the understanding of the generation of clusters and regular formations of hydrogen and other chemisorbed atoms on graphene.

Dynamics of coupled mode solitons in bursting neural networks.

PubMed

Nfor, N Oma; Ghomsi, P Guemkam; Moukam Kakmeni, F M

2018-02-01

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

Continuous functional magnetic resonance imaging reveals dynamic nonlinearities of "dose-response" curves for finger opposition.

PubMed

Berns, G S; Song, A W; Mao, H

1999-07-15

Linear experimental designs have dominated the field of functional neuroimaging, but although successful at mapping regions of relative brain activation, the technique assumes that both cognition and brain activation are linear processes. To test these assumptions, we performed a continuous functional magnetic resonance imaging (MRI) experiment of finger opposition. Subjects performed a visually paced bimanual finger-tapping task. The frequency of finger tapping was continuously varied between 1 and 5 Hz, without any rest blocks. After continuous acquisition of fMRI images, the task-related brain regions were identified with independent components analysis (ICA). When the time courses of the task-related components were plotted against tapping frequency, nonlinear "dose- response" curves were obtained for most subjects. Nonlinearities appeared in both the static and dynamic sense, with hysteresis being prominent in several subjects. The ICA decomposition also demonstrated the spatial dynamics with different components active at different times. These results suggest that the brain response to tapping frequency does not scale linearly, and that it is history-dependent even after accounting for the hemodynamic response function. This implies that finger tapping, as measured with fMRI, is a nonstationary process. When analyzed with a conventional general linear model, a strong correlation to tapping frequency was identified, but the spatiotemporal dynamics were not apparent.

Structural Modeling of a Five-Meter Thin Film Inflatable Antenna/Concentrator With Rigidized Support Struts

NASA Technical Reports Server (NTRS)

Smalley, Kurt B.; Tinker, Michael L.

2001-01-01

Dynamic characterization of a non-rigidized thin film inflatable antenna/solar concentrator structure with rigidized composite support struts is described in detail. A two-step finite element modeling approach in MSC/NASTRAN is utilized, consisting of: (1) a nonlinear static pressurization procedure used to obtain the updated stiffness matrix, and (2) a modal "restart" eigen solution that uses the modified stiffness matrix. Unique problems encountered in modeling of this large 5-m lightweight inflatable are identified, including considerable difficulty in obtaining convergence in the nonlinear pressurization solution. It was found that the extremely thin polyimide film material (.001 in or I mil) presents tremendous problems in obtaining a converged solution when internal pressure loading is applied. It was concluded that the ratios of film thickness to other geometric dimensions such as torus cross-sectional and ring diameter and lenticular diameter are the critical parameters for convergence of the pressurization procedure. Comparison of finite element predictions for frequency and mode shapes with experimental results indicated reasonable agreement considering the complexity of the structure, the film-to-air interaction, and the nonlinear material properties of the film. It was also concluded that analysis should be done using different finite element to codes to determine if a more robust and stable solution can be obtained.

NLOphoric rigid pyrazino-phenanthroline donor-π-acceptor compounds: Investigation of structural and solvent effects on non-linear optical properties using computational methods

NASA Astrophysics Data System (ADS)

Kothavale, Shantaram; Katariya, Santosh; Sekar, Nagaiyan

2018-01-01

Rigid pyrazino-phenanthroline based donor-π-acceptor-π-auxiliary acceptor type compounds have been studied for their linear and non-linear optical properties. The non-linear optical (NLO) behavior of these dyes was studied by calculating the values of static α , β and γ using solvatochromic as well as computational methods. The results obtained by solvatochromic method are correlated theoretically with Density Functional Theory (DFT) using B3LYP/6-31G (d), CAM B3LYP/6-31 G(d), B3LYP/6-31++ g(d,P) and CAM B3LYP/6-31++ g(d,P) methods. The results reveal that, among all four computational methods CAM-B3LYP/6-31++ g(d,P) performs well for the calculation of linear polarizability (α) and first order hyperpolarizability (β), while CAM-B3LYP/6-31 g(d,P) for the calculation of second order hyperpolarizability (ϒ). Overall TPA depends on the molecular structure variation with increase in complexity and molecular weight, which implies that both the number of branches and the size of π-framework are important factors for the molecular TPA in this chromophoric system. Generalized Mulliken-Hush (GMH) analysis is performed to study the effective charge transfer from donor to acceptor.

NL(q) Theory: A Neural Control Framework with Global Asymptotic Stability Criteria.

PubMed

Vandewalle, Joos; De Moor, Bart L.R.; Suykens, Johan A.K.

1997-06-01

In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NL(q) system form. NL(q) systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NL(q)s sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L(2)-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NL(q) stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H( infinity ) control theory and &mgr; theory. Copyright 1997 Elsevier Science Ltd.

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.

An Instructional Method for the AutoCAD Modeling Environment.

ERIC Educational Resources Information Center

Mohler, James L.

1997-01-01

Presents a command organizer for AutoCAD to aid new uses in operating within the 3-D modeling environment. Addresses analyzing the problem, visualization skills, nonlinear tools, a static view of a dynamic model, the AutoCAD organizer, environment attributes, and control of the environment. Contains 11 references. (JRH)

Computer Power. Part 2: Electrical Power Problems and Their Amelioration.

ERIC Educational Resources Information Center

Price, Bennett J.

1989-01-01

Describes electrical power problems that affect computer users, including spikes, sags, outages, noise, frequency variations, and static electricity. Ways in which these problems may be diagnosed and cured are discussed. Sidebars consider transformers; power distribution units; surge currents/linear and non-linear loads; and sizing the power…

Tableau Economique: Teaching Economics with a Tablet Computer

ERIC Educational Resources Information Center

Scott, Robert H., III

2011-01-01

The typical method of instruction in economics is chalk and talk. Economics courses often require writing equations and drawing graphs and charts, which are all best done in freehand. Unlike static PowerPoint presentations, tablet computers create dynamic nonlinear presentations. Wireless technology allows professors to write on their tablets and…

Response of a PCF-based modal interferometer to lateral stress: Resonant behavior and performance as sensor

NASA Astrophysics Data System (ADS)

Sanz-Felipe, Á.; Martín, J. C.

2017-11-01

The performance of a fiber-based modal interferometer as lateral stress sensor has been analyzed, both for static and periodic forces applied on it. The central fiber of the interferometer is a photonic crystal fiber. Forces are applied on it perpendicular to its axis, so that they squeeze it. In static situations, changes in the transmission spectrum of the interferometer are studied as a function of the charges applied. Measurements with several interferometers have been carried out in order to analyze the influence of its length and of its splices' transmission on the device operation, looking for optimization of its linearity and sensibility. The effect of periodic charges, as an emulation of vibrations, has also been studied. The analysis is centered on the frequency dependence of the response. In linear regime (small enough periodic charges), the results obtained are satisfactorily explained by treating the central fiber of the interferometer as a mechanical resonator whose vibration modes coincide with the ones of a cylinder with clamped ends. In nonlinear regime, period doubling and other anharmonic behaviors have been observed.

Control-Relevant Modeling, Analysis, and Design for Scramjet-Powered Hypersonic Vehicles

NASA Technical Reports Server (NTRS)

Rodriguez, Armando A.; Dickeson, Jeffrey J.; Sridharan, Srikanth; Benavides, Jose; Soloway, Don; Kelkar, Atul; Vogel, Jerald M.

2009-01-01

Within this paper, control-relevant vehicle design concepts are examined using a widely used 3 DOF (plus flexibility) nonlinear model for the longitudinal dynamics of a generic carrot-shaped scramjet powered hypersonic vehicle. Trade studies associated with vehicle/engine parameters are examined. The impact of parameters on control-relevant static properties (e.g. level-flight trimmable region, trim controls, AOA, thrust margin) and dynamic properties (e.g. instability and right half plane zero associated with flight path angle) are examined. Specific parameters considered include: inlet height, diffuser area ratio, lower forebody compression ramp inclination angle, engine location, center of gravity, and mass. Vehicle optimizations is also examined. Both static and dynamic considerations are addressed. The gap-metric optimized vehicle is obtained to illustrate how this control-centric concept can be used to "reduce" scheduling requirements for the final control system. A classic inner-outer loop control architecture and methodology is used to shed light on how specific vehicle/engine design parameter selections impact control system design. In short, the work represents an important first step toward revealing fundamental tradeoffs and systematically treating control-relevant vehicle design.

Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations

NASA Astrophysics Data System (ADS)

Kao, Chiu Yen; Osher, Stanley; Qian, Jianliang

2004-05-01

We propose a simple, fast sweeping method based on the Lax-Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton-Jacobi equations in any number of spatial dimensions. By using the Lax-Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss-Seidel type nonlinear iterative method can be utilized. Furthermore, by incorporating a group-wise causality principle into the Gauss-Seidel iteration by following a finite group of characteristics, we have an easy-to-implement, sweeping-type, and fast convergent numerical method. However, unlike other methods based on the Godunov numerical Hamiltonian, some computational boundary conditions are needed in the implementation. We give a simple recipe which enforces a version of discrete min-max principle. Some convergence analysis is done for the one-dimensional eikonal equation. Extensive 2-D and 3-D numerical examples illustrate the efficiency and accuracy of the new approach. To our knowledge, this is the first fast numerical method based on discretizing the Hamilton-Jacobi equation directly without assuming convexity and/or homogeneity of the Hamiltonian.

Buckling and postbuckling of size-dependent cracked microbeams based on a modified couple stress theory

NASA Astrophysics Data System (ADS)

Akbarzadeh Khorshidi, M.; Shariati, M.

2017-07-01

The elastic buckling analysis and the static postbuckling response of the Euler-Bernoulli microbeams containing an open edge crack are studied based on a modified couple stress theory. The cracked section is modeled by a massless elastic rotational spring. This model contains a material length scale parameter and can capture the size effect. The von Kármán nonlinearity is applied to display the postbuckling behavior. Analytical solutions of a critical buckling load and the postbuckling response are presented for simply supported cracked microbeams. This parametric study indicates the effects of the crack location, crack severity, and length scale parameter on the buckling and postbuckling behaviors of cracked microbeams.

A numerical study of the thermal stability of low-lying coronal loops

NASA Technical Reports Server (NTRS)

Klimchuk, J. A.; Antiochos, S. K.; Mariska, J. T.

1986-01-01

The nonlinear evolution of loops that are subjected to a variety of small but finite perturbations was studied. Only the low-lying loops are considered. The analysis was performed numerically using a one-dimensional hydrodynamical model developed at the Naval Research Laboratory. The computer codes solve the time-dependent equations for mass, momentum, and energy transport. The primary interest is the active region filaments, hence a geometry appropriate to those structures was considered. The static solutions were subjected to a moderate sized perturbation and allowed to evolve. The results suggest that both hot and cool loops of the geometry considered are thermally stable against amplitude perturbations of all kinds.

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

Milani, Gabriele, E-mail: milani@stru.polimi.it, E-mail: gabriele.milani@polimi.it; Valente, Marco

This study presents some FE results regarding the behavior under horizontal loads of eight existing masonry towers located in the North-East of Italy. The towers, albeit unique for geometric and architectural features, show some affinities which justify a comparative analysis, as for instance the location and the similar masonry material. Their structural behavior under horizontal loads is therefore influenced by geometrical issues, such as slenderness, walls thickness, perforations, irregularities, presence of internal vaults, etc., all features which may be responsible for a peculiar output. The geometry of the towers is deduced from both existing available documentation and in-situ surveys. Onmore » the basis of such geometrical data, a detailed 3D realistic mesh is conceived, with a point by point characterization of each single geometric element. The FE models are analysed under seismic loads acting along geometric axes of the plan section, both under non-linear static (pushover) and non-linear dynamic excitation assumptions. A damage-plasticity material model exhibiting softening in both tension and compression, already available in the commercial code Abaqus, is used for masonry. Pushover analyses are performed with both G1 and G2 horizontal loads distribution, according to Italian code requirements, along X+/− and Y+/− directions. Non-linear dynamic analyses are performed along both X and Y directions with a real accelerogram scaled to different peak ground accelerations. Some few results are presented in this paper. It is found that the results obtained with pushover analyses reasonably well fit expensive non-linear dynamic simulations, with a slightly less conservative trend.« less

Heisenberg spin-glass behaviour in Ga0.99Yb0.01FeO3

NASA Astrophysics Data System (ADS)

Neacsa, Daniela Maria; Gruener, Gisèle; Hebert, Sylvie; Soret, Jean-Claude

2017-06-01

The dynamic and static magnetic properties of Ga0.99Yb0.01FeO3 are studied in detail using ac susceptibility and dc magnetization measurements. The study shows that the compound undergoes a spin-glass freezing at Tg ≈ 213 K . The dynamic scaling analysis of ac susceptibility data reveals typical features characteristic of canonical spin-glasses, i.e., relaxation time τ∗ ∼10-14 s , critical exponent νz = 4.1 ± 0.2 , and frequency sensitivity parameter δf ∼10-3 within three frequency decades. The analysis of the critical behaviour of the static nonlinear susceptibility yields the critical exponents γ = 4.3 ± 0.1, β = 1.0 ± 0.1 , and δ = 5.5 ± 0.5 , which lie between those typical of three-dimensional (3D) weakly anisotropic Heisenberg and Ising spin glasses. The analysis of the field-cooled and zero-field-cooled magnetization data allows to define two characteristic temperatures depending on the applied magnetic field. The upper one, Tirr(H) , is the threshold temperature corresponding to the appearance of weak irreversibility, whereas the lower one, Ts(H) , marks the onset of strong irreversibility. The resulting field-temperature phase diagram turns out to be in good quantitative agreement with the mean-field predictions for 3D Heisenberg spin-glass with random magnetic anisotropy, and appears consistent with the chiral driven freezing scenario.

Updated Chemical Kinetics and Sensitivity Analysis Code

NASA Technical Reports Server (NTRS)

Radhakrishnan, Krishnan

2005-01-01

An updated version of the General Chemical Kinetics and Sensitivity Analysis (LSENS) computer code has become available. A prior version of LSENS was described in "Program Helps to Determine Chemical-Reaction Mechanisms" (LEW-15758), NASA Tech Briefs, Vol. 19, No. 5 (May 1995), page 66. To recapitulate: LSENS solves complex, homogeneous, gas-phase, chemical-kinetics problems (e.g., combustion of fuels) that are represented by sets of many coupled, nonlinear, first-order ordinary differential equations. LSENS has been designed for flexibility, convenience, and computational efficiency. The present version of LSENS incorporates mathematical models for (1) a static system; (2) steady, one-dimensional inviscid flow; (3) reaction behind an incident shock wave, including boundary layer correction; (4) a perfectly stirred reactor; and (5) a perfectly stirred reactor followed by a plug-flow reactor. In addition, LSENS can compute equilibrium properties for the following assigned states: enthalpy and pressure, temperature and pressure, internal energy and volume, and temperature and volume. For static and one-dimensional-flow problems, including those behind an incident shock wave and following a perfectly stirred reactor calculation, LSENS can compute sensitivity coefficients of dependent variables and their derivatives, with respect to the initial values of dependent variables and/or the rate-coefficient parameters of the chemical reactions.

Visual Detection Under Uncertainty Operates Via an Early Static, Not Late Dynamic, Non-Linearity

PubMed Central

Neri, Peter

2010-01-01

Signals in the environment are rarely specified exactly: our visual system may know what to look for (e.g., a specific face), but not its exact configuration (e.g., where in the room, or in what orientation). Uncertainty, and the ability to deal with it, is a fundamental aspect of visual processing. The MAX model is the current gold standard for describing how human vision handles uncertainty: of all possible configurations for the signal, the observer chooses the one corresponding to the template associated with the largest response. We propose an alternative model in which the MAX operation, which is a dynamic non-linearity (depends on multiple inputs from several stimulus locations) and happens after the input stimulus has been matched to the possible templates, is replaced by an early static non-linearity (depends only on one input corresponding to one stimulus location) which is applied before template matching. By exploiting an integrated set of analytical and experimental tools, we show that this model is able to account for a number of empirical observations otherwise unaccounted for by the MAX model, and is more robust with respect to the realistic limitations imposed by the available neural hardware. We then discuss how these results, currently restricted to a simple visual detection task, may extend to a wider range of problems in sensory processing. PMID:21212835

On the Chaotic Vibrations of Electrostatically Actuated Arch Micro/Nano Resonators: A Parametric Study

NASA Astrophysics Data System (ADS)

Tajaddodianfar, Farid; Hairi Yazdi, Mohammad Reza; Pishkenari, Hossein Nejat

Motivated by specific applications, electrostatically actuated bistable arch shaped micro-nano resonators have attracted growing attention in the research community in recent years. Nevertheless, some issues relating to their nonlinear dynamics, including the possibility of chaos, are still not well known. In this paper, we investigate the chaotic vibrations of a bistable resonator comprised of a double clamped initially curved microbeam under combined harmonic AC and static DC distributed electrostatic actuation. A reduced order equation obtained by the application of the Galerkin method to the nonlinear partial differential equation of motion, given in the framework of Euler-Bernoulli beam theory, is used for the investigation in this paper. We numerically integrate the obtained equation to study the chaotic vibrations of the proposed system. Moreover, we investigate the effects of various parameters including the arch curvature, the actuation parameters and the quality factor of the resonator, which are effective in the formation of both static and dynamic behaviors of the system. Using appropriate numerical tools, including Poincaré maps, bifurcation diagrams, Fourier spectrum and Lyapunov exponents we scrutinize the effects of various parameters on the formation of chaotic regions in the parametric space of the resonator. Results of this work provide better insight into the problem of nonlinear dynamics of the investigated family of bistable micro/nano resonators, and facilitate the design of arch resonators for applications such as filters.

Emergent universe with wormholes in massive gravity

NASA Astrophysics Data System (ADS)

Paul, B. C.; Majumdar, A. S.

2018-03-01

An emergent universe (EU) scenario is proposed to obtain a universe free from big-bang singularity. In this framework the present universe emerged from a static Einstein universe phase in the infinite past. A flat EU scenario is found to exist in Einstein’s gravity with a non-linear equation of state (EoS). It has been shown subsequently that a physically realistic EU model can be obtained considering cosmic fluid composed of interacting fluids with a non-linear equation of state. It results a viable cosmological model accommodating both early inflation and present accelerating phases. In the present paper, the origin of an initial static Einstein universe needed in the EU model is explored in a massive gravity theory which subsequently emerged to be a dynamically evolving universe. A new gravitational instanton solution in a flat universe is obtained in the massive gravity theory which is a dynamical wormhole that might play an important role in realizing the origin of the initial state of the emergent universe. The emergence of a Lorentzian universe from a Euclidean gravity is understood by a Wick rotation τ = i t . A universe with radiation at the beginning finally transits into the present observed universe with a non-linear EoS as the interactions among the fluids set in. Thus a viable flat EU scenario where the universe stretches back into time infinitely, with no big bang is permitted in a massive gravity.

Integrated optimization of nonlinear R/C frames with reliability constraints

NASA Technical Reports Server (NTRS)

Soeiro, Alfredo; Hoit, Marc

1989-01-01

A structural optimization algorithm was researched including global displacements as decision variables. The algorithm was applied to planar reinforced concrete frames with nonlinear material behavior submitted to static loading. The flexural performance of the elements was evaluated as a function of the actual stress-strain diagrams of the materials. Formation of rotational hinges with strain hardening were allowed and the equilibrium constraints were updated accordingly. The adequacy of the frames was guaranteed by imposing as constraints required reliability indices for the members, maximum global displacements for the structure and a maximum system probability of failure.

Non-linear wave interaction in a plasma column

NASA Technical Reports Server (NTRS)

Larsen, J.-M.; Crawford, F. W.

1979-01-01

Non-linear three-wave interaction is analysed for propagation along a cylindrical plasma column surrounded by an infinite dielectric, in the absence of a static magnetic field. An averaged-Lagrangian method is used, and the results are specialized to parametric interaction and mode conversion, assuming an undepleted pump wave. The theory for these two types of interactions is extended to include imperfect synchronism, and the effects of loss. Computations are presented indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma column parameters.

A theoretical and experimental investigation of the linear and nonlinear impulse responses from a magnetoplasma column

NASA Technical Reports Server (NTRS)

Grody, N. C.

1973-01-01

Linear and nonlinear responses of a magnetoplasma resulting from inhomogeneity in the background plasma density are studied. The plasma response to an impulse electric field was measured and the results are compared with the theory of an inhomogeneous cold plasma. Impulse responses were recorded for the different plasma densities, static magnetic fields, and neutral pressures and generally appeared as modulated, damped oscillations. The frequency spectra of the waveforms consisted of two separated resonance peaks. For weak excitation, the results correlate with the linear theory of a cold, inhomogeneous, cylindrical magnetoplasma. The damping mechanism is identified with that of phase mixing due to inhomogeneity in plasma density. With increasing excitation voltage, the nonlinear impulse responses display stronger damping and a small increase in the frequency of oscillation.

Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

NASA Astrophysics Data System (ADS)

Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.

2012-11-01

Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)

Closed-loop control of a core free rolled EAP actuator

NASA Astrophysics Data System (ADS)

Sarban, Rahimullah; Oubaek, Jakob; Jones, Richard W.

2009-03-01

Tubular dielectric electro-active polymer actuators, also referred as tubular InLastors, have many possible applications. One of the most obvious is as a positioning push-type device. This work examines the feedback closed-loop control of a core-free tubular InLastor fabricated from sheets of PolyPowerTM, an EAP material developed by Danfoss PolyPower A/S, which uses a silicone elastomer in conjunction with smart compliant electrode technology. This is part of an ongoing study to develop a precision positioning feedback control system for this device. Initially proportional and integral (PI) control is considered to provide position control of the tubular InLastor. Control of the tubular Inlastors require more than conventional control, used for linear actuators, because the InLastors display highly nonlinear static voltage-strain and voltage-force characteristics as well as dynamic hysteresis and time-dependent strain behavior. In an attempt to overcome the nonlinear static voltage-strain characteristics of the Inlastors and for improving the dynamic performance of the controlled device, a gain scheduling algorithm is then integrated into the PI controlled system.

The Effect of Adaptive Nonlinear Frequency Compression on Phoneme Perception.

PubMed

Glista, Danielle; Hawkins, Marianne; Bohnert, Andrea; Rehmann, Julia; Wolfe, Jace; Scollie, Susan

2017-12-12

This study implemented a fitting method, developed for use with frequency lowering hearing aids, across multiple testing sites, participants, and hearing aid conditions to evaluate speech perception with a novel type of frequency lowering. A total of 8 participants, including children and young adults, participated in real-world hearing aid trials. A blinded crossover design, including posttrial withdrawal testing, was used to assess aided phoneme perception. The hearing aid conditions included adaptive nonlinear frequency compression (NFC), static NFC, and conventional processing. Enabling either adaptive NFC or static NFC improved group-level detection and recognition results for some high-frequency phonemes, when compared with conventional processing. Mean results for the distinction component of the Phoneme Perception Test (Schmitt, Winkler, Boretzki, & Holube, 2016) were similar to those obtained with conventional processing. Findings suggest that both types of NFC tested in this study provided a similar amount of speech perception benefit, when compared with group-level performance with conventional hearing aid technology. Individual-level results are presented with discussion around patterns of results that differ from the group average.

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2015-12-21

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

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

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Studies of electron-polyatomic-molecule collisions Applications to e-CH4

NASA Technical Reports Server (NTRS)

Lima, M. A. P.; Gibson, T. L.; Mckoy, V.; Huo, W. M.

1985-01-01

The first application of the Schwinger multichannel formulation to low-energy electron collisions with a nonlinear polyatomic target is reported. Integral and differential cross sections are obtained for e-CH4 collisions from 3 to 20 eV at the static-plus-exchange interaction level. In these studies, the exchange potential is directly evaluated and not approximated by local models. An interesting feature of the small-angle differential cross section is ascribed to polarization effects and not reproduced at the static-plus-exchange level. These differential cross sections are found to be in reasonable agreement with existing measurements at 7.5 eV and higher energies.

Static behavior and the effects of thermal cycling in hybrid laminates

NASA Technical Reports Server (NTRS)

Liber, T. M.; Daniel, I. M.; Chamis, C. C.

1977-01-01

Static stiffness, strength and ultimate strain after thermal cycling were investigated for graphite/Kevlar 49/epoxy and graphite/S-glass/epoxy angle-ply laminates. Tensile stress-strain curves to failure and uniaxial tensile properties were determined, and theoretical predictions of modulus, Poisson's ratio and ultimate strain, based on linear lamination theory, constituent ply properties and measured strength, were made. No significant influence on tensile stress properties due to stacking sequence variations was observed. In general, specimens containing two 0-degree Kevlar or S-glass plies were found to behave linearly to failure, while specimens containing 4 0-degree Kevlar or S-glass plies showed some nonlinear behavior.

Static Einstein-Maxwell Black Holes with No Spatial Isometries in AdS Space.

PubMed

Herdeiro, Carlos A R; Radu, Eugen

2016-11-25

We explicitly construct static black hole solutions to the fully nonlinear, D=4, Einstein-Maxwell-anti-de Sitter (AdS) equations that have no continuous spatial symmetries. These black holes have a smooth, topologically spherical horizon (section), but without isometries, and approach, asymptotically, global AdS spacetime. They are interpreted as bound states of a horizon with the Einstein-Maxwell-AdS solitons recently discovered, for appropriate boundary data. In sharp contrast to the uniqueness results for a Minkowski electrovacuum, the existence of these black holes shows that single, equilibrium, black hole solutions in an AdS electrovacuum admit an arbitrary multipole structure.

Computational assessment of promising mid-infrared nonlinear optical materials Mg–IV–V2 (IV = Si, Ge, Sn; V = P, As): a first-principles study

NASA Astrophysics Data System (ADS)

Xiao, Jianping; Zhu, Shifu; Zhao, Beijun; Chen, Baojun; Liu, Hui; He, Zhiyu

2018-03-01

The mid-infrared (mid-IR) nonlinear optical (NLO) capabilities of Mg–IV–V2 (IV = Si, Ge, Sn; V = P, As) are systematically assessed by the first-principles calculation. The results show that the compounds in this group except MgSiP2 and MgSnP2 have moderate birefringence values to fulfill the phase-matching conditions. In particular, MgGeP2 and MgSiAs2 possess relatively large band gaps and almost three to four times larger static SHG coefficients than the benchmark material AgGaSe2, exhibiting good potential for mid-IR NLO application. According to the detailed analysis of the electronic structures, it is found that the dominant SHG contributions are from the orbitals of the asymmetry anionic unit [IV–V2]2‑. Moreover, the further evaluation reveals that MgSiAs2, MgGeAs2, MgSnP2 and MgSnAs2 are not thermodynamically stable and the new synthesis strategy (i.e. synthesis under non-equilibrium conditions) should be considered.

Vibration isolation using extreme geometric nonlinearity

NASA Astrophysics Data System (ADS)

Virgin, L. N.; Santillan, S. T.; Plaut, R. H.

2008-08-01

A highly deformed, slender beam (or strip), attached to a vertically oscillating base, is used in a vibration isolation application to reduce the motion of a supported mass. The isolator is a thin strip that is bent so that the two ends are clamped together, forming a loop. The clamped ends are attached to an excitation source and the supported system is attached at the loop midpoint directly above the base. The strip is modeled as an elastica, and the resulting nonlinear boundary value problem is solved numerically using a shooting method. First the equilibrium shapes of the loop with varying static loads and lengths are studied. The analysis reveals a large degree of stiffness tunability; the stiffness is dependent on the geometric configuration, which itself is determined by the supported mass, loop length, and loop self-weight. Free vibration frequencies and mode shapes are also found. Finally, the case of forced vibration is studied, and the displacement transmissibility over a large range of forcing frequencies is determined for varying parameter values. Experiments using polycarbonate strips are conducted to verify equilibrium and dynamic behavior.

Extremal black holes, Stueckelberg scalars and phase transitions

NASA Astrophysics Data System (ADS)

Marrani, Alessio; Miskovic, Olivera; Leon, Paula Quezada

2018-02-01

We calculate the entropy of a static extremal black hole in 4D gravity, non-linearly coupled to a massive Stueckelberg scalar. We find that the scalar field does not allow the black hole to be magnetically charged. We also show that the system can exhibit a phase transition due to electric charge variations. For spherical and hyperbolic horizons, the critical point exists only in presence of a cosmological constant, and if the scalar is massive and non-linearly coupled to electromagnetic field. On one side of the critical point, two extremal solutions coexist: Reissner-Nordström (A)dS black hole and the charged hairy (A)dS black hole, while on the other side of the critical point the black hole does not have hair. A near-critical analysis reveals that the hairy black hole has larger entropy, thus giving rise to a zero temperature phase transition. This is characterized by a discontinuous second derivative of the entropy with respect to the electric charge at the critical point. The results obtained here are analytical and based on the entropy function formalism and the second law of thermodynamics.

A geometrically exact formulation for three-dimensional numerical simulation of the umbilical cable in a deep-sea ROV system

NASA Astrophysics Data System (ADS)

Quan, Wei-cai; Zhang, Zhu-ying; Zhang, Ai-qun; Zhang, Qi-feng; Tian, Yu

2015-04-01

This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle (ROV) system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized- α implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.

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.

Nonlinear Viscoelastic Characterization of the Porcine Spinal Cord

PubMed Central

Shetye, Snehal; Troyer, Kevin; Streijger, Femke; Lee, Jae H. T.; Kwon, Brian K.; Cripton, Peter; Puttlitz, Christian M.

2014-01-01

Although quasi-static and quasi-linear viscoelastic properties of the spinal cord have been reported previously, there are no published studies that have investigated the fully (strain-dependent) nonlinear viscoelastic properties of the spinal cord. In this study, stress relaxation experiments and dynamic cycling were performed on six fresh porcine lumbar cord specimens to examine their viscoelastic mechanical properties. The stress relaxation data were fitted to a modified superposition formulation and a novel finite ramp time correction technique was applied. The parameters obtained from this fitting methodology were used to predict the average dynamic cyclic viscoelastic behavior of the porcine cord. The data indicate that the porcine spinal cord exhibited fully nonlinear viscoelastic behavior. The average weighted RMSE for a Heaviside ramp fit was 2.8kPa, which was significantly greater (p < 0.001) than that of the nonlinear (comprehensive viscoelastic characterization (CVC) method) fit (0.365kPa). Further, the nonlinear mechanical parameters obtained were able to accurately predict the dynamic behavior, thus exemplifying the reliability of the obtained nonlinear parameters. These parameters will be important for future studies investigating various damage mechanisms of the spinal cord and studies developing high resolution finite elements models of the spine. PMID:24211612

Discrete-Time Mapping for an Impulsive Goodwin Oscillator with Three Delays

NASA Astrophysics Data System (ADS)

Churilov, Alexander N.; Medvedev, Alexander; Zhusubaliyev, Zhanybai T.

A popular biomathematics model of the Goodwin oscillator has been previously generalized to a more biologically plausible construct by introducing three time delays to portray the transport phenomena arising due to the spatial distribution of the model states. The present paper addresses a similar conversion of an impulsive version of the Goodwin oscillator that has found application in mathematical modeling, e.g. in endocrine systems with pulsatile hormone secretion. While the cascade structure of the linear continuous part pertinent to the Goodwin oscillator is preserved in the impulsive Goodwin oscillator, the static nonlinear feedback of the former is substituted with a pulse modulation mechanism thus resulting in hybrid dynamics of the closed-loop system. To facilitate the analysis of the mathematical model under investigation, a discrete mapping propagating the continuous state variables through the firing times of the impulsive feedback is derived. Due to the presence of multiple time delays in the considered model, previously developed mapping derivation approaches are not applicable here and a novel technique is proposed and applied. The mapping captures the dynamics of the original hybrid system and is instrumental in studying complex nonlinear phenomena arising in the impulsive Goodwin oscillator. A simulation example is presented to demonstrate the utility of the proposed approach in bifurcation analysis.

Modeling of composite beams and plates for static and dynamic analysis

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Sutyrin, Vladislav G.; Lee, Bok Woo

1993-01-01

The main purpose of this research was to develop a rigorous theory and corresponding computational algorithms for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants for a plate and to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. This also requires the development of finite deformation plate equations which are compatible with the through-the-thickness analyses. After about one year's work, we settled on the variational-asymptotical method (VAM) as a suitable framework in which to solve these types of problems. VAM was applied to laminated plates with constant thickness in the work of Atilgan and Hodges. The corresponding geometrically nonlinear global deformation analysis of plates was developed by Hodges, Atilgan, and Danielson. A different application of VAM, along with numerical results, was obtained by Hodges, Lee, and Atilgan. An expanded version of this last paper was submitted for publication in the AIAA Journal.

Fundamental period of Italian reinforced concrete buildings: comparison between numerical, experimental and Italian code simplified values

NASA Astrophysics Data System (ADS)

Ditommaso, Rocco; Carlo Ponzo, Felice; Auletta, Gianluca; Iacovino, Chiara; Nigro, Antonella

2015-04-01

Aim of this study is a comparison among the fundamental period of reinforced concrete buildings evaluated using the simplified approach proposed by the Italian Seismic code (NTC 2008), numerical models and real values retrieved from an experimental campaign performed on several buildings located in Basilicata region (Italy). With the intention of proposing simplified relationships to evaluate the fundamental period of reinforced concrete buildings, scientists and engineers performed several numerical and experimental campaigns, on different structures all around the world, to calibrate different kind of formulas. Most of formulas retrieved from both numerical and experimental analyses provides vibration periods smaller than those suggested by the Italian seismic code. However, it is well known that the fundamental period of a structure play a key role in the correct evaluation of the spectral acceleration for seismic static analyses. Generally, simplified approaches impose the use of safety factors greater than those related to in depth nonlinear analyses with the aim to cover possible unexpected uncertainties. Using the simplified formula proposed by the Italian seismic code the fundamental period is quite higher than fundamental periods experimentally evaluated on real structures, with the consequence that the spectral acceleration adopted in the seismic static analysis may be significantly different than real spectral acceleration. This approach could produces a decreasing in safety factors obtained using linear and nonlinear seismic static analyses. Finally, the authors suggest a possible update of the Italian seismic code formula for the simplified estimation of the fundamental period of vibration of existing RC buildings, taking into account both elastic and inelastic structural behaviour and the interaction between structural and non-structural elements. 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, M. Vona, M. R. Gallipoli and M. Mucciarelli (2013). Evaluation and considerations about fundamental periods of damaged reinforced concrete buildings. Nat. Hazards Earth Syst. Sci., 13, 1903-1912, 2013. www.nat-hazards-earth-syst-sci.net/13/1903/2013. doi:10.5194/nhess-13-1903-2013

Aerodynamic analysis and simulation of a twin-tail tilt-duct unmanned aerial vehicle

NASA Astrophysics Data System (ADS)

Abdollahi, Cyrus

The tilt-duct vertical takeoff and landing (VTOL) concept has been around since the early 1960s; however, to date the design has never passed the research phase and development phase. Nearly 50 years later, American Dynamics Flight Systems (ADFS) is developing the AD-150, a 2,250lb weight class unmanned aerial vehicle (UAV) configured with rotating ducts on each wingtip. Unlike its predecessor, the Doak VZ-4, the AD-150 features a V tail and wing sweep -- both of which affect the aerodynamic behavior of the aircraft. Because no aircraft of this type has been built and tested, vital aerodynamic research was conducted on the bare airframe behavior (without wingtip ducts). Two weeks of static and dynamic testing were performed on a 3/10th scale model at the University of Maryland's 7' x 10' low speed wind tunnel to facilitate the construction of a nonlinear flight simulator. A total of 70 dynamic tests were performed to obtain damping parameter estimates using the ordinary least squares methodology. Validation, based on agreement between static and dynamic estimates of the pitch and yaw stiffness terms, showed an average percent error of 14.0% and 39.6%, respectively. These inconsistencies were attributed to: large dynamic displacements not encountered during static testing, regressor collinearity, and, while not conclusively proven, differences in static and dynamic boundary layer development. Overall, the damping estimates were consistent and repeatable, with low scatter over a 95% confidence interval. Finally, a basic open loop simulation was executed to demonstrate the instability of the aircraft. As a result, it is recommended that future work be performed to determine trim points and linear models for controls development.

Finite Element Modeling of Non-linear Coupled Interacting Fault System

NASA Astrophysics Data System (ADS)

Xing, H. L.; Zhang, J.; Wyborn, D.

2009-04-01

PANDAS - Parallel Adaptive static/dynamic Nonlinear Deformation Analysis System - a novel supercomputer simulation tool is developed for simulating the highly non-linear coupled geomechanical-fluid flow-thermal systems involving heterogeneously fractured geomaterials. PANDAS includes the following key components: Pandas/Pre, ESyS_Crustal, Pandas/Thermo, Pandas/Fluid and Pandas/Post as detailed in the following: • Pandas/Pre is developed to visualise the microseismicity events recorded during the hydraulic stimulation process to further evaluate the fracture location and evolution and geological setting of a certain reservoir, and then generate the mesh by it and/or other commercial graphics software (such as Patran) for the further finite element analysis of various cases; The Delaunay algorithm is applied as a suitable method for mesh generation using such a point set; • ESyS_Crustal is a finite element code developed for the interacting fault system simulation, which employs the adaptive static/dynamic algorithm to simulate the dynamics and evolution of interacting fault systems and processes that are relevant on short to mediate time scales in which several dynamic phenomena related with stick-slip instability along the faults need to be taken into account, i.e. (a). slow quasi-static stress accumulation, (b) rapid dynamic rupture, (c) wave propagation and (d) corresponding stress redistribution due to the energy release along the multiple fault boundaries; those are needed to better describe ruputure/microseimicity/earthquake related phenomena with applications in earthquake forecasting, hazard quantification, exploration, and environmental problems. It has been verified with various available experimental results[1-3]; • Pandas/Thermo is a finite element method based module for the thermal analysis of the fractured porous media; the temperature distribution is calculated from the heat transfer induced by the thermal boundary conditions without/with the coupled fluid effects and the geomechanical energy conversion for the pure/coupled thermal analysis. • Pandas/Fluid is a finite element method based module for simulating the fluid flow in the fractured porous media; the fluid flow velocity and pressure are calculated from energy equilibrium equations without/together with the coupling effects of the thermal and solid rock deformation for an independent/coupled fluid flow analysis; • Pandas/Post is to visualise the simulation results through the integration of VTK and/or Patran. All the above modules can be used independently/together to simulate individual/coupled phenomena (such as interacting fault system dynamics, heat flow and fluid flow) without/with coupling effects. PANDAS has been applied to the following issues: • visualisation of the microseismic events to monitor and determine where/how the underground rupture proceeds during a hydraulic stimulation, to generate the mesh using the recorded data for determining the domain of the ruptured zone and to evaluate the material parameters (i.e. the permeability) for the further numerical analysis; • interacting fault system simulation to determine the relevant complicated dynamic rupture process. • geomechanical-fluid flow coupling analysis to investigate the interactions between fluid flow and deformation in the fractured porous media under different loading conditions. • thermo-fluid flow coupling analysis of a fractured geothermal reservoir system. PANDAS will be further developed for a multiscale simulation of multiphase dynamic behaviour for a certain fractured geothermal reservoir. More details and additional application examples will be given during the presentation. References [1] Xing, H. L., Makinouchi, A. and Mora, P. (2007). Finite element modeling of interacting fault system, Physics of the Earth and Planetary Interiors, 163, 106-121.doi:10.1016/j.pepi.2007.05.006 [2] Xing, H. L., Mora, P., Makinouchi, A. (2006). An unified friction description and its application to simulation of frictional instability using finite element method. Philosophy Magazine, 86, 3453-3475 [3] Xing, H. L., Mora, P.(2006). Construction of an intraplate fault system model of South Australia, and simulation tool for the iSERVO institute seed project.. Pure and Applied Geophysics. 163, 2297-2316. DOI 10.1007/s00024-006-0127-x

Structural analysis of the space shuttle solid rocket booster/external tank attach ring

NASA Technical Reports Server (NTRS)

Dorsey, John T.

1988-01-01

An External Tank (ET) attach ring is used in the Space Shuttle System to transfer lateral loads between the ET and the Solid Rocket Booster (SRB). Following the Challenger (51-L) accident, the flight performance of the ET attach ring was reviewed, and negative margins of safety and failed bolts in the attach ring were subsequently identified. The analyses described in this report were performed in order to understand the existing ET attach ring structural response to motor case internal pressurization as well as to aid in an ET attach ring redesign effort undertaken by NASA LaRC. The finite element model as well as the results from linear and nonlinear static structural analyses are described.

Ground-state energies of simple metals

NASA Technical Reports Server (NTRS)

Hammerberg, J.; Ashcroft, N. W.

1974-01-01

A structural expansion for the static ground-state energy of a simple metal is derived. Two methods are presented, one an approach based on single-particle band structure which treats the electron gas as a nonlinear dielectric, the other a more general many-particle analysis using finite-temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi-surface distortions, and chemical-potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron-ion interaction and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero-temperature thermodynamic functions of atomic hydrogen are reported.

Structural expansions for the ground state energy of a simple metal

NASA Technical Reports Server (NTRS)

Hammerberg, J.; Ashcroft, N. W.

1973-01-01

A structural expansion for the static ground state energy of a simple metal is derived. An approach based on single particle band structure which treats the electron gas as a non-linear dielectric is presented, along with a more general many particle analysis using finite temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi surface distortions, and chemical potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron ion interaction, and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero temperature thermodynamic functions of atomic hydrogen are reported.

Assessment of input-output properties and control of neuroprosthetic hand grasp.

PubMed

Hines, A E; Owens, N E; Crago, P E

1992-06-01

Three tests have been developed to evaluate rapidly and quantitatively the input-output properties and patient control of neuroprosthetic hand grasp. Each test utilizes a visual pursuit tracking task during which the subject controls the grasp force and grasp opening (position) of the hand. The first test characterizes the static input-output properties of the hand grasp, where the input is a slowly changing patient generated command signal and the outputs are grasp force and grasp opening. Nonlinearities and inappropriate slopes have been documented in these relationships, and in some instances the need for system returning has been indicated. For each subject larger grasp forces were produced when grasping larger objects, and for some subjects the shapes of the relationships also varied with object size. The second test quantifies the ability of the subject to control the hand grasp outputs while tracking steps and ramps. Neuroprosthesis users had rms errors two to three times larger when tracking steps versus ramps, and had rms errors four to five times larger than normals when tracking ramps. The third test provides an estimate of the frequency response of the hand grasp system dynamics, from input and output data collected during a random tracking task. Transfer functions were estimated by spectral analysis after removal of the static input-output nonlinearities measured in the first test. The dynamics had low-pass filter characteristics with 3 dB cutoff frequencies from 1.0 to 1.4 Hz. The tests developed in this study provide a rapid evaluation of both the system and the user. They provide information to 1) help interpret subject performance of functional tasks, 2) evaluate the efficacy of system features such as closed-loop control, and 3) screen the neuroprosthesis to indicate the need for retuning.

Recent developments in heterodyne laser interferometry at Harbin Institute of Technology

NASA Astrophysics Data System (ADS)

Hu, P. C.; Tan, J. B. B.; Yang, H. X. X.; Fu, H. J. J.; Wang, Q.

2013-01-01

In order to fulfill the requirements for high-resolution and high-precision heterodyne interferometric technologies and instruments, the laser interferometry group of HIT has developed some novel techniques for high-resolution and high-precision heterodyne interferometers, such as high accuracy laser frequency stabilization, dynamic sub-nanometer resolution phase interpolation and dynamic nonlinearity measurement. Based on a novel lock point correction method and an asymmetric thermal structure, the frequency stabilized laser achieves a long term stability of 1.2×10-8, and it can be steadily stabilized even in the air flowing up to 1 m/s. In order to achieve dynamic sub-nanometer resolution of laser heterodyne interferometers, a novel phase interpolation method based on digital delay line is proposed. Experimental results show that, the proposed 0.62 nm, phase interpolator built with a 64 multiple PLL and an 8-tap digital delay line achieves a static accuracy better than 0.31nm and a dynamic accuracy better than 0.62 nm over the velocity ranging from -2 m/s to 2 m/s. Meanwhile, an accuracy beam polarization measuring setup is proposed to check and ensure the light's polarization state of the dual frequency laser head, and a dynamic optical nonlinearity measuring setup is built to measure the optical nonlinearity of the heterodyne system accurately and quickly. Analysis and experimental results show that, the beam polarization measuring setup can achieve an accuracy of 0.03° in ellipticity angles and an accuracy of 0.04° in the non-orthogonality angle respectively, and the optical nonlinearity measuring setup can achieve an accuracy of 0.13°.

Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates

PubMed Central

Batra, Romesh C.; Porfiri, Maurizio; Spinello, Davide

2008-01-01

We study the influence of von Kármán nonlinearity, van der Waals force, and thermal stresses on pull-in instability and small vibrations of electrostatically actuated microplates. We use the Galerkin method to develop a tractable reduced-order model for electrostatically actuated clamped rectangular microplates in the presence of van der Waals forces and thermal stresses. More specifically, we reduce the governing two-dimensional nonlinear transient boundary-value problem to a single nonlinear ordinary differential equation. For the static problem, the pull-in voltage and the pull-in displacement are determined by solving a pair of nonlinear algebraic equations. The fundamental vibration frequency corresponding to a deflected configuration of the microplate is determined by solving a linear algebraic equation. The proposed reduced-order model allows for accurately estimating the combined effects of van der Waals force and thermal stresses on the pull-in voltage and the pull-in deflection profile with an extremely limited computational effort. PMID:27879752

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.

Numerical Assessment of Rockbursting.

DTIC Science & Technology

1987-05-27

static equilibrium, nonlinear elasticity, strain-softening • material , unstable propagation of pre-existing cracks , and finally - surface...structure of LINOS, which is common to most of the large finite element codes, the library of element and material subroutines can be easily expanded... material model subroutines , are tested by comparing finite element results with analytical or numerical results derived for hypo-elastic and

METCAN demonstration manual, version 1.0

NASA Technical Reports Server (NTRS)

Lee, H.-J.; Murthy, P. L. N.

1992-01-01

The various features of the Metal Matrix Composite Analyzer (METCAN) computer program to simulate the high temperature nonlinear behavior of continuous fiber reinforced metal matrix composites are demonstrated. Different problems are used to demonstrate various capabilities of METCAN for both static and cyclic analyses. A complete description of the METCAN output file is also included to help interpret results.

Effective thermal conductivity determination for low-density insulating materials

NASA Technical Reports Server (NTRS)

Williams, S. D.; Curry, D. M.

1978-01-01

That nonlinear least squares can be used to determine effective thermal conductivity was demonstrated, and a method for assessing the relative error associated with these predicted values was provided. The differences between dynamic and static determination of effective thermal conductivity of low-density materials that transfer heat by a combination of conduction, convection, and radiation were discussed.

Static Analysis Using Abstract Interpretation

NASA Technical Reports Server (NTRS)

Arthaud, Maxime

2017-01-01

Short presentation about static analysis and most particularly abstract interpretation. It starts with a brief explanation on why static analysis is used at NASA. Then, it describes the IKOS (Inference Kernel for Open Static Analyzers) tool chain. Results on NASA projects are shown. Several well known algorithms from the static analysis literature are then explained (such as pointer analyses, memory analyses, weak relational abstract domains, function summarization, etc.). It ends with interesting problems we encountered (such as C++ analysis with exception handling, or the detection of integer overflow).

A higher-order theory for geometrically nonlinear analysis of composite laminates

NASA Technical Reports Server (NTRS)

Reddy, J. N.; Liu, C. F.

1987-01-01

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Synthesis, characterization and calculated non-linear optical properties of two new chalcones

NASA Astrophysics Data System (ADS)

Singh, Ashok Kumar; Saxena, Gunjan; Prasad, Rajendra; Kumar, Abhinav

2012-06-01

Two new chalcones viz 3-(4-(benzyloxy)phenyl)-1-(2-hydroxyphenyl)prop-2-en-1-one (1) and 3-(4-chlorophenyl)-1-(2-hydroxyphenyl)prop-2-en-1-one (2) have been prepared and characterized by micro analyses, 1H NMR, IR, UV-Vis spectroscopy and single crystal X-ray. The first static hyperpolarizability (β) for both the compounds has been investigated by density functional theory (DFT). Also, the solvent-induced effects on the non-linear optical properties (NLO) were studied by using self-consistent reaction field (SCRF) method. As the solvent polarity increases, the β value increases monotonically. The electronic absorption bands of both 1 and 2 have been assigned by time dependent density functional theory (TD-DFT). Both the compounds displayed better non-linear optical (NLO) responses than the standard p-nitroaniline (pNA).

Gauge invariant gluon spin operator for spinless nonlinear wave solutions

NASA Astrophysics Data System (ADS)

Lee, Bum-Hoon; Kim, Youngman; Pak, D. G.; Tsukioka, Takuya; Zhang, P. M.

2017-04-01

We consider nonlinear wave type solutions with intrinsic mass scale parameter and zero spin in a pure SU(2) quantum chromodynamics (QCD). A new stationary solution which can be treated as a system of static Wu-Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered nonlinear wave type solutions have common features: presence of the mass scale parameter, nonvanishing projection of the color fields along the propagation direction and zero spin. The last property requires revision of the gauge invariant definition of the spin density operator which is supposed to produce spin one states for the massless vector gluon field. We construct a gauge invariant definition of the classical gluon spin density operator which is unique and Lorentz frame independent.

Laser-driven interactions and resultant instabilities in materials with high dielectric constant

NASA Astrophysics Data System (ADS)

Rajpoot, Moolchandra; Dixit, Sanjay

2015-07-01

An analytical investigation of nonlinear interactions resulting in parametric amplification of acoustic wave is made by obtaining the dispersion relation using hydrodynamic model of inhomogeneous plasma by applying large static field at an arbitrary angle with the pump wave. The investigation shows that many early studies have neglected dependence of dielectric constant on deformation of materials but deformation of materials does infect depends on the dielectric constant of medium. Thus we have assumed to high dielectric material like BaTiO3 which resulted in substantially high growth rate of threshold electric field which opens a new dimension to study nonlinear interactions and instabilities.

Method of performing computational aeroelastic analyses

NASA Technical Reports Server (NTRS)

Silva, Walter A. (Inventor)

2011-01-01

Computational aeroelastic analyses typically use a mathematical model for the structural modes of a flexible structure and a nonlinear aerodynamic model that can generate a plurality of unsteady aerodynamic responses based on the structural modes for conditions defining an aerodynamic condition of the flexible structure. In the present invention, a linear state-space model is generated using a single execution of the nonlinear aerodynamic model for all of the structural modes where a family of orthogonal functions is used as the inputs. Then, static and dynamic aeroelastic solutions are generated using computational interaction between the mathematical model and the linear state-space model for a plurality of periodic points in time.

REVIEWS OF TOPICAL PROBLEMS: Nonlinear dynamics of the brain: emotion and cognition

NASA Astrophysics Data System (ADS)

Rabinovich, Mikhail I.; Muezzinoglu, M. K.

2010-07-01

Experimental investigations of neural system functioning and brain activity are standardly based on the assumption that perceptions, emotions, and cognitive functions can be understood by analyzing steady-state neural processes and static tomographic snapshots. The new approaches discussed in this review are based on the analysis of transient processes and metastable states. Transient dynamics is characterized by two basic properties, structural stability and information sensitivity. The ideas and methods that we discuss provide an explanation for the occurrence of and successive transitions between metastable states observed in experiments, and offer new approaches to behavior analysis. Models of the emotional and cognitive functions of the brain are suggested. The mathematical object that represents the observed transient brain processes in the phase space of the model is a structurally stable heteroclinic channel. The possibility of using the suggested models to construct a quantitative theory of some emotional and cognitive functions is illustrated.

Unsteady aerodynamic flow field analysis of the space shuttle configuration. Part 1: Orbiter aerodynamics

NASA Technical Reports Server (NTRS)

Ericsson, L. E.; Reding, J. P.

1976-01-01

An analysis of the steady and unsteady aerodynamics of the space shuttle orbiter has been performed. It is shown that slender wing theory can be modified to account for the effect of Mach number and leading edge roundness on both attached and separated flow loads. The orbiter unsteady aerodynamics can be computed by defining two equivalent slender wings, one for attached flow loads and another for the vortex-induced loads. It is found that the orbiter is in the transonic speed region subject to vortex-shock-boundary layer interactions that cause highly nonlinear or discontinuous load changes which can endanger the structural integrity of the orbiter wing and possibly cause snap roll problems. It is presently impossible to simulate these interactions in a wind tunnel test even in the static case. Thus, a well planned combined analytic and experimental approach is needed to solve the problem.

Static analysis of C-shape SMA middle ear prosthesis

NASA Astrophysics Data System (ADS)

Latalski, Jarosław; Rusinek, Rafał

2017-08-01

Shape memory alloys are a family of metals with the ability to change specimen shape depending on their temperature. This unique property is useful in many areas of mechanical and biomechanical engineering. A new half-ring middle ear prosthesis design made of a shape memory alloy, that is undergoing initial clinical tests, is investigated in this research paper. The analytical model of the studied structure made of nonlinear constitutive material is solved to identify the temperature-dependent stiffness characteristics of the proposed design on the basis of the Crotti-Engesser theorem. The final integral expression for the element deflection is highly complex, thus the solution has to be computed numerically. The final results show the proposed shape memory C-shape element to behave linearly in the analysed range of loadings and temperatures. This is an important observation that significantly simplifies the analysis of the prototype structure and opens wide perspectives for further possible applications of shape memory alloys.

Loading Deformation Characteristic Simulation Study of Engineering Vehicle Refurbished Tire

NASA Astrophysics Data System (ADS)

Qiang, Wang; Xiaojie, Qi; Zhao, Yang; Yunlong, Wang; Guotian, Wang; Degang, Lv

2018-05-01

The paper constructed engineering vehicle refurbished tire computer geometry model, mechanics model, contact model, finite element analysis model, did simulation study on load-deformation property of engineering vehicle refurbished tire by comparing with that of the new and the same type tire, got load-deformation of engineering vehicle refurbished tire under the working condition of static state and ground contact. The analysis result shows that change rules of radial-direction deformation and side-direction deformation of engineering vehicle refurbished tire are close to that of the new tire, radial-direction and side-direction deformation value is a little less than that of the new tire. When air inflation pressure was certain, radial-direction deformation linear rule of engineer vehicle refurbished tire would increase with load adding, however, side-direction deformation showed linear change rule, when air inflation pressure was low; and it would show increase of non-linear change rule, when air inflation pressure was very high.

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

Sesigur, Haluk; Cili, Feridun

Seismic isolation is an effective design strategy to mitigate the seismic hazard wherein the structure and its contents are protected from the damaging effects of an earthquake. This paper presents the Hangar Project in Sabiha Goekcen Airport which is located in Istanbul, Turkey. Seismic isolation system where the isolation layer arranged at the top of the columns is selected. The seismic hazard analysis, superstructure design, isolator design and testing were based on the Uniform Building Code (1997) and met all requirements of the Turkish Earthquake Code (2007). The substructure which has the steel vertical trusses on facades and RC Hmore » shaped columns in the middle axis of the building was designed with an R factor limited to 2.0 in accordance with Turkish Earthquake Code. In order to verify the effectiveness of the isolation system, nonlinear static and dynamic analyses are performed. The analysis revealed that isolated building has lower base shear (approximately 1/4) against the non-isolated structure.« less

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.

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.

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

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

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2017-03-29

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Instability of a gravity gradient satellite due to thermal distortion

NASA Technical Reports Server (NTRS)

Goldman, R. L.

1975-01-01

A nonlinear analytical model and a corresponding computer program were developed to study the influence of solar heating on the anomalous low frequency, orbital instability of the Naval Research Laboratory's gravity gradient satellite 164. The model's formulation was based on a quasi-static approach in which deflections of the satellite's booms were determined in terms of thermally induced bending without consideration of boom vibration. Calculations, which were made for variations in absorptivity, sun angle, thermal lag, and hinge stiffness, demonstrated that, within the confines of a relatively narrow stability criteria, the quasi-static model of NRL 164 not only becomes unstable, but, in a number of cases, responses were computed that closely resembled flight data.

Thin film assembly of nanosized cobalt(II) bis(5-phenyl-azo-8-hydroxyquinolate) using static step-by-step soft surface reaction technique: Structural characterization and optical properties.

PubMed

Seleim, S M; Hamdalla, Taymour A; Mahmoud, Mohamed E

2017-09-05

Nanosized (NS) cobalt (II) bis(5-phenyl-azo-8-hydroxyquinolate) (NS Co(II)-(5PA-8HQ) 2 ) thin films have been synthesized using static step-by-step soft surface reaction (SS-b-SSR) technique. Structural and optical characterizations of these thin films have been carried out using thermal gravimetric analysis (TGA), Fourier transform infrared (FT-IR), scanning electron microscopy (SEM), high resolution transmission electron microscopy (HR-TEM) and X-ray diffraction (XRD). The HR-TEM results revealed that the assembled Co(II)-complex exhibited a uniformly NS structure particles in the form of nanorods with width and length up to 16.90nm and 506.38nm, respectively. The linear and nonlinear optical properties have been investigated. The identified energy gap of the designed thin film materials was found 4.01eV. The refractive index of deposited Co(II)-complex thin film was identified by thickness-dependence and found as 1.9 at wavelength 1100nm. In addition, the refractive index was varied by about 0.15 due to an increase in the thickness by 19nm. Copyright © 2017 Elsevier B.V. All rights reserved.

On steady two-dimensional Carreau fluid flow over a wedge in the presence of infinite shear rate viscosity

NASA Astrophysics Data System (ADS)

Khan, Masood; Sardar, Humara

2018-03-01

This paper investigates the steady two-dimensional flow over a moving/static wedge in a Carreau viscosity model with infinite shear rate viscosity. Additionally, heat transfer analysis is performed. Using suitable transformations, nonlinear partial differential equations are transformed into ordinary differential equations and solved numerically using the Runge-Kutta Fehlberg method coupled with the shooting technique. The effects of various physical parameters on the velocity and temperature distributions are displayed graphically and discussed qualitatively. A comparison with the earlier reported results has been made with an excellent agreement. It is important to note that the increasing values of the wedge angle parameter enhance the fluid velocity while the opposite trend is observed for the temperature field for both shear thinning and thickening fluids. Generally, our results reveal that the velocity and temperature distributions are marginally influenced by the viscosity ratio parameter. Further, it is noted that augmented values of viscosity ratio parameter thin the momentum and thermal boundary layer thickness in shear thickening fluid and reverse is true for shear thinning fluid. Moreover, it is noticed that the velocity in case of moving wedge is higher than static wedge.

A Comparative Study of Some Dynamic Stall Models

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Kaza, K. R. V.

1987-01-01

Three semi-empirical aerodynamic stall models are compared with respect to their lift and moment hysteresis loop prediction, limit cycle behavior, easy implementation, and feasibility in developing the parameters required for stall flutter prediction of advanced turbines. For the comparison of aeroelastic response prediction including stall, a typical section model and a plate structural model are considered. The response analysis includes both plunging and pitching motions of the blades. In model A, a correction to the angle of attack is applied when the angle of attack exceeds the static stall angle. In model B, a synthesis procedure is used for angles of attack above static stall angles and the time history effects are accounted through the Wagner function. In both models the life and moment coefficients for angle of attack below stall are obtained from tabular data for a given Mach number and angle of attack. In model C, referred to an the ONERA model, the life and moment coefficients are given in the form of two differential equations, one for angles below stall, and the other for angles above stall. The parameters of those equations are nonlinear functions of the angle of attack.

Ion-Scale Excitations in a Strongly Coupled Astrophysical Plasma with Nuclei of Heavy Elements

NASA Astrophysics Data System (ADS)

Hossen, M. R.; Ema, S. A.; Mamun, A. A.

2017-12-01

The linear and nonlinear propagation of ultrarelativistic and nonrelativistic analysis on modified ion-acoustic (MIA) waves in a strongly coupled unmagnetized collisionless relativistic space plasma system is carried out. Plasma system is assumed to contain strongly coupled nonrelativistic ion fluids, both nonrelativistic and ultrarelativistic degenerate electron and positron fluids, and positively charged static heavy elements. The restoring force is provided by the degenerate pressure of the electron and positron fluids, whereas the inertia is provided by the mass of ions. The positively charged static heavy elements participate only in maintaining the quasineutrality condition at equilibrium. The well-known reductive perturbation method is used to derive the Burgers and Korteweg-de Vries equations. Their shock and solitary wave solutions are numerically analyzed to understand the localized electrostatic disturbances. The basic characteristics of MIA shock and solitary waves are found to be significantly modified by the effects of degenerate pressures of electron, positron, and ion fluids, their number densities, and various charge state of heavy elements. The implications of our results to dense plasmas in compact astrophysical objects (e.g., nonrotating white dwarfs, neutron stars, etc.) are briefly discussed.

Dynamic Relaxation: A Technique for Detailed Thermo-Elastic Structural Analysis of Transportation Structures

NASA Astrophysics Data System (ADS)

Shoukry, Samir N.; William, Gergis W.; Riad, Mourad Y.; McBride, Kevyn C.

2006-08-01

Dynamic relaxation is a technique developed to solve static problems through an explicit integration in finite element. The main advantage of such a technique is the ability to solve a large problem in a relatively short time compared with the traditional implicit techniques, especially when using nonlinear material models. This paper describes the use of such a technique in analyzing large transportation structures as dowel jointed concrete pavements and 306-m-long, reinforced concrete bridge superstructure under the effect of temperature variations. The main feature of the pavement model is the detailed modeling of dowel bars and their interfaces with the surrounding concrete using extremely fine mesh of solid elements, while in the bridge structure it is the detailed modeling of the girder-deck interface as well as the bracing members between the girders. The 3DFE results were found to be in a good agreement with experimentally measured data obtained from an instrumented pavements sections and a highway bridge constructed in West Virginia. Thus, such a technique provides a good tool for analyzing the response of large structures to static loads in a fraction of the time required by traditional, implicit finite element methods.

A 6DOF passive vibration isolator using X-shape supporting structures

NASA Astrophysics Data System (ADS)

Wu, Zhijing; Jing, Xingjian; Sun, Bo; Li, Fengming

2016-10-01

A novel 6 degree of freedom (6-DOF) passive vibration isolator is studied theoretically and validated with experiments. Based on the Stewart platform configuration, the 6-DOF isolator is constructed by 6 X-shape structures as legs, which can realize very good and tunable vibration isolation performance in all 6 directions with a passive manner. The mechanic model is established for static analysis of the working range, static stiffness and loading capacity. Thereafter, the equation of motion of the isolator is derived with the Hamilton principle. The equivalent stiffness and the displacement transmissibility in the six decoupled DOFs direction are then discussed with experimental results for validation. The results reveal that (a) by designing the structure parameters, the system can possess flexible stiffness such as negative, quasi-zero and positive stiffness, (b) due to the combination of the Stewart platform and the X-shape structure, the system can have very good vibration isolation performance in all the 6 directions and in a passive manner, and (c) compared with the simplified linear-stiffness legs, the nonlinearity of the X-shape structures enhance the passive isolator to have much better vibration isolation performance.

A generalized analytical approach to the coupled effect of SMA actuation and elastica deflection

NASA Astrophysics Data System (ADS)

Sreekumar, M.; Singaperumal, M.

2009-11-01

A compliant miniature parallel manipulator made of superelastic nitinol pipe as its central pillar and actuated by three symmetrically attached shape memory alloy (SMA) wires is under development. The mobility for the platform is obtained by the selective actuation of one or two wires at a time. If one wire is actuated, the other two unactuated wires provide the counter effect. Similarly, if two wires are actuated simultaneously or in a differential manner, the third unactuated wire resists the movement of the platform. In an earlier work of the authors, the static displacement analysis was presented without considering the effect of unactuated wires. In this contribution, the force-displacement analysis is presented considering the effect of both actuated and unactuated wires. Subsequently, an attempt has been made to obtain a generalized approach from which six types of actuation methods are identified using a group of conditional parameters. Each method leads to a set of large deflection expressions suitable for a particular actuation method. As the large deflection expressions derived for the mechanism are nonlinear and involve interdependent parameters, their simplified form using a parametric approximation have also been obtained using Howell's algorithm. The generalized approach and the solution algorithm developed can be applied to any kind of compliant mechanism having large deflection capabilities, including planar and spatial MEMS devices and stability analysis of long slender columns supported by wires or cables. The procedure developed is also suitable for the static analysis of spatial compliant mechanisms actuated by multiple SMA actuators.

Modeling, Analysis, and Control of a Hypersonic Vehicle with Significant Aero-Thermo-Elastic-Propulsion Interactions: Elastic, Thermal and Mass Uncertainty

NASA Astrophysics Data System (ADS)

Khatri, Jaidev

This thesis examines themodeling, analysis, and control system design issues for scramjet powered hypersonic vehicles. A nonlinear three degrees of freedom longitudinal model which includes aero-propulsion-elasticity effects was used for all analyses. This model is based upon classical compressible flow and Euler-Bernouli structural concepts. Higher fidelity computational fluid dynamics and finite element methods are needed for more precise intermediate and final evaluations. The methods presented within this thesis were shown to be useful for guiding initial control relevant design. The model was used to examine the vehicle's static and dynamic characteristics over the vehicle's trimmable region. The vehicle has significant longitudinal coupling between the fuel equivalency ratio (FER) and the flight path angle (FPA). For control system design, a two-input two-output plant (FER - elevator to speed-FPA) with 11 states (including 3 flexible modes) was used. Velocity, FPA, and pitch were assumed to be available for feedback. Aerodynamic heat modeling and design for the assumed TPS was incorporated to original Bolender's model to study the change in static and dynamic properties. De-centralized control stability, feasibility and limitations issues were dealt with the change in TPS elasticity, mass and physical dimension. The impact of elasticity due to TPS mass, TPS physical dimension as well as prolonged heating was also analyzed to understand performance limitations of de-centralized control designed for nominal model.

A wide-frequency-range air-jet shaker

NASA Technical Reports Server (NTRS)

Herr, Robert W

1957-01-01

This paper presents a description of a simple air-jet shaker. Its force can be calibrated statically and appears to be constant with frequency. It is relatively easy to use, and it has essentially massless characteristics. This shaker is applied to define the unstable branch of a frequency-response curve obtained for a nonlinear spring with a single degree of freedom.

Circadian rhythms and fractal fluctuations in forearm motion

NASA Astrophysics Data System (ADS)

Hu, Kun; Hilton, Michael F.

2005-03-01

Recent studies have shown that the circadian pacemaker --- an internal body clock located in the brain which is normally synchronized with the sleep/wake behavioral cycles --- influences key physiologic functions such as the body temperature, hormone secretion and heart rate. Surprisingly, no previous studies have investigated whether the circadian pacemaker impacts human motor activity --- a fundamental physiologic function. We investigate high-frequency actigraph recordings of forearm motion from a group of young and healthy subjects during a forced desynchrony protocol which allows to decouple the sleep/wake cycles from the endogenous circadian cycle while controlling scheduled behaviors. We investigate both static properties (mean value, standard deviation), dynamical characteristics (long-range correlations), and nonlinear features (magnitude and Fourier-phase correlations) in the fluctuations of forearm acceleration across different circadian phases. We demonstrate that while the static properties exhibit significant circadian rhythms with a broad peak in the afternoon, the dynamical and nonlinear characteristics remain invariant with circadian phase. This finding suggests an intrinsic multi-scale dynamic regulation of forearm motion the mechanism of which is not influenced by the circadian pacemaker, thus suggesting that increased cardiac risk in the early morning hours is not related to circadian-mediated influences on motor activity.

Oscillation Amplitude Growth for a Decelerating Object with Constant Pitch Damping

NASA Technical Reports Server (NTRS)

Schoenenberger, Mark; Queen, Eric M.; Litton, Daniel

2006-01-01

The equations governing the deceleration and oscillation of a blunt body moving along a planar trajectory are re-expressed in the form of the Euler-Cauchy equation. An analytic solution of this equation describes the oscillation amplitude growth and frequency dilation with time for a statically stable decelerating body with constant pitch damping. The oscillation histories for several constant pitch damping values, predicted by the solution of the Euler-Cauchy equation are compared to POST six degree-of-freedom (6-DoF) trajectory simulations. The simulations use simplified aerodynamic coefficients matching the Euler-Cauchy approximations. Agreement between the model predictions and simulation results are excellent. Euler-Cauchy curves are also fit through nonlinear 6-DoF simulations and ballistic range data to identify static stability and pitch damping coefficients. The model os shown to closely fit through the data points and capture the behavior of the blunt body observed in simulation and experiment. The extracted coefficients are in reasonable agreement with higher fidelity, nonlinear parameter identification results. Finally, a nondimensional version of the Euler-Cauchy equation is presented and shown to be a simple and effective tool for designing dynamically scaled experiments for decelerating blunt capsule flight.

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

Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks

NASA Astrophysics Data System (ADS)

Sebastian, Resmi; Sitharam, T. G.

2018-01-01

Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.

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.

IKOS: A Framework for Static Analysis based on Abstract Interpretation (Tool Paper)

NASA Technical Reports Server (NTRS)

Brat, Guillaume P.; Laserna, Jorge A.; Shi, Nija; Venet, Arnaud Jean

2014-01-01

The RTCA standard (DO-178C) for developing avionic software and getting certification credits includes an extension (DO-333) that describes how developers can use static analysis in certification. In this paper, we give an overview of the IKOS static analysis framework that helps developing static analyses that are both precise and scalable. IKOS harnesses the power of Abstract Interpretation and makes it accessible to a larger class of static analysis developers by separating concerns such as code parsing, model development, abstract domain management, results management, and analysis strategy. The benefits of the approach is demonstrated by a buffer overflow analysis applied to flight control systems.

Imitative modeling automatic system Control of steam pressure in the main steam collector with the influence on the main Servomotor steam turbine

NASA Astrophysics Data System (ADS)

Andriushin, A. V.; Zverkov, V. P.; Kuzishchin, V. F.; Ryzhkov, O. S.; Sabanin, V. R.

2017-11-01

The research and setting results of steam pressure in the main steam collector “Do itself” automatic control system (ACS) with high-speed feedback on steam pressure in the turbine regulating stage are presented. The ACS setup is performed on the simulation model of the controlled object developed for this purpose with load-dependent static and dynamic characteristics and a non-linear control algorithm with pulse control of the turbine main servomotor. A method for tuning nonlinear ACS with a numerical algorithm for multiparametric optimization and a procedure for separate dynamic adjustment of control devices in a two-loop ACS are proposed and implemented. It is shown that the nonlinear ACS adjusted with the proposed method with the regulators constant parameters ensures reliable and high-quality operation without the occurrence of oscillations in the transient processes the operating range of the turbine loads.

Network evolution by nonlinear preferential rewiring of edges

NASA Astrophysics Data System (ADS)

Xu, Xin-Jian; Hu, Xiao-Ming; Zhang, Li-Jie

2011-06-01

The mathematical framework for small-world networks proposed in a seminal paper by Watts and Strogatz sparked a widespread interest in modeling complex networks in the past decade. However, most of research contributing to static models is in contrast to real-world dynamic networks, such as social and biological networks, which are characterized by rearrangements of connections among agents. In this paper, we study dynamic networks evolved by nonlinear preferential rewiring of edges. The total numbers of vertices and edges of the network are conserved, but edges are continuously rewired according to the nonlinear preference. Assuming power-law kernels with exponents α and β, the network structures in stationary states display a distinct behavior, depending only on β. For β>1, the network is highly heterogeneous with the emergence of starlike structures. For β<1, the network is widely homogeneous with a typical connectivity. At β=1, the network is scale free with an exponential cutoff.

A predication model for combustion modes of the scramjet-powered aerospace vehicle based on the nonlinear features of the isolator flow field

NASA Astrophysics Data System (ADS)

Yang, Qingchun; Wang, Hongxin; Chetehouna, Khaled; Gascoin, Nicolas

2017-01-01

The supersonic combustion ramjet (scramjet) engine remains the most promising airbreathing engine cycle for hypersonic flight, particularly the high-performance dual-mode scramjet in the range of flight Mach number from 4 to 7, because it can operates under different combustion modes. Isolator is a very key component of the dual-mode scramjet engine. In this paper, nonlinear characteristics of combustion mode transition is theoretically analyzed. The discontinuous sudden changes of static pressure and Mach number are obtained as the mode transition occurs, which emphasizing the importance of predication and control of combustion modes. In this paper, a predication model of different combustion modes is developed based on these these nonlinear features in the isolator flow field. it can provide a valuable reference for control system design of the scramjet-powered aerospace vehicle.

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.

Electron cyclotron harmonic wave acceleration

NASA Technical Reports Server (NTRS)

Karimabadi, H.; Menyuk, C. R.; Sprangle, P.; Vlahos, L.

1987-01-01

A nonlinear analysis of particle acceleration in a finite bandwidth, obliquely propagating electromagnetic cyclotron wave is presented. It has been suggested by Sprangle and Vlahos in 1983 that the narrow bandwidth cyclotron radiation emitted by the unstable electron distribution inside a flaring solar loop can accelerate electrons outside the loop by the interaction of a monochromatic wave propagating along the ambient magnetic field with the ambient electrons. It is shown here that electrons gyrating and streaming along a uniform, static magnetic field can be accelerated by interacting with the fundamental or second harmonic of a monochromatic, obliquely propagating cyclotron wave. It is also shown that the acceleration is virtually unchanged when a wave with finite bandwidth is considered. This acceleration mechanism can explain the observed high-energy electrons in type III bursts.

HRV analysis and blood pressure monitoring on weighing scale using BCG.

PubMed

Shin, Jae Hyuk; Park, Kwang Suk

2012-01-01

Using the Ballistocardiogram(BCG) measured on weighing scale, heart rate variability(HRV) and blood pressure were estimated. BCG was measured while subjects were on weighing scale in resting state and under the Valsalva maneuver and static exercise condition to induce the change in cardiac autonomic rhythm. Time domain, frequency domain and nonlinear HRV parameters were estimated from the measured BCG and compared with the ones calculated from ECG measured simultaneously. For blood pressure(BP) estimation, ECG was measured additionally on the feet using dry electrodes simultaneously installed on weighing scale and R-J intervals were extracted as a BP correlated parameter at every beat cycle. HRV estimation results shows the correlation higher than 0.97, and the estimated BP was similar to the measured BP with a reliable correlations.

Numerical analysis of THz radiation wave using upper hybrid wave wiggler

NASA Astrophysics Data System (ADS)

Malik, Pratibha; Sharma, Suresh C.; Panwar, Jyotsna; Sharma, Rinku

2018-03-01

A theory for upper hybrid wave induced by relativistic electron beam in magnetized plasma emits tuneable and coherent terahertz radiation. The nonlinear interaction with REB is used to generate terahertz radiation. The enhancement in the amplitude of THz wave is also observed when pre-bunched REB is used. The ponderomotive force applied on beam electrons due to radiation wave and upper wave wiggler modifies the dispersion relation. By solving the dispersion relation, we have derived the growth rate of the radiation wave. Numerical studies indicate that by increasing the beam energy the growth rate of the radiation wave decreases, while it increases with wiggler frequency. Besides this, the growth rate of the radiation wave increases with beam density and decreases with radiation frequency and static magnetic field.

Feshbach resonance management for Bose-Einstein condensates.

PubMed

Kevrekidis, P G; Theocharis, G; Frantzeskakis, D J; Malomed, Boris A

2003-06-13

An experimentally realizable scheme of periodic sign-changing modulation of the scattering length is proposed for Bose-Einstein condensates similar to dispersion-management schemes in fiber optics. Because of controlling the scattering length via the Feshbach resonance, the scheme is named Feshbach-resonance management. The modulational-instability analysis of the quasiuniform condensate driven by this scheme leads to an analog of the Kronig-Penney model. The ensuing stable localized structures are found. These include breathers, which oscillate between the Thomas-Fermi and Gaussian configuration, or may be similar to the 2-soliton state of the nonlinear Schrödinger equation, and a nearly static state ("odd soliton") with a nested dark soliton. An overall phase diagram for breathers is constructed, and full stability of the odd solitons is numerically established.

Maximum capacity model of grid-connected multi-wind farms considering static security constraints in electrical grids

NASA Astrophysics Data System (ADS)

Zhou, W.; Qiu, G. Y.; Oodo, S. O.; He, H.

2013-03-01

An increasing interest in wind energy and the advance of related technologies have increased the connection of wind power generation into electrical grids. This paper proposes an optimization model for determining the maximum capacity of wind farms in a power system. In this model, generator power output limits, voltage limits and thermal limits of branches in the grid system were considered in order to limit the steady-state security influence of wind generators on the power system. The optimization model was solved by a nonlinear primal-dual interior-point method. An IEEE-30 bus system with two wind farms was tested through simulation studies, plus an analysis conducted to verify the effectiveness of the proposed model. The results indicated that the model is efficient and reasonable.

A new formation control of multiple underactuated surface vessels

NASA Astrophysics Data System (ADS)

Xie, Wenjing; Ma, Baoli; Fernando, Tyrone; Iu, Herbert Ho-Ching

2018-05-01

This work investigates a new formation control problem of multiple underactuated surface vessels. The controller design is based on input-output linearisation technique, graph theory, consensus idea and some nonlinear tools. The proposed smooth time-varying distributed control law guarantees that the multiple underactuated surface vessels globally exponentially converge to some desired geometric shape, which is especially centred at the initial average position of vessels. Furthermore, the stability analysis of zero dynamics proves that the orientations of vessels tend to some constants that are dependent on the initial values of vessels, and the velocities and control inputs of the vessels decay to zero. All the results are obtained under the communication scenarios of static directed balanced graph with a spanning tree. Effectiveness of the proposed distributed control scheme is demonstrated using a simulation example.

Substructure analysis using NICE/SPAR and applications of force to linear and nonlinear structures. [spacecraft masts

NASA Technical Reports Server (NTRS)

Razzaq, Zia; Prasad, Venkatesh; Darbhamulla, Siva Prasad; Bhati, Ravinder; Lin, Cai

1987-01-01

Parallel computing studies are presented for a variety of structural analysis problems. Included are the substructure planar analysis of rectangular panels with and without a hole, the static analysis of space mast, using NICE/SPAR and FORCE, and substructure analysis of plane rigid-jointed frames using FORCE. The computations are carried out on the Flex/32 MultiComputer using one to eighteen processors. The NICE/SPAR runstream samples are documented for the panel problem. For the substructure analysis of plane frames, a computer program is developed to demonstrate the effectiveness of a substructuring technique when FORCE is enforced. Ongoing research activities for an elasto-plastic stability analysis problem using FORCE, and stability analysis of the focus problem using NICE/SPAR are briefly summarized. Speedup curves for the panel, the mast, and the frame problems provide a basic understanding of the effectiveness of parallel computing procedures utilized or developed, within the domain of the parameters considered. Although the speedup curves obtained exhibit various levels of computational efficiency, they clearly demonstrate the excellent promise which parallel computing holds for the structural analysis problem. Source code is given for the elasto-plastic stability problem and the FORCE program.

Parallel-vector computation for structural analysis and nonlinear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.

1990-01-01

Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process where one starts with an initial design, a finite element structure analysis is then performed to calculate the response of the system (such as displacements, stresses, eigenvalues, etc.). Based upon the sensitivity information on the objective and constraint functions, an optimizer such as ADS or IDESIGN, can be used to find the new, improved design. For the structural analysis phase, the equation solver for the system of simultaneous, linear equations plays a key role since it is needed for either static, or eigenvalue, or dynamic analysis. For practical, large-scale structural analysis-synthesis applications, computational time can be excessively large. Thus, it is necessary to have a new structural analysis-synthesis code which employs new solution algorithms to exploit both parallel and vector capabilities offered by modern, high performance computers such as the Convex, Cray-2 and Cray-YMP computers. The objective of this research project is, therefore, to incorporate the latest development in the parallel-vector equation solver, PVSOLVE into the widely popular finite-element production code, such as the SAP-4. Furthermore, several nonlinear unconstrained optimization subroutines have also been developed and tested under a parallel computer environment. The unconstrained optimization subroutines are not only useful in their own right, but they can also be incorporated into a more popular constrained optimization code, such as ADS.

Small Angle Neutron Scattering Observation of Chain Retraction after a Large Step Deformation

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

Blanchard, A.; Heinrich, M.; Pyckhout-Hintzen, W.

The process of retraction in entangled linear chains after a fast nonlinear stretch was detected from time-resolved but quenched small angle neutron scattering (SANS) experiments on long, well-entangled polyisoprene chains. The statically obtained SANS data cover the relevant time regime for retraction, and they provide a direct, microscopic verification of this nonlinear process as predicted by the tube model. Clear, quantitative agreement is found with recent theories of contour length fluctuations and convective constraint release, using parameters obtained mainly from linear rheology. The theory captures the full range of scattering vectors once the crossover to fluctuations on length scales belowmore » the tube diameter is accounted for.« less

A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler-Bernoulli beams

NASA Astrophysics Data System (ADS)

Andreaus, Ugo; Spagnuolo, Mario; Lekszycki, Tomasz; Eugster, Simon R.

2018-04-01

We present a finite element discrete model for pantographic lattices, based on a continuous Euler-Bernoulli beam for modeling the fibers composing the pantographic sheet. This model takes into account large displacements, rotations and deformations; the Euler-Bernoulli beam is described by using nonlinear interpolation functions, a Green-Lagrange strain for elongation and a curvature depending on elongation. On the basis of the introduced discrete model of a pantographic lattice, we perform some numerical simulations. We then compare the obtained results to an experimental BIAS extension test on a pantograph printed with polyamide PA2200. The pantographic structures involved in the numerical as well as in the experimental investigations are not proper fabrics: They are composed by just a few fibers for theoretically allowing the use of the Euler-Bernoulli beam theory in the description of the fibers. We compare the experiments to numerical simulations in which we allow the fibers to elastically slide one with respect to the other in correspondence of the interconnecting pivot. We present as result a very good agreement between the numerical simulation, based on the introduced model, and the experimental measures.

Model updating in flexible-link multibody systems

NASA Astrophysics Data System (ADS)

Belotti, R.; Caneva, G.; Palomba, I.; Richiedei, D.; Trevisani, A.

2016-09-01

The dynamic response of flexible-link multibody systems (FLMSs) can be predicted through nonlinear models based on finite elements, to describe the coupling between rigid- body and elastic behaviour. Their accuracy should be as high as possible to synthesize controllers and observers. Model updating based on experimental measurements is hence necessary. By taking advantage of the experimental modal analysis, this work proposes a model updating procedure for FLMSs and applies it experimentally to a planar robot. Indeed, several peculiarities of the model of FLMS should be carefully tackled. On the one hand, nonlinear models of a FLMS should be linearized about static equilibrium configurations. On the other, the experimental mode shapes should be corrected to be consistent with the elastic displacements represented in the model, which are defined with respect to a fictitious moving reference (the equivalent rigid link system). Then, since rotational degrees of freedom are also represented in the model, interpolation of the experimental data should be performed to match the model displacement vector. Model updating has been finally cast as an optimization problem in the presence of bounds on the feasible values, by also adopting methods to improve the numerical conditioning and to compute meaningful updated inertial and elastic parameters.

High Reynolds number analysis of flat plate and separated afterbody flow using non-linear turbulence models

NASA Technical Reports Server (NTRS)

Carlson, John R.

1996-01-01

The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.

Nonlinear solar cycle forecasting: theory and perspectives

NASA Astrophysics Data System (ADS)

Baranovski, A. L.; Clette, F.; Nollau, V.

2008-02-01

In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters - the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.

Non-linear dynamic analysis of geared systems. Final Report Ph.D. Thesis

NASA Technical Reports Server (NTRS)

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

1990-01-01

Under driving conditions, a typical geared system may be subjected to large dynamic loads. Also, the vibration level of the geared system is directly related to the noise radiated from the gear box. The steady state dynamic behavior of the system is examined in order to design reliable and quiet transmissions. The scope is limited to a system containing a spur gear pair with backlash and periodically time varying mesh stiffness, and rolling element bearings with clearance type nonlinearities. The internal static transmission error at the gear mesh, which is of importance from high frequency noise and vibration control view point, is considered in the formulation in sinusoidal or periodic form. 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 forced vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solutions with the finite element model results. Using the reduced order formulations, a three degree of freedom dynamic model is developed which includes nonlinearities associated with radical clearances in the radial rolling element bearings, backlash between a spur gear pair and periodically varying gear mesh stiffness. As a limiting case, a single degree of freedom model of the spur gear pair with backlash is considered and mathematical conditions for tooth separation and back collision are defined. Both digital simulation technique and analytical models such as method of harmonic balance and the method of multiple scales were used to develop the steady state frequency response characteristics for various nonlinear and/or time varying cases.

Monitoring Damage Propagation in Glass Fiber Composites Using Carbon Nanofibers.

PubMed

Al-Sabagh, Ahmed; Taha, Eman; Kandil, Usama; Nasr, Gamal-Abdelnaser; Reda Taha, Mahmoud

2016-09-10

In this work, we report the potential use of novel carbon nanofibers (CNFs), dispersed during fabrication of glass fiber composites to monitor damage propagation under static loading. The use of CNFs enables a transformation of the typically non-conductive glass fiber composites into new fiber composites with appreciable electrical conductivity. The percolation limit of CNFs/epoxy nanocomposites was first quantified. The electromechanical responses of glass fiber composites fabricated using CNFs/epoxy nanocomposite were examined under static tension loads. The experimental observations showed a nonlinear change of electrical conductivity of glass fiber composites incorporating CNFs versus the stress level under static load. Microstructural investigations proved the ability of CNFs to alter the polymer matrix and to produce a new polymer nanocomposite with a connected nanofiber network with improved electrical properties and different mechanical properties compared with the neat epoxy. It is concluded that incorporating CNFs during fabrication of glass fiber composites can provide an innovative means of self-sensing that will allow damage propagation to be monitored in glass fiber composites.

The fluid trampoline: droplets bouncing on a soap film

NASA Astrophysics Data System (ADS)

Bush, John; Gilet, Tristan

2008-11-01

We present the results of a combined experimental and theoretical investigation of droplets falling onto a horizontal soap film. Both static and vertically vibrated soap films are considered. A quasi-static description of the soap film shape yields a force-displacement relation that provides excellent agreement with experiment, and allows us to model the film as a nonlinear spring. This approach yields an accurate criterion for the transition between droplet bouncing and crossing on the static film; moreover, it allows us to rationalize the observed constancy of the contact time and scaling for the coefficient of restitution in the bouncing states. On the vibrating film, a variety of bouncing behaviours were observed, including simple and complex periodic states, multiperiodicity and chaos. A simple theoretical model is developed that captures the essential physics of the bouncing process, reproducing all observed bouncing states. Quantitative agreement between model and experiment is deduced for simple periodic modes, and qualitative agreement for more complex periodic and chaotic bouncing states.

Self-gravitating static non-critical black holes in 4 D Einstein-Klein-Gordon system with nonminimal derivative coupling

NASA Astrophysics Data System (ADS)

Gunara, Bobby Eka; Yaqin, Ainol

2018-06-01

We study static non-critical hairy black holes of four dimensional gravitational model with nonminimal derivative coupling and a scalar potential turned on. By taking an ansatz, namely, the first derivative of the scalar field is proportional to square root of a metric function, we reduce the Einstein field equation and the scalar field equation of motions into a single highly nonlinear differential equation. This setup implies that the hair is secondary-like since the scalar charge-like depends on the non-constant mass-like quantity in the asymptotic limit. Then, we show that near boundaries the solution is not the critical point of the scalar potential and the effective geometries become spaces of constant scalar curvature.

Aeroelastic Analysis Of Joined Wing Of High Altitude Long Endurance (HALE) Aircraft Based On The Sensor-Craft Configuration

NASA Astrophysics Data System (ADS)

Marisarla, Soujanya; Ghia, Urmila; "Karman" Ghia, Kirti

2002-11-01

Towards a comprehensive aeroelastic analysis of a joined wing, fluid dynamics and structural analyses are initially performed separately. Steady flow calculations are currently performed using 3-D compressible Navier-Stokes equations. Flow analysis of M6-Onera wing served to validate the software for the fluid dynamics analysis. The complex flow field of the joined wing is analyzed and the prevailing fluid dynamic forces are computed using COBALT software. Currently, these forces are being transferred as fluid loads on the structure. For the structural analysis, several test cases were run considering the wing as a cantilever beam; these served as validation cases. A nonlinear structural analysis of the wing is being performed using ANSYS software to predict the deflections and stresses on the joined wing. Issues related to modeling, and selecting appropriate mesh for the structure were addressed by first performing a linear analysis. The frequencies and mode shapes of the deformed wing are obtained from modal analysis. Both static and dynamic analyses are carried out, and the results obtained are carefully analyzed. Loose coupling between the fluid and structural analyses is currently being examined.

Thermodynamic properties of asymptotically Reissner–Nordström black holes

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

Hendi, S.H., E-mail: hendi@shirazu.ac.ir

2014-07-15

Motivated by possible relation between Born–Infeld type nonlinear electrodynamics and an effective low-energy action of open string theory, asymptotically Reissner–Nordström black holes whose electric field is described by a nonlinear electrodynamics (NLED) are studied. We take into account a four dimensional topological static black hole ansatz and solve the field equations, exactly, in terms of the NLED as a matter field. The main goal of this paper is investigation of thermodynamic properties of the obtained black holes. Moreover, we calculate the heat capacity and find that the nonlinearity affects the minimum size of stable black holes. We also use Legendre-invariantmore » metric proposed by Quevedo to obtain scalar curvature divergences. We find that the singularities of the Ricci scalar in Geometrothermodynamics (GTD) method take place at the Davies points. -- Highlights: •We examine the thermodynamical properties of black holes in Einstein gravity with nonlinear electrodynamics. •We investigate thermodynamic stability and discuss about the size of stable black holes. •We obtain analytical solutions of higher dimensional theory.« less

Nonlinear bending models for beams and plates

PubMed Central

Antipov, Y. A.

2014-01-01

A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler–Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition. PMID:25294960

Nonlocal modeling and buckling features of cracked nanobeams with von Karman nonlinearity

NASA Astrophysics Data System (ADS)

Akbarzadeh Khorshidi, Majid; Shaat, Mohamed; Abdelkefi, Abdessattar; Shariati, Mahmoud

2017-01-01

Buckling and postbuckling behaviors of cracked nanobeams made of single-crystalline nanomaterials are investigated. The nonlocal elasticity theory is used to model the nonlocal interatomic effects on the beam's performance accounting for the beam's axial stretching via von Karman nonlinear theory. The crack is then represented as torsional spring where the crack severity factor is derived accounting for the nonlocal features of the beam. By converting the beam into an equivalent infinite long plate with an edge crack subjected to a tensile stress at the far field, the crack energy release rate, intensity factor, and severity factor are derived according to the nonlocal elasticity theory. An analytical solution for the buckling and the postbuckling responses of cracked nonlocal nanobeams accounting for the beam axial stretching according to von Karman nonlinear theory of kinematics is derived. The impacts of the nonlocal parameter on the critical buckling loads and the static nonlinear postbuckling responses of cracked nonlocal nanobeams are studied. The results indicate that the buckling and postbuckling behaviors of cracked nanobeams are strongly affected by the crack location, crack depth, nonlocal parameter, and length-to-thickness ratio.

Evidence of low dimensional chaos in renal blood flow control in genetic and experimental hypertension

NASA Astrophysics Data System (ADS)

Yip, K.-P.; Marsh, D. J.; Holstein-Rathlou, N.-H.

1995-01-01

We applied a surrogate data technique to test for nonlinear structure in spontaneous fluctuations of hydrostatic pressure in renal tubules of hypertensive rats. Tubular pressure oscillates at 0.03-0.05 Hz in animals with normal blood pressure, but the fluctuations become irregular with chronic hypertension. Using time series from rats with hypertension we produced surrogate data sets to test whether they represent linearly correlated noise or ‘static’ nonlinear transforms of a linear stochastic process. The correlation dimension and the forecasting error were used as discriminating statistics to compare surrogate with experimental data. The results show that the original experimental time series can be distinguished from both linearly and static nonlinearly correlated noise, indicating that the nonlinear behavior is due to the intrinsic dynamics of the system. Together with other evidence this strongly suggests that a low dimensional chaotic attractor governs renal hemodynamics in hypertension. This appears to be the first demonstration of a transition to chaotic dynamics in an integrated physiological control system occurring in association with a pathological condition.

Assessment of regional ventilation and deformation using 4D-CT imaging for healthy human lungs during tidal breathing

PubMed Central

Jahani, Nariman; Choi, Jiwoong; Iyer, Krishna; Hoffman, Eric A.

2015-01-01

This study aims to assess regional ventilation, nonlinearity, and hysteresis of human lungs during dynamic breathing via image registration of four-dimensional computed tomography (4D-CT) scans. Six healthy adult humans were studied by spiral multidetector-row CT during controlled tidal breathing as well as during total lung capacity and functional residual capacity breath holds. Static images were utilized to contrast static vs. dynamic (deep vs. tidal) breathing. A rolling-seal piston system was employed to maintain consistent tidal breathing during 4D-CT spiral image acquisition, providing required between-breath consistency for physiologically meaningful reconstructed respiratory motion. Registration-derived variables including local air volume and anisotropic deformation index (ADI, an indicator of preferential deformation in response to local force) were employed to assess regional ventilation and lung deformation. Lobar distributions of air volume change during tidal breathing were correlated with those of deep breathing (R2 ≈ 0.84). Small discrepancies between tidal and deep breathing were shown to be likely due to different distributions of air volume change in the left and the right lungs. We also demonstrated an asymmetric characteristic of flow rate between inhalation and exhalation. With ADI, we were able to quantify nonlinearity and hysteresis of lung deformation that can only be captured in dynamic images. Nonlinearity quantified by ADI is greater during inhalation, and it is stronger in the lower lobes (P < 0.05). Lung hysteresis estimated by the difference of ADI between inhalation and exhalation is more significant in the right lungs than that in the left lungs. PMID:26316512

The Elementary Operations of Human Vision Are Not Reducible to Template-Matching

PubMed Central

Neri, Peter

2015-01-01

It is generally acknowledged that biological vision presents nonlinear characteristics, yet linear filtering accounts of visual processing are ubiquitous. The template-matching operation implemented by the linear-nonlinear cascade (linear filter followed by static nonlinearity) is the most widely adopted computational tool in systems neuroscience. This simple model achieves remarkable explanatory power while retaining analytical tractability, potentially extending its reach to a wide range of systems and levels in sensory processing. The extent of its applicability to human behaviour, however, remains unclear. Because sensory stimuli possess multiple attributes (e.g. position, orientation, size), the issue of applicability may be asked by considering each attribute one at a time in relation to a family of linear-nonlinear models, or by considering all attributes collectively in relation to a specified implementation of the linear-nonlinear cascade. We demonstrate that human visual processing can operate under conditions that are indistinguishable from linear-nonlinear transduction with respect to substantially different stimulus attributes of a uniquely specified target signal with associated behavioural task. However, no specific implementation of a linear-nonlinear cascade is able to account for the entire collection of results across attributes; a satisfactory account at this level requires the introduction of a small gain-control circuit, resulting in a model that no longer belongs to the linear-nonlinear family. Our results inform and constrain efforts at obtaining and interpreting comprehensive characterizations of the human sensory process by demonstrating its inescapably nonlinear nature, even under conditions that have been painstakingly fine-tuned to facilitate template-matching behaviour and to produce results that, at some level of inspection, do conform to linear filtering predictions. They also suggest that compliance with linear transduction may be the targeted outcome of carefully crafted nonlinear circuits, rather than default behaviour exhibited by basic components. PMID:26556758

Transonic aerodynamic design experience

NASA Technical Reports Server (NTRS)

Bonner, E.

1989-01-01

Advancements have occurred in transonic numerical simulation that place aerodynamic performance design into a relatively well developed status. Efficient broad band operating characteristics can be reliably developed at the conceptual design level. Recent aeroelastic and separated flow simulation results indicate that systematic consideration of an increased range of design problems appears promising. This emerging capability addresses static and dynamic structural/aerodynamic coupling and nonlinearities associated with viscous dominated flows.

Symmetric Missile Dynamic Instabilities - A Review

DTIC Science & Technology

1980-03-01

and a Magnus side moment must be added to the total aerodynamic moment. Since statically stable missiles are usually spun to reduce the effect of...Identify by block~ numbef) Symmetric Missile Roil Moment Resonance Spin Dynamic Stability Side Moment Damxping Moment Trim Moment Magnus Moment Moving...dlamping moments for nonspin- ning re-entry vehicles, nonlinear Magnus moments for spinning missiles, and internal resonances with moving payload

Visual aftereffects and sensory nonlinearities from a single statistical framework

PubMed Central

Laparra, Valero; Malo, Jesús

2015-01-01

When adapted to a particular scenery our senses may fool us: colors are misinterpreted, certain spatial patterns seem to fade out, and static objects appear to move in reverse. A mere empirical description of the mechanisms tuned to color, texture, and motion may tell us where these visual illusions come from. However, such empirical models of gain control do not explain why these mechanisms work in this apparently dysfunctional manner. Current normative explanations of aftereffects based on scene statistics derive gain changes by (1) invoking decorrelation and linear manifold matching/equalization, or (2) using nonlinear divisive normalization obtained from parametric scene models. These principled approaches have different drawbacks: the first is not compatible with the known saturation nonlinearities in the sensors and it cannot fully accomplish information maximization due to its linear nature. In the second, gain change is almost determined a priori by the assumed parametric image model linked to divisive normalization. In this study we show that both the response changes that lead to aftereffects and the nonlinear behavior can be simultaneously derived from a single statistical framework: the Sequential Principal Curves Analysis (SPCA). As opposed to mechanistic models, SPCA is not intended to describe how physiological sensors work, but it is focused on explaining why they behave as they do. Nonparametric SPCA has two key advantages as a normative model of adaptation: (i) it is better than linear techniques as it is a flexible equalization that can be tuned for more sensible criteria other than plain decorrelation (either full information maximization or error minimization); and (ii) it makes no a priori functional assumption regarding the nonlinearity, so the saturations emerge directly from the scene data and the goal (and not from the assumed function). It turns out that the optimal responses derived from these more sensible criteria and SPCA are consistent with dysfunctional behaviors such as aftereffects. PMID:26528165

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

NASA Technical Reports Server (NTRS)

Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.

1998-01-01

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling

PubMed Central

Ye, Hao; Beamish, Richard J.; Glaser, Sarah M.; Grant, Sue C. H.; Hsieh, Chih-hao; Richards, Laura J.; Schnute, Jon T.; Sugihara, George

2015-01-01

It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner–recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts. PMID:25733874

High-Fidelity Buckling Analysis of Composite Cylinders Using the STAGS Finite Element Code

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.

2014-01-01

Results from previous shell buckling studies are presented that illustrate some of the unique and powerful capabilities in the STAGS finite element analysis code that have made it an indispensable tool in structures research at NASA over the past few decades. In particular, prototypical results from the development and validation of high-fidelity buckling simulations are presented for several unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells along with a discussion on the specific methods and user-defined subroutines in STAGS that are used to carry out the high-fidelity simulations. These simulations accurately account for the effects of geometric shell-wall imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and elastic boundary conditions. The analysis procedure uses a combination of nonlinear quasi-static and transient dynamic solution algorithms to predict the prebuckling and unstable collapse response characteristics of the cylinders. Finally, the use of high-fidelity models in the development of analysis-based shell-buckling knockdown (design) factors is demonstrated.

Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Elber, W.

1984-01-01

A geometrically nonlinear finite-element analysis has been developed to calculate the strain energy released by delaminating plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, GI, and shear sliding, GII, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow first before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, GI, for a near-surface delamination can be as high as 0.5GII, and can contribute significantly to the delamination growth.

Origami-based mechanical metamaterials with tunable frequency band structures (Conference Presentation)

NASA Astrophysics Data System (ADS)

Yasuda, Hiromi; Pratt, Riley; Yang, Jinkyu

2017-04-01

We investigate wave dynamics in origami-based mechanical metamaterials composed of bellows-like origami structures, specifically the Tachi-Miura Polyhedron (TMP). One of the unique features of the TMP is that its structural deformations take place only along the crease lines, therefore the structure can be made of rigid plates and hinges. By utilizing this feature, we introduce linear torsional springs to model the crease lines and derive the force and displacement relationship of the TMP structure along the longitudinal direction. Our analysis shows strain softening/hardening behaviors in compression/tensile regions respectively, and the force-displacement curve can be manipulated by altering the initial configuration of the TMP (e.g., the initial folding angle). We also fabricate physical prototypes and measure the force-displacement behavior to verify our analytical model. Based on this static analysis on the TMP, we simplify the TMP structure into a linkage model, preserving the tunable strain softening/hardening behaviors. Dynamic analysis is also conducted numerically to analyze the frequency response of the simplified TMP unit cell under harmonic excitations. The simplified TMP exhibits a transition between linear and nonlinear behaviors, which depends on the amplitude of the excitation and the initial configuration. In addition, we design a 1D system composed of simplified TMP unit cells and analyze the relationship between frequency and wave number. If two different configurations of the unit cell (e.g., different initial folding angles) are connected in an alternating arrangement, the system develops frequency bandgaps. These unique static/dynamic behaviors can be exploited to design engineering devices which can handle vibrations and impact in an efficient manner.

Nonlinear dual-axis biodynamic response of the semi-supine human body during vertical whole-body vibration

NASA Astrophysics Data System (ADS)

Huang, Ya; Griffin, Michael J.

2008-04-01

Nonlinear biodynamic responses are evident in many studies of the apparent masses of sitting and standing subjects in static postures that require muscle activity for postural control. In the present study, 12 male subjects adopted a relaxed semi-supine posture assumed to involve less muscle activity than during static sitting and standing. The supine subjects were exposed to two types of vertical vibration (in the x-axis of the semi-supine body): (i) continuous random vibration (0.25-20 Hz) at five magnitudes (0.125, 0.25, 0.5, 0.75, and 1.0 m s -2 rms); (ii) intermittent random vibration (0.25-20 Hz) alternately at 0.25 and 1.0 m s -2 rms. With continuous random vibration, the dominant primary resonance frequency in the median normalised apparent mass decreased from 10.35 to 7.32 Hz as the vibration magnitude increased from 0.125 to 1.0 m s -2 rms. This nonlinear response was apparent in both the vertical ( x-axis) apparent mass and in the horizontal ( z-axis) cross-axis apparent mass. As the vibration magnitude increased from 0.25 to 1.0 m s -2 rms, the median resonance frequency of the apparent mass with intermittent random vibration decreased from 9.28 to 8.06 Hz whereas, over the same range of magnitudes with continuous random vibration, the resonance frequency decreased from 9.62 to 7.81 Hz. The median change in the resonance frequency (between 0.25 and 1.0 m s -2 rms) was 1.37 Hz with the intermittent random vibration and 1.71 with the continuous random vibration. With the intermittent vibration, the resonance frequency was higher at the high magnitude and lower at the low magnitude than with continuous vibration of the same magnitudes. The response was typical of thixotropy that may be a primary cause of the nonlinear biodynamic responses to whole-body vibration.

Evidence for initiation of frictional partial slip as the mechanism behind nonlinear stress-strain hysteresis in rock fractures under seismic-frequency torsion

NASA Astrophysics Data System (ADS)

Saltiel, S.; Bonner, B. P.; Delbridge, B. G.; Ajo Franklin, J. B.

2016-12-01

We have adapted a low-frequency (0.1 - 64 Hz) torsional apparatus to explore the pure shear behavior of rock fractures under low normal stresses, simulating low effective stress environments - shallow depths and/or under high pore pressures. The instrument is unique in this ability to measure under very low confinement as well as to probe partial slip on the outside of asperities, before full slip nucleation occurs. Using a sinusoidal oscillation around this condition, we can probe the stress-strain constitutive relation at a range of strain amplitudes and the rate-dependence of the initiation of asperity slip. We find different, nonlinear, stress-strain constitutive relations for dolomite, rhyolite, and granite fractured samples, but all show softening at high strain amplitudes (above microstrain or micron-scale displacement). All measured samples exhibit qualitatively similar time-series hysteresis loops and frequency-dependence. The low frequency stress-strain loops stiffen at the high strain static end of the sinusoidal oscillation. This shape is determined by harmonic generation in the strain, while the stress signal has low power in harmonics, confirming that the driver and electronics are not the source of this nonlinearity. We also observe that this stiffening cusp does not occur as frequency increases above 8 Hz (opposite to normal dispersion seen at higher normal stresses). We monitor the fracture surface wear with repeated cycles to show the extent of slip on mapped asperities. These observations suggest that a rate dependent, healing, process causes the nonlinear responce of fracture faces under low normal stress to periodic shear. We propose that static friction at the low strain-rate part of the cycle, when given enough time at low oscillation frequencies, causes this stiffening cusp shape in the hysteretic stress-strain curve. An analytic model with idealized contact area is used to constrain the rate-state friction constitutive model parameters needed to provide this dynamic behavior.

Combining Static Analysis and Model Checking for Software Analysis

NASA Technical Reports Server (NTRS)

Brat, Guillaume; Visser, Willem; Clancy, Daniel (Technical Monitor)

2003-01-01

We present an iterative technique in which model checking and static analysis are combined to verify large software systems. The role of the static analysis is to compute partial order information which the model checker uses to reduce the state space. During exploration, the model checker also computes aliasing information that it gives to the static analyzer which can then refine its analysis. The result of this refined analysis is then fed back to the model checker which updates its partial order reduction. At each step of this iterative process, the static analysis computes optimistic information which results in an unsafe reduction of the state space. However we show that the process converges to a fired point at which time the partial order information is safe and the whole state space is explored.

Negative stiffness honeycombs as tunable elastic metamaterials

NASA Astrophysics Data System (ADS)

Goldsberry, Benjamin M.; Haberman, Michael R.

2018-03-01

Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion associated with infinitesimal motion superposed on the externally imposed pre-strain. A finite element model is utilized to model the static deformation and subsequent linear wave motion at the pre-strained state. Analysis of the slowness surface and group velocity demonstrates that the NSH exhibits significant tunability and a high degree of anisotropy which can be used to guide wave energy depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices.

Refraction traveltime tomography based on damped wave equation for irregular topographic model

NASA Astrophysics Data System (ADS)

Park, Yunhui; Pyun, Sukjoon

2018-03-01

Land seismic data generally have time-static issues due to irregular topography and weathered layers at shallow depths. Unless the time static is handled appropriately, interpretation of the subsurface structures can be easily distorted. Therefore, static corrections are commonly applied to land seismic data. The near-surface velocity, which is required for static corrections, can be inferred from first-arrival traveltime tomography, which must consider the irregular topography, as the land seismic data are generally obtained in irregular topography. This paper proposes a refraction traveltime tomography technique that is applicable to an irregular topographic model. This technique uses unstructured meshes to express an irregular topography, and traveltimes calculated from the frequency-domain damped wavefields using the finite element method. The diagonal elements of the approximate Hessian matrix were adopted for preconditioning, and the principle of reciprocity was introduced to efficiently calculate the Fréchet derivative. We also included regularization to resolve the ill-posed inverse problem, and used the nonlinear conjugate gradient method to solve the inverse problem. As the damped wavefields were used, there were no issues associated with artificial reflections caused by unstructured meshes. In addition, the shadow zone problem could be circumvented because this method is based on the exact wave equation, which does not require a high-frequency assumption. Furthermore, the proposed method was both robust to an initial velocity model and efficient compared to full wavefield inversions. Through synthetic and field data examples, our method was shown to successfully reconstruct shallow velocity structures. To verify our method, static corrections were roughly applied to the field data using the estimated near-surface velocity. By comparing common shot gathers and stack sections with and without static corrections, we confirmed that the proposed tomography algorithm can be used to correct the statics of land seismic data.

Balloon Borne Arc-Second Pointer Feasibility Study

NASA Technical Reports Server (NTRS)

Ward, Philip R.; DeWeese, Keith D.

2003-01-01

For many years scientists have been utilizing stratospheric balloons as low-cost platforms on which to conduct space science experiments. A major hurdle in extending the range of experiments for which these vehicles are useful has been the imposition of the gondola dynamics on the accuracy with which an instrument can be kept pointed at a celestial target. A significant number of scientists have sought the ability to point their instruments with jitter in the arc-second range. This paper presents the design and analysis of a stratospheric balloon borne pointing system that is able to meet this requirement. The foundation for a high fidelity controller simulation is presented. The flexibility of the flight train is represented through generalized modal analysis. A multiple controller scheme is introduced for coarse and fine pointing. Coarse azimuth pointing is accomplished by an established pointing system, with extensive flight history, residing above the gondola structure. A pitch-yaw gimbal mount is used for fine pointing, providing orthogonal axes when nominally on target. Fine pointing actuation is from direct drive dc motors, eliminating backlash problems. An analysis of friction nonlinearities and a demonstration of the necessity in eliminating static fiction are provided. A unique bearing hub design is introduced that eliminates static fiction from the system dynamics. A control scheme involving linear accelerometers for enhanced disturbance rejection is also presented. Results from a linear analysis of the total system and the high fidelity simulation are given. This paper establishes that the proposed control strategy can be made robustly stable with significant design margins. Also demonstrated is the efficacy of the proposed system in rejecting disturbances larger than those considered realistic. Finally, we see that sub arc-second pointing stability can be achieved for a large instrument pointing at an inertial target.

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.

Numerical Study of Steady and Unsteady Canard-Wing-Body Aerodynamics

NASA Technical Reports Server (NTRS)

Eugene, L. Tu

1996-01-01

The use of canards in advanced aircraft for control and improved aerodynamic performance is a topic of continued interest and research. In addition to providing maneuver control and trim, the influence of canards on wing aerodynamics can often result in increased maximum lift and decreased trim drag. In many canard-configured aircraft, the main benefits of canards are realized during maneuver or other dynamic conditions. Therefore, the detailed study and understanding of canards requires the accurate prediction of the non-linear unsteady aerodynamics of such configurations. For close-coupled canards, the unsteady aerodynamic performance associated with the canard-wing interaction is of particular interest. The presence of a canard in close proximity to the wing results in a highly coupled canard-wing aerodynamic flowfield which can include downwash/upwash effects, vortex-vortex interactions and vortex-surface interactions. For unsteady conditions, these complexities of the canard-wing flowfield are further increased. The development and integration of advanced computational technologies provide for the time-accurate Navier-Stokes simulations of the steady and unsteady canard-wing-body flox,fields. Simulation, are performed for non-linear flight regimes at transonic Mach numbers and for a wide range of angles of attack. For the static configurations, the effects of canard positioning and fixed deflection angles on aerodynamic performance and canard-wing vortex interaction are considered. For non-static configurations, the analyses of the canard-wing body flowfield includes the unsteady aerodynamics associated with pitch-up ramp and pitch oscillatory motions of the entire geometry. The unsteady flowfield associated with moving canards which are typically used as primary control surfaces are considered as well. The steady and unsteady effects of the canard on surface pressure integrated forces and moments, and canard-wing vortex interaction are presented in detail including the effects of the canard on the static and dynamic stability characteristics. The current study provides an understanding of the steady and unsteady canard-wing-body flowfield. Emphasis is placed on the effects of the canard on aerodynamic performance as well as the detailed flow physics of the canard-wing flowfield interactions. The computational tools developed to accurately predict the time-accurate flowfield of moving canards provides for the capability of coupled fluids-controls simulations desired in the detailed design and analysis of advanced aircraft.

Optimization-Based Inverse Identification of the Parameters of a Concrete Cap Material Model

NASA Astrophysics Data System (ADS)

Král, Petr; Hokeš, Filip; Hušek, Martin; Kala, Jiří; Hradil, Petr

2017-10-01

Issues concerning the advanced numerical analysis of concrete building structures in sophisticated computing systems currently require the involvement of nonlinear mechanics tools. The efforts to design safer, more durable and mainly more economically efficient concrete structures are supported via the use of advanced nonlinear concrete material models and the geometrically nonlinear approach. The application of nonlinear mechanics tools undoubtedly presents another step towards the approximation of the real behaviour of concrete building structures within the framework of computer numerical simulations. However, the success rate of this application depends on having a perfect understanding of the behaviour of the concrete material models used and having a perfect understanding of the used material model parameters meaning. The effective application of nonlinear concrete material models within computer simulations often becomes very problematic because these material models very often contain parameters (material constants) whose values are difficult to obtain. However, getting of the correct values of material parameters is very important to ensure proper function of a concrete material model used. Today, one possibility, which permits successful solution of the mentioned problem, is the use of optimization algorithms for the purpose of the optimization-based inverse material parameter identification. Parameter identification goes hand in hand with experimental investigation while it trying to find parameter values of the used material model so that the resulting data obtained from the computer simulation will best approximate the experimental data. This paper is focused on the optimization-based inverse identification of the parameters of a concrete cap material model which is known under the name the Continuous Surface Cap Model. Within this paper, material parameters of the model are identified on the basis of interaction between nonlinear computer simulations, gradient based and nature inspired optimization algorithms and experimental data, the latter of which take the form of a load-extension curve obtained from the evaluation of uniaxial tensile test results. The aim of this research was to obtain material model parameters corresponding to the quasi-static tensile loading which may be further used for the research involving dynamic and high-speed tensile loading. Based on the obtained results it can be concluded that the set goal has been reached.

Performance evaluation of nonlinear energy harvesting with magnetically coupled dual beams

NASA Astrophysics Data System (ADS)

Lan, Chunbo; Tang, Lihua; Qin, Weiyang

2017-04-01

To enhance the output power and broaden the operation bandwidth of vibration energy harvesters (VEH), nonlinear two degree-of-freedom (DOF) energy harvesters have attracted wide attention recently. In this paper, we investigate the performance of a nonlinear VEH with magnetically coupled dual beams and compare it with the typical Duffing-type VEH to find the advantages and drawbacks of this nonlinear 2-DOF VEH. First, based on the lumped parameter model, the characteristics of potential energy shapes and static equilibriums are analyzed. It is noted that the dual beam configuration is much easy to be transformed from a mono-stable state into a bi-stable state when the repulsive magnet force increases. Based on the equilibrium positions and different kinds of nonlinearities, four nonlinearity regimes are determined. Second, the performance of 1-DOF and 2-DOF configurations are compared respectively in these four nonlinearity regimes by simulating the forward sweep responses of these two nonlinear VEHs under different acceleration levels. Several meaningful conclusions are obtained. First, the main alternative to enlarge the operation bandwidth for dual-beam configuration is chaotic oscillation, in which two beams jump between two stable positions chaotically. However, the large-amplitude periodic oscillations, such as inter-well oscillation, cannot take place in both piezoelectric and parasitic beams at the same time. Generally speaking, both of the magnetically coupled dual-beam energy harvester and Duffingtype energy harvester, have their own advantages and disadvantages, while given a large enough base excitation, the maximum voltages of these two systems are almost the same in all these four regimes.

Structural Dynamic Analyses And Test Predictions For Spacecraft Structures With Non-Linearities

NASA Astrophysics Data System (ADS)

Vergniaud, Jean-Baptiste; Soula, Laurent; Newerla, Alfred

2012-07-01

The overall objective of the mechanical development and verification process is to ensure that the spacecraft structure is able to sustain the mechanical environments encountered during launch. In general the spacecraft structures are a-priori assumed to behave linear, i.e. the responses to a static load or dynamic excitation, respectively, will increase or decrease proportionally to the amplitude of the load or excitation induced. However, past experiences have shown that various non-linearities might exist in spacecraft structures and the consequences of their dynamic effects can significantly affect the development and verification process. Current processes are mainly adapted to linear spacecraft structure behaviour. No clear rules exist for dealing with major structure non-linearities. They are handled outside the process by individual analysis and margin policy, and analyses after tests to justify the CLA coverage. Non-linearities can primarily affect the current spacecraft development and verification process on two aspects. Prediction of flights loads by launcher/satellite coupled loads analyses (CLA): only linear satellite models are delivered for performing CLA and no well-established rules exist how to properly linearize a model when non- linearities are present. The potential impact of the linearization on the results of the CLA has not yet been properly analyzed. There are thus difficulties to assess that CLA results will cover actual flight levels. Management of satellite verification tests: the CLA results generated with a linear satellite FEM are assumed flight representative. If the internal non- linearities are present in the tested satellite then there might be difficulties to determine which input level must be passed to cover satellite internal loads. The non-linear behaviour can also disturb the shaker control, putting the satellite at risk by potentially imposing too high levels. This paper presents the results of a test campaign performed in the frame of an ESA TRP study [1]. A bread-board including typical non-linearities has been designed, manufactured and tested through a typical spacecraft dynamic test campaign. The study has demonstrate the capabilities to perform non-linear dynamic test predictions on a flight representative spacecraft, the good correlation of test results with respect to Finite Elements Model (FEM) prediction and the possibility to identify modal behaviour and to characterize non-linearities characteristics from test results. As a synthesis for this study, overall guidelines have been derived on the mechanical verification process to improve level of expertise on tests involving spacecraft including non-linearity.

Accelerated fatigue durability of a high performance composite

NASA Technical Reports Server (NTRS)

Rotem, A.

1982-01-01

The fatigue behavior of multidirectional graphite-epoxy laminates was analyzed theoretically and experimentally in an effort to establish an accelerated testing methodology. Analysis of the failure mechanism in fatigue of the laminates led to the determination of the failure mode governing fracture. The nonlinear, cyclic-dependent shear modulus was used to calculate the changing stress field in the laminate during the fatigue loading. Fatigue tests were performed at three different temperatures: 25 C, 74 C, and 114 C. The prediction of the S-N curves was made based on the artificial static strength artificial static strength at a reference temperature and the fatigue functions associated with them. The prediction of an S-N curve at other temperatures was performed using shifting factors determined for the specific failure mode. For multidirectional laminates, different S-N curves at different temperatures could be predicted using these shifting factors. Different S-N curves at different temperatures occur only when the fatigue failure mode is matrix dominated. It was found that whenever the fatigue failure mode is fiber dominated, temperature, over the range investigated, had no influence on the fatigue life. These results permit the prediction of long-time, low temperature fatigue behavior from data obtained in short time, high temperature testing, for laminates governed by a matrix failure mode.

Static and Dynamic Characteristics of a Long-Span Cable-Stayed Bridge with CFRP Cables

PubMed Central

Xie, Xu; Li, Xiaozhang; Shen, Yonggang

2014-01-01

In this study, the scope of CFRP cables in cable-stayed bridges is studied by establishing a numerical model of a 1400-m span of the same. The mechanical properties and characteristics of CFRP stay cables and of a cable-stayed bridge with CFRP cables are here subjected to comprehensive analysis. The anomalies in the damping properties of free vibration, nonlinear parametric vibration and wind fluctuating vibration between steel cables and CFRP cables are determined. The structural stiffness, wind resistance and traffic vibration of the cable-stayed bridge with CFRP cables are also analyzed. It was found that the static performances of a cable-stayed bridge with CFRP cables and steel cables are basically the same. The natural frequencies of CFRP cables do not coincide with the major natural frequencies of the cable-stayed bridge, so the likelihood of CFRP cable-bridge coupling vibration is minuscule. For CFRP cables, the response amplitudes of both parametric vibration and wind fluctuating vibration are smaller than those of steel cables. It can be concluded from the research that the use of CFRP cables does not change the dynamic characteristics of the vehicle-bridge coupling vibration. Therefore, they can be used in long-span cable-stayed bridges with an excellent mechanical performance. PMID:28788710

Static and Dynamic Characteristics of a Long-Span Cable-Stayed Bridge with CFRP Cables.

PubMed

Xie, Xu; Li, Xiaozhang; Shen, Yonggang

2014-06-23

In this study, the scope of CFRP cables in cable-stayed bridges is studied by establishing a numerical model of a 1400-m span of the same. The mechanical properties and characteristics of CFRP stay cables and of a cable-stayed bridge with CFRP cables are here subjected to comprehensive analysis. The anomalies in the damping properties of free vibration, nonlinear parametric vibration and wind fluctuating vibration between steel cables and CFRP cables are determined. The structural stiffness, wind resistance and traffic vibration of the cable-stayed bridge with CFRP cables are also analyzed. It was found that the static performances of a cable-stayed bridge with CFRP cables and steel cables are basically the same. The natural frequencies of CFRP cables do not coincide with the major natural frequencies of the cable-stayed bridge, so the likelihood of CFRP cable-bridge coupling vibration is minuscule. For CFRP cables, the response amplitudes of both parametric vibration and wind fluctuating vibration are smaller than those of steel cables. It can be concluded from the research that the use of CFRP cables does not change the dynamic characteristics of the vehicle-bridge coupling vibration. Therefore, they can be used in long-span cable-stayed bridges with an excellent mechanical performance.

Low-Velocity Impact Response of Sandwich Beams with Functionally Graded Core

NASA Technical Reports Server (NTRS)

Apetre, N. A.; Sankar, B. V.; Ambur, D. R.

2006-01-01

The problem of low-speed impact of a one-dimensional sandwich panel by a rigid cylindrical projectile is considered. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The problem is a combination of static contact problem and dynamic response of the sandwich panel obtained via a simple nonlinear spring-mass model (quasi-static approximation). The variation of core Young's modulus is represented by a polynomial in the thickness coordinate, but the Poisson's ratio is kept constant. The two-dimensional elasticity equations for the plane sandwich structure are solved using a combination of Fourier series and Galerkin method. The contact problem is solved using the assumed contact stress distribution method. For the impact problem we used a simple dynamic model based on quasi-static behavior of the panel - the sandwich beam was modeled as a combination of two springs, a linear spring to account for the global deflection and a nonlinear spring to represent the local indentation effects. Results indicate that the contact stiffness of thc beam with graded core Increases causing the contact stresses and other stress components in the vicinity of contact to increase. However, the values of maximum strains corresponding to the maximum impact load arc reduced considerably due to grading of thc core properties. For a better comparison, the thickness of the functionally graded cores was chosen such that the flexural stiffness was equal to that of a beam with homogeneous core. The results indicate that functionally graded cores can be used effectively to mitigate or completely prevent impact damage in sandwich composites.

Nonlinear Programming shallow tomography improves deep structure imaging

NASA Astrophysics Data System (ADS)

Li, J.; Morozov, I.

2004-05-01

In areas with strong variations in topography or near-surface lithology, conventional seismic data processing methods do not produce clear images, neither shallow nor deep. The conventional reflection data processing methods do not resolve stacking velocities at very shallow depth; however, refraction tomography can be used to obtain the near-surface velocities. We use Nonlinear Programming (NP) via known velocity and depth in points from shallow boreholes and outcrop as well as derivation of slowness as constraint conditions to gain accurate shallow velocities. We apply this method to a 2D reflection survey shot across the Flame Mountain, a typical mountain with high gas reserve volume in Western China, by PetroChina and BGP in 1990s. The area has a highly rugged topography with strong variations of lithology near the surface. Over its hillside, the quality of reflection data is very good, but on the mountain ridge, reflection quality is poorer. Because of strong noise, only the first breaks are clear in the records, with velocities varying by more than 3 times in the near offsets. Because this region contains a steep cliff and an overthrust fold, it is very difficult to find a standard refraction horizon, therefore, GLI refractive statics conventional field and residual statics do not result in a good image. Our processing approach includes: 1) The Herglotz-Wiechert method to derive a starting velocity model which is better than horizontal velocity model; 2) using shallow boreholes and geological data, construct smoothness constraints on the velocity field as well as; 3) perform tomographic velocity inversion by NP algorithm; 4) by using the resulting accurate shallow velocities, derive the statics to correct the seismic data for the complex near-surface velocity variations. The result indicates that shallow refraction tomography can greatly improve deep seismic images in complex surface conditions.

Line Narrowing of Excited-State Transitions in Nonlinear Polarization Spectroscopy: Application to Water-Soluble Chlorophyll-Binding Protein

NASA Astrophysics Data System (ADS)

Schoth, Mario; Richter, Marten; Knorr, Andreas; Renger, Thomas

2012-04-01

The homogeneous linewidth of dye aggregates like photosynthetic light-harvesting complexes contains important information about energy transfer and relaxation times that is, however, masked by inhomogeneous broadening caused by static disorder. Whereas there exist line narrowing techniques for the study of low-energy exciton states, the homogeneous linewidth of the high-energy states is not so easy to decipher. Here we present a microscopic theory for nonlinear polarization spectroscopy in the frequency domain that contains a dynamic aggregate selection revealing the homogeneous linewidth of these states. The theory is applied to the water-soluble chlorophyll-binding protein for which the high-energy exciton state was predicted to exhibit a sub-100-fs lifetime.

Fundamentals of Plasma Physics

NASA Astrophysics Data System (ADS)

Bellan, Paul M.

2008-07-01

Preface; 1. Basic concepts; 2. The Vlasov, two-fluid, and MHD models of plasma dynamics; 3. Motion of a single plasma particle; 4. Elementary plasma waves; 5. Streaming instabilities and the Landau problem; 6. Cold plasma waves in a magnetized plasma; 7. Waves in inhomogeneous plasmas and wave energy relations; 8. Vlasov theory of warm electrostatic waves in a magnetized plasma; 9. MHD equilibria; 10. Stability of static MHD equilibria; 11. Magnetic helicity interpreted and Woltjer-Taylor relaxation; 12. Magnetic reconnection; 13. Fokker-Planck theory of collisions; 14. Wave-particle nonlinearities; 15. Wave-wave nonlinearities; 16. Non-neutral plasmas; 17. Dusty plasmas; Appendix A. Intuitive method for vector calculus identities; Appendix B. Vector calculus in orthogonal curvilinear coordinates; Appendix C. Frequently used physical constants and formulae; Bibliography; References; Index.

Nonlinear PET parametric image reconstruction with MRI information using kernel method

NASA Astrophysics Data System (ADS)

Gong, Kuang; Wang, Guobao; Chen, Kevin T.; Catana, Ciprian; Qi, Jinyi

2017-03-01

Positron Emission Tomography (PET) is a functional imaging modality widely used in oncology, cardiology, and neurology. It is highly sensitive, but suffers from relatively poor spatial resolution, as compared with anatomical imaging modalities, such as magnetic resonance imaging (MRI). With the recent development of combined PET/MR systems, we can improve the PET image quality by incorporating MR information. Previously we have used kernel learning to embed MR information in static PET reconstruction and direct Patlak reconstruction. Here we extend this method to direct reconstruction of nonlinear parameters in a compartment model by using the alternating direction of multiplier method (ADMM) algorithm. Simulation studies show that the proposed method can produce superior parametric images compared with existing methods.

Yielding in colloidal gels due to nonlinear microstructure bending mechanics.

PubMed

Furst, Eric M; Pantina, John P

2007-05-01

We report measurements of the nonlinear micromechanics of strongly flocculated model colloidal aggregates. Linear aggregates directly assembled using laser tweezers are subjected to bending loads until a critical bending moment is reached, which is identified by a stictionlike rearrangement of a single colloidal bond. This nanoscale phenomenon provides a quantitative basis for understanding the macroscopic shear yield stresses of strongly flocculated polystyrene latex gels, based on the maximum bending moment exceeding the critical moment of the constituent colloidal bonds of the gel microstructure. These mechanics are consistent with the local bending moment overcoming the static friction force between neighboring adhesive particles. This results in a direct relationship between the rheology of these gels and the boundary friction between Brownian particles.

Nonalgebraic integrability of one reversible dynamical system of the Cremona type

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

1998-05-01

A reversible dynamical system (RDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions [the Chew-Low-type equations with crossing-symmetry matrix A(l,1)], are considered. This RDS is split into one- and two-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous three-point functional equation. Nonalgebraic integrability of RDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a nonresonant fixed point.

Aeroelastic equations of motion of a Darrieus vertical-axis wind-turbine blade

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.; Kvaternik, R. G.

1979-01-01

The second-degree nonlinear aeroelastic equations of motion for a slender, flexible, nonuniform, Darrieus vertical-axis wind turbine blade which is undergoing combined flatwise bending, edgewise bending, torsion, and extension are developed using Hamilton's principle. The blade aerodynamic loading is obtained from strip theory based on a quasi-steady approximation of two-dimensional incompressible unsteady airfoil theory. The derivation of the equations has its basis in the geometric nonlinear theory of elasticity and the resulting equations are consistent with the small deformation approximation in which the elongations and shears are negligible compared to unity. These equations are suitable for studying vibrations, static and dynamic aeroelastic instabilities, and dynamic response. Several possible methods of solution of the equations, which have periodic coefficients, are discussed.

Switchable and spacing-tunable dual-wavelength thulium-doped silica fiber laser based on a nonlinear amplifier loop mirror.

PubMed

Liu, Shuo; Yan, Fengping; Feng, Ting; Wu, Beilei; Dong, Ze; Chang, Gee-Kung

2014-08-20

A kind of switchable and spacing-tunable dual-wavelength thulium-doped silica fiber laser based on a nonlinear amplifier loop mirror is presented and experimentally demonstrated. By adjusting the polarization controllers (PCs), stable dual-wavelength operation is obtained at the 2 μm band. The optical signal-to-noise ratio (OSNR) is better than 56 dB. The wavelength tuning is performed by applying static strain into the fiber Bragg grating. A tuning range from 0 to 5.14 nm is achieved for the dual-wavelength spacing. By adjusting the PCs properly, the fiber laser can also operate in single-wavelength state with the OSNR for each wavelength more than 50 dB.

Local existence of solutions to the Euler-Poisson system, including densities without compact support

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

Multiphase-field model of small strain elasto-plasticity according to the mechanical jump conditions

NASA Astrophysics Data System (ADS)

Herrmann, Christoph; Schoof, Ephraim; Schneider, Daniel; Schwab, Felix; Reiter, Andreas; Selzer, Michael; Nestler, Britta

2018-04-01

We introduce a small strain elasto-plastic multiphase-field model according to the mechanical jump conditions. A rate-independent J_2 -plasticity model with linear isotropic hardening and without kinematic hardening is applied exemplary. Generally, any physically nonlinear mechanical model is compatible with the subsequently presented procedure. In contrast to models with interpolated material parameters, the proposed model is able to apply different nonlinear mechanical constitutive equations for each phase separately. The Hadamard compatibility condition and the static force balance are employed as homogenization approaches to calculate the phase-inherent stresses and strains. Several verification cases are discussed. The applicability of the proposed model is demonstrated by simulations of the martensitic transformation and quantitative parameters.

Ultrafast frequency-selective optical switching based on thin self-assembled organic chromophoric films with a large second-order nonlinear response

NASA Astrophysics Data System (ADS)

Wang, Gang; Zhu, Peiwang; Marks, Tobin J.; Ketterson, J. B.

2002-09-01

Thin films consisting of self-assembled chromophoric superlattices exhibit very large second-order nonlinear responses [chi](2). Using such films, a "static" diffraction grating is created by the interference of two coherent infrared beams from a pulsed yttritium-aluminum-garnet laser. This grating is used to switch the second-harmonic and third-harmonic "signal" beams (generated from the fundamental "pump" beam or mixed within the chromophoric superlattice) into different channels (directions). Ultrafast switching response as a function of the time overlap of the pumping beams is demonstrated. It is suggested that such devices can be used to spatially and temporally separate signal trains consisting of pulses having different frequencies and arrival times.

Modeling and control of a dielectric elastomer actuator

NASA Astrophysics Data System (ADS)

Gupta, Ujjaval; Gu, Guo-Ying; Zhu, Jian

2016-04-01

The emerging field of soft robotics offers the prospect of applying soft actuators as artificial muscles in the robots, replacing traditional actuators based on hard materials, such as electric motors, piezoceramic actuators, etc. Dielectric elastomers are one class of soft actuators, which can deform in response to voltage and can resemble biological muscles in the aspects of large deformation, high energy density and fast response. Recent research into dielectric elastomers has mainly focused on issues regarding mechanics, physics, material designs and mechanical designs, whereas less importance is given to the control of these soft actuators. Strong nonlinearities due to large deformation and electromechanical coupling make control of the dielectric elastomer actuators challenging. This paper investigates feed-forward control of a dielectric elastomer actuator by using a nonlinear dynamic model. The material and physical parameters in the model are identified by quasi-static and dynamic experiments. A feed-forward controller is developed based on this nonlinear dynamic model. Experimental evidence shows that this controller can control the soft actuator to track the desired trajectories effectively. The present study confirms that dielectric elastomer actuators are capable of being precisely controlled with the nonlinear dynamic model despite the presence of material nonlinearity and electromechanical coupling. It is expected that the reported results can promote the applications of dielectric elastomer actuators to soft robots or biomimetic robots.

Wideband electromagnetic energy harvesting from ambient vibrations

NASA Astrophysics Data System (ADS)

Mallick, Dhiman; Podder, Pranay; Roy, Saibal

2015-06-01

Different bandwidth widening schemes of electromagnetic energy harvesters have been reported in this work. The devices are fabricated on FR4 substrate using laser micromachining techniques. The linear device operate in a narrow band around the resonance; in order to tune resonant frequency of the device electrically, two different types of complex load topologies are adopted. Using capacitive load, the resonant frequency is tuned in the low frequency direction whereas using inductive load, the resonant frequency is tuned in the high frequency direction. An overall tuning range of ˜2.4 Hz is obtained at 0.3g though the output power dropped significantly over the tuning range. In order to improve the off-resonance performance, nonlinear oscillation based systems are adopted. A specially designed spring arm with fixed-guided configuration produced single well nonlinear monostable configuration. With increasing input acceleration, wider bandwidth is obtained with such a system as large displacement, stretching nonlinearity comes into play and 9.55 Hz bandwidth is obtained at 0.5g. The repulsive force between one static and one vibrating oppositely polarized magnets are used to generate bistable nonlinear potential system. The distance between the mentioned magnets is varied between 4 to 10 mm to produce tunable nonlinearity with a maximum half power bandwidth over 3 Hz at 0.5g.

Vortex Dynamics

DTIC Science & Technology

1989-08-07

One class (I. discussed in §4) of bifurcating flows is again coiumnar. so there are no axial varations: a second class Il1. §6) consists of solitary...34Amplitude Expansion for Viscous Rotating Pipe Flow Near a Degenerate Bifurcation Point ( A . Mahalov & S. Leibovich) American Physical Society Division of...Fluid Mechanics, Buffalo, NY, November 22, 1988. "Fully Nonlinear Waves on Vortices" ( A . Kribus & S. Leibovich) Seminars "Static bifurcations of vortex

Postbuckling delamination of a stiffened composite panel using finite element methods

NASA Technical Reports Server (NTRS)

Natsiavas, S.; Babcock, C. D.; Knauss, W. G.

1987-01-01

A combined numerical and experimental study is carried out for the postbuckling behavior of a stiffened composite panel. The panel is rectangular and is subjected to static in-plane compression on two opposite edges to the collapse level. Nonlinear (large deflection) plate theory is employed, together with an experimentally based failure criterion. It is found that the stiffened composite panel can exhibit significant postbuckling strength.

Cyclovergence: the motor response to cyclodisparity.

PubMed

Hooten, K; Myers, E; Worrall, R; Stark, L

1979-03-05

Static photographic evidence of the occurrence of cyclovergence is presented that supports and extends the result of Crone and Everhard-Halm (1975). Wide-angle complex targets were a necessary condition; simple horizontal line targets were insufficient. Our asymmetrical disparity targets supported in part the conformance of cyclovergence to Hering's Law but raised questions relating to the computational process that also acts to remove cyclodisparity and permits cyclofusion. Saturation and hysteresis nonlinearities were observed.

Acceleration Wave Propagation in Hyperelastic Rods of Variable Cross-Section.

DTIC Science & Technology

1981-07-01

direction of propagation. Many authors have considered both static and dynamic problems for such materials, of whom we mention only Antman [2] and... Antman and Jordan [3] who studied the Kirchhoff problem for nonlinearly elastic rods and qualitative properties in general, Jeffrey and Teymur [4] and...Jeffrey and Suhubi [5] who considered shock wave formation and acceleration wave propagation through periodically layered media, and Antman and Liu [6

TORO II: A finite element computer program for nonlinear quasi-static problems in electromagnetics: Part 2, User`s manual

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

Gartling, D.K.

User instructions are given for the finite element, electromagnetics program, TORO II. The theoretical background and numerical methods used in the program are documented in SAND95-2472. The present document also describes a number of example problems that have been analyzed with the code and provides sample input files for typical simulations. 20 refs., 34 figs., 3 tabs.

A Geometrically Nonlinear Phase Field Theory of Brittle Fracture

DTIC Science & Technology

2014-10-01

of crack propagation. Philos Mag 91:75–95 Sun X, Khaleel M (2004) Modeling of glass fracture damage using continuum damage mechanics -static spherical...elastic fracture mechanics ). Engineering finite element (FE) simula- tions often invoke continuum damage mechanics the- ories, wherein the tangent...stiffness of a material ele- ment degrades as “damage” accumulates.Conventional continuum damage mechanics theories (Clayton and McDowell 2003, 2004; Sun and

Multiaxial mechanical properties and constitutive modeling of human adipose tissue: a basis for preoperative simulations in plastic and reconstructive surgery.

PubMed

Sommer, Gerhard; Eder, Maximilian; Kovacs, Laszlo; Pathak, Heramb; Bonitz, Lars; Mueller, Christoph; Regitnig, Peter; Holzapfel, Gerhard A

2013-11-01

A preoperative simulation of soft tissue deformations during plastic and reconstructive surgery is desirable to support the surgeon's planning and to improve surgical outcomes. The current development of constitutive adipose tissue models, for the implementation in multilayer computational frameworks for the simulation of human soft tissue deformations, has proved difficult because knowledge of the required mechanical parameters of fat tissue is limited. Therefore, for the first time, human abdominal adipose tissues were mechanically investigated by biaxial tensile and triaxial shear tests. The results of this study suggest that human abdominal adipose tissues under quasi-static and dynamic multiaxial loadings can be characterized as a nonlinear, anisotropic and viscoelastic soft biological material. The nonlinear and anisotropic features are consequences of the material's collagenous microstructure. The aligned collagenous septa observed in histological investigations causes the anisotropy of the tissue. A hyperelastic model used in this study was appropriate to represent the quasi-static multiaxial mechanical behavior of fat tissue. The constitutive parameters are intended to serve as a basis for soft tissue simulations using the finite element method, which is an apparent method for obtaining promising results in the field of plastic and reconstructive surgery. Copyright © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A cascade model of information processing and encoding for retinal prosthesis.

PubMed

Pei, Zhi-Jun; Gao, Guan-Xin; Hao, Bo; Qiao, Qing-Li; Ai, Hui-Jian

2016-04-01

Retinal prosthesis offers a potential treatment for individuals suffering from photoreceptor degeneration diseases. Establishing biological retinal models and simulating how the biological retina convert incoming light signal into spike trains that can be properly decoded by the brain is a key issue. Some retinal models have been presented, ranking from structural models inspired by the layered architecture to functional models originated from a set of specific physiological phenomena. However, Most of these focus on stimulus image compression, edge detection and reconstruction, but do not generate spike trains corresponding to visual image. In this study, based on state-of-the-art retinal physiological mechanism, including effective visual information extraction, static nonlinear rectification of biological systems and neurons Poisson coding, a cascade model of the retina including the out plexiform layer for information processing and the inner plexiform layer for information encoding was brought forward, which integrates both anatomic connections and functional computations of retina. Using MATLAB software, spike trains corresponding to stimulus image were numerically computed by four steps: linear spatiotemporal filtering, static nonlinear rectification, radial sampling and then Poisson spike generation. The simulated results suggested that such a cascade model could recreate visual information processing and encoding functionalities of the retina, which is helpful in developing artificial retina for the retinally blind.

Closed-form Static Analysis with Inertia Relief and Displacement-Dependent Loads Using a MSC/NASTRAN DMAP Alter

NASA Technical Reports Server (NTRS)

Barnett, Alan R.; Widrick, Timothy W.; Ludwiczak, Damian R.

1995-01-01

Solving for the displacements of free-free coupled systems acted upon by static loads is commonly performed throughout the aerospace industry. Many times, these problems are solved using static analysis with inertia relief. This solution technique allows for a free-free static analysis by balancing the applied loads with inertia loads generated by the applied loads. For some engineering applications, the displacements of the free-free coupled system induce additional static loads. Hence, the applied loads are equal to the original loads plus displacement-dependent loads. Solving for the final displacements of such systems is commonly performed using iterative solution techniques. Unfortunately, these techniques can be time-consuming and labor-intensive. Since the coupled system equations for free-free systems with displacement-dependent loads can be written in closed-form, it is advantageous to solve for the displacements in this manner. Implementing closed-form equations in static analysis with inertia relief is analogous to implementing transfer functions in dynamic analysis. Using a MSC/NASTRAN DMAP Alter, displacement-dependent loads have been included in static analysis with inertia relief. Such an Alter has been used successfully to solve efficiently a common aerospace problem typically solved using an iterative technique.

Experimental Validation of a Thermoelastic Model for SMA Hybrid Composites

NASA Technical Reports Server (NTRS)

Turner, Travis L.

2001-01-01

This study presents results from experimental validation of a recently developed model for predicting the thermomechanical behavior of shape memory alloy hybrid composite (SMAHC) structures, composite structures with an embedded SMA constituent. The model captures the material nonlinearity of the material system with temperature and is capable of modeling constrained, restrained, or free recovery behavior from experimental measurement of fundamental engineering properties. A brief description of the model and analysis procedures is given, followed by an overview of a parallel effort to fabricate and characterize the material system of SMAHC specimens. Static and dynamic experimental configurations for the SMAHC specimens are described and experimental results for thermal post-buckling and random response are presented. Excellent agreement is achieved between the measured and predicted results, fully validating the theoretical model for constrained recovery behavior of SMAHC structures.

Metabolic networks in motion: 13C-based flux analysis

PubMed Central

Sauer, Uwe

2006-01-01

Many properties of complex networks cannot be understood from monitoring the components—not even when comprehensively monitoring all protein or metabolite concentrations—unless such information is connected and integrated through mathematical models. The reason is that static component concentrations, albeit extremely informative, do not contain functional information per se. The functional behavior of a network emerges only through the nonlinear gene, protein, and metabolite interactions across multiple metabolic and regulatory layers. I argue here that intracellular reaction rates are the functional end points of these interactions in metabolic networks, hence are highly relevant for systems biology. Methods for experimental determination of metabolic fluxes differ fundamentally from component concentration measurements; that is, intracellular reaction rates cannot be detected directly, but must be estimated through computer model-based interpretation of stable isotope patterns in products of metabolism. PMID:17102807

Helicity in dynamic atmospheric processes

NASA Astrophysics Data System (ADS)

Kurgansky, M. V.

2017-03-01

An overview on the helicity of the velocity field and the role played by this concept in modern research in the field of geophysical fluid dynamics and dynamic meteorology is given. Different (both previously known in the literature and first presented) formulations of the equation of helicity balance in atmospheric motions (including those with allowance for effects of air compressibility and Earth's rotation) are brought together. Equations and relationships are given which are valid in different approximations accepted in dynamic meteorology: Boussinesq approximation, quasi-static approximation, and quasi-geostrophic approximation. Emphasis is placed on the analysis of helicity budget in large-scale quasi-geostrophic systems of motion; a formula for the helicity flux across the upper boundary of the nonlinear Ekman boundary layer is given, and this flux is shown to be exactly compensated for by the helicity destruction inside the Ekman boundary layer.

A new hydrodynamic analysis of double layers

NASA Technical Reports Server (NTRS)

Hora, Heinrich

1987-01-01

A genuine two-fluid model of plasmas with collisions permits the calculation of dynamic (not necessarily static) electric fields and double layers inside of plasmas including oscillations and damping. For the first time a macroscopic model for coupling of electromagnetic and Langmuir waves was achieved with realistic damping. Starting points were laser-produced plasmas showing very high dynamic electric fields in nonlinear force-produced cavitous and inverted double layers in agreement with experiments. Applications for any inhomogeneous plasma as in laboratory or in astrophysical plasmas can then be followed up by a transparent hydrodynamic description. Results are the rotation of plasmas in magnetic fields and a new second harmonic resonance, explanation of the measured inverted double layers, explanation of the observed density-independent, second harmonics emission from laser-produced plasmas, and a laser acceleration scheme by the very high fields of the double layers.

Hybrid Wing Body Model Identification Using Forced-Oscillation Water Tunnel Data

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.; Vicroy, Dan D.; Kramer, Brian; Kerho, Michael

2014-01-01

Static and dynamic testing of the NASA 0.7 percent scale Hybrid Wing Body (HWB) configuration was conducted in the Rolling Hills Research Corporation water tunnel to investigate aerodynamic behavior over a large range of angle-of-attack and to develop models that can predict aircraft response in nonlinear unsteady flight regimes. This paper reports primarily on the longitudinal axis results. Flow visualization tests were also performed. These tests provide additional static data and new dynamic data that complement tests conducted at NASA Langley 14- by 22-Foot Subsonic Tunnel. HWB was developed to support the NASA Environmentally Responsible Aviation Project goals of lower noise, emissions, and fuel burn. This study also supports the NASA Aviation Safety Program efforts to model and control advanced transport configurations in loss-of-control conditions.

Continuum Modeling of Inductor Hysteresis and Eddy Current Loss Effects in Resonant Circuits

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

Pries, Jason L.; Tang, Lixin; Burress, Timothy A.

This paper presents experimental validation of a high-fidelity toroid inductor modeling technique. The aim of this research is to accurately model the instantaneous magnetization state and core losses in ferromagnetic materials. Quasi–static hysteresis effects are captured using a Preisach model. Eddy currents are included by coupling the associated quasi-static Everett function to a simple finite element model representing the inductor cross sectional area. The modeling technique is validated against the nonlinear frequency response from two different series RLC resonant circuits using inductors made of electrical steel and soft ferrite. The method is shown to accurately model shifts in resonant frequencymore » and quality factor. The technique also successfully predicts a discontinuity in the frequency response of the ferrite inductor resonant circuit.« less

Summary of Research Report

NASA Technical Reports Server (NTRS)

Elishakoff, Isaac

1998-01-01

Ten papers, published in various publications, on buckling, and the effects of imperfections on various structures are presented. These papers are: (1) Buckling mode localization in elastic plates due to misplacement in the stiffner location; (2) On vibrational imperfection sensitivity on Augusti's model structure in the vicinity of a non-linear static state; (3) Imperfection sensitivity due to elastic moduli in the Roorda Koiter frame; (4) Buckling mode localization in a multi-span periodic structure with a disorder in a single span; (5) Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling; (6) Derivation of multi-dimensional ellipsoidal convex model for experimental data; (7) Passive control of buckling deformation via Anderson localization phenomenon; (8)Effect of the thickness and initial im perfection on buckling on composite cylindrical shells: asymptotic analysis and numerical results by BOSOR4 and PANDA2; (9) Worst case estimation of homology design by convex analysis; (10) Buckling of structures with uncertain imperfections - Personal perspective.

Towards an Aero-Propulso-Servo-Elasticity Analysis of a Commercial Supersonic Transport

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George; Chwalowski, Pawel; Sanetrik, Mark D.; Carlson, Jan-Renee; Silva, Walt A.; McNamara, Jack

2016-01-01

This paper covers the development of an aero-propulso-servo-elastic (APSE) model using computational fluid dynamics (CFD) and linear structural deformations. The APSE model provides the integration of the following two previously developed nonlinear dynamic simulations: a variable cycle turbofan engine and an elastic supersonic commercial transport vehicle. The primary focus of this study is to provide a means to include relevant dynamics of a turbomachinery propulsion system into the aeroelastic studies conducted during a vehicle design, which have historically neglected propulsion effects. A high fidelity CFD tool is used here for the integration platform. The elastic vehicle neglecting the propulsion system serves as a comparison of traditional approaches to the APSE results. An overview of the methodology is presented for integrating the propulsion system and elastic vehicle. Static aeroelastic analysis comparisons between the traditional and developed APSE models for a wing tip detection indicate that the propulsion system impact on the vehicle elastic response could increase the detection by approximately ten percent.

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 1: Theoretical manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1991-01-01

Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.

An atomic finite element model for biodegradable polymers. Part 1. Formulation of the finite elements.

PubMed

Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David

2015-11-01

Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide). Copyright © 2015 Elsevier Ltd. All rights reserved.

Nonlinear vibration of a hemispherical dome under external water pressure

NASA Astrophysics Data System (ADS)

Ross, C. T. F.; McLennan, A.; Little, A. P. F.

2011-07-01

The aim of this study was to analyse the behaviour of a hemi-spherical dome when vibrated under external water pressure, using the commercial computer package ANSYS 11.0. In order to achieve this aim, the dome was modelled and vibrated in air and then in water, before finally being vibrated under external water pressure. The results collected during each of the analyses were compared to the previous studies, and this demonstrated that ANSYS was a suitable program and produced accurate results for this type of analysis, together with excellent graphical displays. The analysis under external water pressure, clearly demonstrated that as external water pressure was increased, the resonant frequencies decreased and a type of dynamic buckling became likely; because the static buckling eigenmode was similar to the vibration eigenmode. ANSYS compared favourably with the in-house software, but had the advantage that it produced graphical displays. This also led to the identification of previously undetected meridional modes of vibration; which were not detected with the in-house software.

Effect of functionalization of boron nitride flakes by main group metal clusters on their optoelectronic properties

NASA Astrophysics Data System (ADS)

Chakraborty, Debdutta; Chattaraj, Pratim Kumar

2017-10-01

The possibility of functionalizing boron nitride flakes (BNFs) with some selected main group metal clusters, viz. OLi4, NLi5, CLi6, BLI7 and Al12Be, has been analyzed with the aid of density functional theory (DFT) based computations. Thermochemical as well as energetic considerations suggest that all the metal clusters interact with the BNF moiety in a favorable fashion. As a result of functionalization, the static (first) hyperpolarizability (β ) values of the metal cluster supported BNF moieties increase quite significantly as compared to that in the case of pristine BNF. Time dependent DFT analysis reveals that the metal clusters can lower the transition energies associated with the dominant electronic transitions quite significantly thereby enabling the metal cluster supported BNF moieties to exhibit significant non-linear optical activity. Moreover, the studied systems demonstrate broad band absorption capability spanning the UV-visible as well as infra-red domains. Energy decomposition analysis reveals that the electrostatic interactions principally stabilize the metal cluster supported BNF moieties.

Effect of functionalization of boron nitride flakes by main group metal clusters on their optoelectronic properties.

PubMed

Chakraborty, Debdutta; Chattaraj, Pratim Kumar

2017-10-25

The possibility of functionalizing boron nitride flakes (BNFs) with some selected main group metal clusters, viz. OLi 4 , NLi 5 , CLi 6 , BLI 7 and Al 12 Be, has been analyzed with the aid of density functional theory (DFT) based computations. Thermochemical as well as energetic considerations suggest that all the metal clusters interact with the BNF moiety in a favorable fashion. As a result of functionalization, the static (first) hyperpolarizability ([Formula: see text]) values of the metal cluster supported BNF moieties increase quite significantly as compared to that in the case of pristine BNF. Time dependent DFT analysis reveals that the metal clusters can lower the transition energies associated with the dominant electronic transitions quite significantly thereby enabling the metal cluster supported BNF moieties to exhibit significant non-linear optical activity. Moreover, the studied systems demonstrate broad band absorption capability spanning the UV-visible as well as infra-red domains. Energy decomposition analysis reveals that the electrostatic interactions principally stabilize the metal cluster supported BNF moieties.

Space Vehicle Pose Estimation via Optical Correlation and Nonlinear Estimation

NASA Technical Reports Server (NTRS)

Rakoczy, John M.; Herren, Kenneth A.

2008-01-01

A technique for 6-degree-of-freedom (6DOF) pose estimation of space vehicles is being developed. This technique draws upon recent developments in implementing optical correlation measurements in a nonlinear estimator, which relates the optical correlation measurements to the pose states (orientation and position). For the optical correlator, the use of both conjugate filters and binary, phase-only filters in the design of synthetic discriminant function (SDF) filters is explored. A static neural network is trained a priori and used as the nonlinear estimator. New commercial animation and image rendering software is exploited to design the SDF filters and to generate a large filter set with which to train the neural network. The technique is applied to pose estimation for rendezvous and docking of free-flying spacecraft and to terrestrial surface mobility systems for NASA's Vision for Space Exploration. Quantitative pose estimation performance will be reported. Advantages and disadvantages of the implementation of this technique are discussed.

Investigation of the linear and second-order nonlinear optical properties of molecular crystals within the local field theory.

PubMed

Seidler, Tomasz; Stadnicka, Katarzyna; Champagne, Benoît

2013-09-21

In this paper it is shown that modest calculations combining first principles evaluations of the molecular properties with electrostatic interaction schemes to account for the crystal environment effects are reliable for predicting and interpreting the experimentally measured electric linear and second-order nonlinear optical susceptibilities of molecular crystals within the experimental error bars. This is illustrated by considering two molecular crystals, namely: 2-methyl-4-nitroaniline and 4-(N,N-dimethylamino)-3-acetamidonitrobenzene. Three types of surrounding effects should be accounted for (i) the polarization due to the surrounding molecules, described here by static electric fields originating from their electric dipoles or charge distributions, (ii) the intermolecular interactions, which affect the geometry and particularly the molecular conformation, and (iii) the screening of the external electric field by the constitutive molecules. This study further highlights the role of electron correlation on the linear and nonlinear responses of molecular crystals and the challenge of describing frequency dispersion.

Dark energy and modified gravity in the Effective Field Theory of Large-Scale Structure

NASA Astrophysics Data System (ADS)

Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo

2018-04-01

We develop an approach to compute observables beyond the linear regime of dark matter perturbations for general dark energy and modified gravity models. We do so by combining the Effective Field Theory of Dark Energy and Effective Field Theory of Large-Scale Structure approaches. In particular, we parametrize the linear and nonlinear effects of dark energy on dark matter clustering in terms of the Lagrangian terms introduced in a companion paper [1], focusing on Horndeski theories and assuming the quasi-static approximation. The Euler equation for dark matter is sourced, via the Newtonian potential, by new nonlinear vertices due to modified gravity and, as in the pure dark matter case, by the effects of short-scale physics in the form of the divergence of an effective stress tensor. The effective fluid introduces a counterterm in the solution to the matter continuity and Euler equations, which allows a controlled expansion of clustering statistics on mildly nonlinear scales. We use this setup to compute the one-loop dark-matter power spectrum.

Space Vehicle Pose Estimation via Optical Correlation and Nonlinear Estimation

NASA Technical Reports Server (NTRS)

Rakoczy, John; Herren, Kenneth

2007-01-01

A technique for 6-degree-of-freedom (6DOF) pose estimation of space vehicles is being developed. This technique draws upon recent developments in implementing optical correlation measurements in a nonlinear estimator, which relates the optical correlation measurements to the pose states (orientation and position). For the optical correlator, the use of both conjugate filters and binary, phase-only filters in the design of synthetic discriminant function (SDF) filters is explored. A static neural network is trained a priori and used as the nonlinear estimator. New commercial animation and image rendering software is exploited to design the SDF filters and to generate a large filter set with which to train the neural network. The technique is applied to pose estimation for rendezvous and docking of free-flying spacecraft and to terrestrial surface mobility systems for NASA's Vision for Space Exploration. Quantitative pose estimation performance will be reported. Advantages and disadvantages of the implementation of this technique are discussed.

Swept optical SSB-SC modulation technique for high-resolution large-dynamic-range static strain measurement using FBG-FP sensors.

PubMed

Huang, Wenzhu; Zhang, Wentao; Li, Fang

2015-04-01

This Letter presents a static strain demodulation technique for FBG-FP sensors using a suppressed carrier LiNbO(3) (LN) optical single sideband (SSB-SC) modulator. A narrow-linewidth tunable laser source is generated by driving the modulator using a linear chirp signal. Then this tunable single-frequency laser is used to interrogate the FBG-FP sensors with the Pound-Drever-Hall (PDH) technique, which is beneficial to eliminate the influence of light intensity fluctuation of the modulator at different tuning frequencies. The static strain is demodulated by calculating the wavelength difference of the PDH signals between the sensing FBG-FP sensor and the reference FBG-FP sensor. As an experimental result using the modulator, the linearity (R²) of the time-frequency response increases from 0.989 to 0.997, and the frequency-swept range (dynamic range) increases from hundreds of MHz to several GHz compared with commercial PZT-tunable lasers. The high-linearity time-wavelength relationship of the modulator is beneficial for improving the strain measurement resolution, as it can solve the problem of the frequency-swept nonlinearity effectively. In the laboratory test, a 0.67 nanostrain static strain resolution, with a 6 GHz dynamic range, is demonstrated.

MHD Simulation for Investigating the Dynamic State Transition Responsible for a Solar Eruption in Active Region 12158

NASA Astrophysics Data System (ADS)

Lee, Hwanhee; Magara, Tetsuya

2018-06-01

We present a magnetohydrodynamic model of solar eruption based on the dynamic state transition from the quasi-static state to the eruptive state of an active region (AR) magnetic field. For the quasi-static state before an eruption, we consider the existence of a slow solar wind originating from an AR, which may continuously make the AR magnetic field deviate from mechanical equilibrium. In this model, we perform a three-dimensional magnetohydrodynamic simulation of AR 12158 producing a coronal mass ejection, where the initial magnetic structure of the simulation is given by a nonlinear force-free field derived from an observed photospheric vector magnetic field. We then apply a pressure-driven outflow to the upper part of the magnetic structure to achieve a quasi-static pre-eruptive state. The simulation shows that the eruptive process observed in this AR may be caused by the dynamic state transition of an AR magnetic field, which is essentially different from the destabilization of a static magnetic field. The dynamic state transition is determined from the shape evolution of the magnetic field line according to the κH-mechanism. This work demonstrates how the mechanism works to produce a solar eruption in the dynamic solar corona governed by the gravitational field and the continuous outflows of solar wind.

Vector form Intrinsic Finite Element Method for the Two-Dimensional Analysis of Marine Risers with Large Deformations

NASA Astrophysics Data System (ADS)

Li, Xiaomin; Guo, Xueli; Guo, Haiyan

2018-06-01

Robust numerical models that describe the complex behaviors of risers are needed because these constitute dynamically sensitive systems. This paper presents a simple and efficient algorithm for the nonlinear static and dynamic analyses of marine risers. The proposed approach uses the vector form intrinsic finite element (VFIFE) method, which is based on vector mechanics theory and numerical calculation. In this method, the risers are described by a set of particles directly governed by Newton's second law and are connected by weightless elements that can only resist internal forces. The method does not require the integration of the stiffness matrix, nor does it need iterations to solve the governing equations. Due to these advantages, the method can easily increase or decrease the element and change the boundary conditions, thus representing an innovative concept of solving nonlinear behaviors, such as large deformation and large displacement. To prove the feasibility of the VFIFE method in the analysis of the risers, rigid and flexible risers belonging to two different categories of marine risers, which usually have differences in modeling and solving methods, are employed in the present study. In the analysis, the plane beam element is adopted in the simulation of interaction forces between the particles and the axial force, shear force, and bending moment are also considered. The results are compared with the conventional finite element method (FEM) and those reported in the related literature. The findings revealed that both the rigid and flexible risers could be modeled in a similar unified analysis model and that the VFIFE method is feasible for solving problems related to the complex behaviors of marine risers.

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

Large Angle Transient Dynamics (LATDYN) user's manual

NASA Technical Reports Server (NTRS)

Abrahamson, A. Louis; Chang, Che-Wei; Powell, Michael G.; Wu, Shih-Chin; Bingel, Bradford D.; Theophilos, Paula M.

1991-01-01

A computer code for modeling the large angle transient dynamics (LATDYN) of structures was developed to investigate techniques for analyzing flexible deformation and control/structure interaction problems associated with large angular motions of spacecraft. This type of analysis is beyond the routine capability of conventional analytical tools without simplifying assumptions. In some instances, the motion may be sufficiently slow and the spacecraft (or component) sufficiently rigid to simplify analyses of dynamics and controls by making pseudo-static and/or rigid body assumptions. The LATDYN introduces a new approach to the problem by combining finite element structural analysis, multi-body dynamics, and control system analysis in a single tool. It includes a type of finite element that can deform and rotate through large angles at the same time, and which can be connected to other finite elements either rigidly or through mechanical joints. The LATDYN also provides symbolic capabilities for modeling control systems which are interfaced directly with the finite element structural model. Thus, the nonlinear equations representing the structural model are integrated along with the equations representing sensors, processing, and controls as a coupled system.