A new beam element for analyzing geometrical and physical nonlinearity
NASA Astrophysics Data System (ADS)
Wang, Xiao-Feng; Yang, Qing-Shan; Zhang, Qi-Lin
2010-08-01
Based on Timoshenko’s beam theory and Vlasov’s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange ( UL) and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.
NASA Astrophysics Data System (ADS)
StojanoviÄ‡, Vladimir
2015-11-01
Geometrically nonlinear vibrations of a Timoshenko beam resting on a nonlinear Winkler and Pasternak elastic foundation with variable discontinuity are investigated in this paper. A p-version finite element method is developed for geometric nonlinear vibrations of a shear deformable beam resting on a nonlinear foundation with discontinuity. The elastic foundation has cubic nonlinearity with the shearing layer. In the study the p-element which comes from the use of explored special displacement shape functions for damaged beams is used and applied to a model with nonlinear foundation. The novelty of the present study lies in the easy generalisation of the approach of natural frequencies, general mode shapes (transverse and rotations of cross sections), and maximal deflections in nonlinear steady state vibrations of the shear deformable beam for any size and location of discontinuity of the nonlinear elastic support. A new set of nonlinear partial differential equations is developed, and they are solved in the time domain using the Newmark method for obtaining the amplitudes and deformed shapes of a beam in the steady state forced vibration regime. The present work consists of the comparison of the results with various stiffnesses of nonlinear elastic supports of the Winkler and Pasternak type.
NASA Astrophysics Data System (ADS)
Rahmouni, A.; Beidouri, Z.; Benamar, R.
2013-09-01
The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the previously developed models of geometrically nonlinear vibrations of Euler-Bernoulli continuous beams, and multidof system models made of N masses placed at the end of elastic bars connected by linear spiral springs, presenting the beam flexural rigidity. The validation of the new model via the analysis of the convergence conditions of the nonlinear frequencies obtained by the N-dof system, when N increases, and those obtained in previous works using a continuous description of the beam. In addition to the above points, the models developed in the present work, may constitute, in our opinion, a good illustration, from the didactic point of view, of the origin of the geometrical nonlinearity induced by large transverse vibration amplitudes of constrained continuous beams, which may appear as a Pythagorean Theorem effect. The first step of the work presented here was the formulation of the problem of nonlinear vibrations of the discrete system shown in Fig. 1 in terms of the semi-analytical method, denoted as SAA, developed in the early 90's by Benamar and coauthors [3], and discussed for example in [6,7]. This method has been applied successfully to various types of geometrically nonlinear problems of structural dynamics [1-3,6-8,10-12] and the objective here was to use it in order to develop a flexible discrete nonlinear model which may be useful for presenting in further works geometrically nonlinear vibrations of real beams with discontinuities in the mass, the section, or the stiffness distributions. The purpose in the present work was restricted to developing and validating the model, via comparison of the obtained dependence of the resonance frequencies of such a system on the amplitude of vibration, with the results obtained previously by continuous beams nonlinear models. In the SAA method, the dynamic system under consideration is described by the mass matrix [M], the rigidity matrix [K], and the nonlinear rigidity matrix [B], which depends on the amplitude of vibration, and involves a fourth-order nonlinearity tensor bijkl. Details are given below, co
Geometrically nonlinear analysis of cross-ply composite beams under transverse loading
NASA Astrophysics Data System (ADS)
Chandrashekhara, K.; Bangera, Kiran M.
The flexural analysis of fiber reinforced composite beams based on a higher-order shear deformation theory is investigated. The geometric nonlinearity is incorporated in the formulation by considering the von Karman strains. The finite element method is used to solve the nonlinear governing equations by direct iteration. Numerical results are presented for symmetrically and unsymmetrically laminated cross-ply beams for various boundary conditions. Compared to the first-order shear deformation theory, the present theory predicts the deflections more accurately, eliminates the need for reduced integration of the shear stiffness terms and does not require shear correction factors.
System level simulation of a micro resonant accelerometer with geometric nonlinear beams
NASA Astrophysics Data System (ADS)
Wenlong, Jiao; Weizheng, Yuan; Honglong, Chang
2015-10-01
Geometric nonlinear behaviors of micro resonators have attracted extensive attention of MEMS (micro-electro-mechanical systems) researchers, and MEMS transducers utilizing these behaviors have been widely researched and used due to the advantages of essentially digital output. Currently, the design of transducers with nonlinear behaviors is mainly performed by numerical method and rarely by system level design method. In this paper, the geometric nonlinear beam structure was modeled and established as a reusable library component by system level modeling and simulation method MuPEN (multi port element network). A resonant accelerometer was constructed and simulated using this model together with MuPEN reusable library. The AC (alternating current) analysis results of MuPEN model agreed well with the results of architect model and the experiment results shown in the existing reference. Therefore, we are convinced that the beam component based on MuPEN method is valid, and MEMS system level design method and related libraries can effectively model and simulate transducers with geometric nonlinear behaviors if appropriate system level components are available.
Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.
Camarena, Francisco; AdriÃ¡n-MartÃnez, Silvia; JimÃ©nez, NoÃ©; SÃ¡nchez-Morcillo, VÃctor
2013-08-01
The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation. PMID:23927186
NASA Astrophysics Data System (ADS)
Ribeiro, P.; van der Heijden, G. H. M.
2009-08-01
A model based on a Timoshenko beam p-version finite element is developed to analyse oscillations that are, simultaneously, elasto-plastic and geometrically nonlinear. The geometrical nonlinearity is represented by Von Kármán type strain-displacement relations and the stress-strain relation is of the bilinear type, with mixed strain hardening. The equations of motion are obtained using the principle of virtual work and are solved in the time domain by an implicit Newmark method. The Von Mises yield criterion is employed and the flow theory of plasticity applied; if plastic flow is found at a point of the domain, the total plastic strain is determined by summation. Numerical examples are carried out in order to demonstrate that the p-version element here advocated has a number of advantages and to show the influence of the plastic and geometrically nonlinear terms on the oscillations of beams.
NASA Astrophysics Data System (ADS)
Al-Qaisia, A. A.; Hamdan, M. N.
2013-09-01
This work presents an investigation on the effect of an initial geometric imperfection wavelength, amplitude and degree of localization on the in-plane nonlinear natural frequencies veering and mode localization of an elastic Euler-Bernoulli beam resting on a Winkler elastic foundation. The beam is assumed to be pinned-pinned with a linear torsional spring at one end. The effect of the axial force induced by mid-plane stretching is accounted for in the derivation of the mathematical model, due to its known importance and significant effect on the nonlinear dynamic behavior of the beam, as it was proved and presented in earlier investigations. The governing partial differential equation is discretized using the assumed mode method and the resulting nonlinear temporal equation was solved using the harmonic balance method to obtain results for the nonlinear natural frequencies and mode shapes. The results are presented in the form of characteristic curves which show the variations of the nonlinear natural frequencies of the first three modes of vibration, for a selected range of physical parameters like; torsional spring constant, elastic foundation stiffness and amplitude and wavelength of a localized and non-localized initial slack.
The geometric phase in nonlinear dissipative systems
Ning, C.Z.; Haken, H. )
1992-10-30
In this paper, the authors review the recent progress made in generalizing the concept of the geometric phase to nonlinear dissipative systems. The authors first illustrate the usual form of the parallel transport law with an elementary example of the parallel shift of a line on the complex plane. Important results about the non-adiabatical geometric (Aharonov and Anandan or AA) phase [sup 18] for the Schrodinger equations are reviewed in order to make a comparison with results for dissipative systems. The authors show that a geometric phase can be defined for dissipative systems with the cyclic attractors. Systems undergoing the Hopf bifurcation with a continuous symmetry are shown to possess such cyclic attractors. Examples from laser physics are discussed to exhibit the applicability of our formalism and the widespread existence of the geometric phase in dissipative systems.
Geometric non-linear hexahedral elements with rotational DOFs
NASA Astrophysics Data System (ADS)
Meftah, Kamel; Zouari, Wajdi; Sedira, Lakhdar; Ayad, Rezak
2015-11-01
This paper presents an extension of two recently published conforming and non conforming eight-node hexahedral finite elements, presenting rotational degrees of freedom in addition to the classical displacement ones, to analyze geometric nonlinear problems. Their formulations are based on the so-called space fiber rotation concept that considers virtual rotations of a nodal fiber within the element which enhances the displacement vector approximation. To demonstrate the efficiency and accuracy of the proposed finite elements, several beam and shell nonlinear assessment tests are presented and the obtained results are principally compared with the classical first-order and second-order hexahedral elements responses as well as other advanced elements from the literature. In particular, it is shown that the proposed elements allow a correct prediction of the studied structures nonlinear behaviors including snap-through and snap-back instabilities and the accuracy of the non conforming element is close to the classical 20-node hexahedral element.
Geometric non-linear hexahedral elements with rotational DOFs
NASA Astrophysics Data System (ADS)
Meftah, Kamel; Zouari, Wajdi; Sedira, Lakhdar; Ayad, Rezak
2016-01-01
This paper presents an extension of two recently published conforming and non conforming eight-node hexahedral finite elements, presenting rotational degrees of freedom in addition to the classical displacement ones, to analyze geometric nonlinear problems. Their formulations are based on the so-called space fiber rotation concept that considers virtual rotations of a nodal fiber within the element which enhances the displacement vector approximation. To demonstrate the efficiency and accuracy of the proposed finite elements, several beam and shell nonlinear assessment tests are presented and the obtained results are principally compared with the classical first-order and second-order hexahedral elements responses as well as other advanced elements from the literature. In particular, it is shown that the proposed elements allow a correct prediction of the studied structures nonlinear behaviors including snap-through and snap-back instabilities and the accuracy of the non conforming element is close to the classical 20-node hexahedral element.
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; Allen, Matthew S.
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 nonlinear 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 clampedâ€“clamped beam model, and a more complicated finite element model of an exhaust panel cover.
Nonlinear Geometric Effects in Bioinspired Multistable Structures
NASA Astrophysics Data System (ADS)
Chen, Zi; Guo, Qiaohang; Chu, Kevin; Shillig, Steven; Li, Chi; Chen, Wenzhe; Taber, Larry; Holmes, Douglas
2013-03-01
Nature features many thin shell structures with spontaneous curvatures, where mechanical instabilities play important roles in the morphogenesis and functioning of the organisms. However, the large deformation and instability phenomena of shells due to geometric nonlinearity, which often arise in morphogenesis and nanofabrication, remain incompletely understood. Here, we create spontaneously curved shapes with pre-strains in tabletop experiments, and study their instabilities with a minimal theory based on linear elasticity. The development of such theoretical and experimental approaches will promote quantitative understanding of the morphogenesis of growing soft tissues, and meet the emergent needs of designing stretchable electronics, artificial muscles and bio-inspired robots. Zi Chen and Qiaohang Guo contributed equally. This work was supported by National Science Foundation of China (No. 11102040), American Academy of Mechanics Founder's Award, and Society in Science - Branco Weiss fellowship, administered by ETH.
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; Allen, Matthew S.
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 nonlinearmoreÂ Â» 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 clampedâ€“clamped beam model, and a more complicated finite element model of an exhaust panel cover.Â«Â less
Geometrical nonlinear behaviour of orthogonally stiffened cylindrical shells
NASA Astrophysics Data System (ADS)
Ghavami, K.; Silveira, R. A. M.
This paper describes an analytical method to predict the large deflection behavior of orthogonally stiffened cylindrical shells subjected to lateral pressure and/or to a combination of lateral and axial load in elastic range, having different types of boundary conditions. In this method, the stiffeners are considered to be beam-column and curved beam elements for longitudinal and transversal stiffeners, respectively. The influences of the stiffeners are incorporated into the equilibrium equations of shell element by considering the compatibility between the shell and the stiffener elements. All equations are developed in finite difference method. For the solution of the geometrical nonlinearity, a combined incremental-iterative formulation is applied. The data obtained from the computer program correlates satisfactorily with those from the alternative method of analysis.
Nonlinear combining of laser beams.
Lushnikov, Pavel M; Vladimirova, Natalia
2014-06-15
We propose to combine multiple laser beams into a single diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. Beams with total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with Kerr nonlinearity. Random fluctuations during propagation eventually trigger a strong self-focusing event and produce a diffraction-limited beam carrying the critical power. PMID:24978503
Geometrical approach to gaussian beam propagation.
Laures, P
1967-04-01
The curvature of the wavefront and the spot size of a propagating Gaussian beam may be determined from simple geometrical transformations of the lateral foci. The analysis starts from the construction of the lateral foci in the case of a spherical Fabry-Perot. Then the cases of Gaussian beam propagation through media with different refractive indices, lenses, and simple optical systems are treated. Constructions show how propagation in the image space is readily determined in each case. This analysis is the generalization of the technique outlined by Deschamps and Mast. The geometrical constructions developed for simple cases are applied to the design of some special cases of interest in laser optics: cavities by a lens, laser zoom telescope, and ring cavity. PMID:20057839
Nonlinear lattices generated from harmonic lattices with geometric constraints
NASA Astrophysics Data System (ADS)
Takeno, S.; Dmitriev, S. V.; Kevrekidis, P. G.; Bishop, A. R.
2005-01-01
Geometrical constraints imposed on higher-dimensional harmonic lattices generally lead to nonlinear dynamical lattice models. Helical lattices obtained by such a procedure are shown to be described by sine- plus linear-lattice equations. The interplay between sinusoidal and quadratic potential terms in such models is shown to yield localized nonlinear modes identified as intrinsic resonant modes.
GAMNAS- GEOMETRIC AND MATERIAL NONLINEAR ANALYSIS OF STRUCTURES
NASA Technical Reports Server (NTRS)
Whitcomb, J. D.
1994-01-01
GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two-dimensional finite element stress analysis program developed to support fracture mechanics studies of debonding and delamination. GAMNAS options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. GAMNAS can analyze plastic deformations of isotropic materials. GAMNAS can calculate strain energy release rates using a virtual crack extension technique. The element available to the GAMMNAS user is a four-node isoparametric quadrilateral with full or reduced integration. GAMNAS has been used to investigate debonding and delamination of adhesively bonded composites. GAMNAS is written in FORTRAN 77 for batch execution and has been implemented on a PRIME 700 series computer. As currently dimensioned for a maximum global stiffness matrix of 1300 degrees of freedom and a bandwidth of 70, GAMNAS has a central memory requirement of approximately 603K of 16 bit words. GAMNAS was developed in 1983.
Bounding solutions of geometrically nonlinear viscoelastic problems
NASA Technical Reports Server (NTRS)
Stubstad, J. M.; Simitses, G. J.
1986-01-01
Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.
Bounding solutions of geometrically nonlinear viscoelastic problems
NASA Technical Reports Server (NTRS)
Stubstad, J. M.; Simitses, G. J.
1985-01-01
Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.
Influence of geometric nonlinearities on skin-stiffener interface stresses
NASA Technical Reports Server (NTRS)
Cohen, D.; Hyer, M. W.
1988-01-01
A method for computing skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The results indicate that the inclusion of geometric nonlinearities is very important for an accurate determination of the interface stresses. Membrane flattening of the panel tends to reduce the tendency of the stiffener to separate.
Geometrical interpretation of nonlinearities from a cylindrical pick-up
Miyamoto, R.; Kopp, S.E.; Jansson, A.; Syphers, M.J.; /Fermilab
2007-06-01
In many accelerators, cylindrical pick-ups are used to measure transverse beam positions. Theoretically, signals from these pick-ups are related to infinite power series of the beam position but, in practice, only finite number of terms are considered and the position measurements degrade when a beam is far from the center of a pick-up. This paper shows there is actually a simple geometrical relation between a beam position and induced signals. With help of the geometrical relation, the beam position can be written in a compact function of signals. The paper is concluded with numerical simulations and a test to show this geometry based expression can calculate a beam position better than the conventional methods.
Geometrically nonlinear analysis of laminated elastic structures
NASA Technical Reports Server (NTRS)
Reddy, J. N.; Chandrashekhara, K.; Chao, W. C.
1993-01-01
This final technical report contains three parts: Part 1 deals with the 2-D shell theory and its element formulation and applications. Part 2 deals with the 3-D degenerated element. These two parts constitute the two major tasks that were completed under the grant. Another related topic that was initiated during the present investigation is the development of a nonlinear material model. This topic is briefly discussed in Part 3. To make each part self-contained, conclusions and references are included in each part. In the interest of brevity, the discussions presented are relatively brief. The details and additional topics are described in the references cited.
NASA Technical Reports Server (NTRS)
Peterson, D.
1979-01-01
Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.
Resonant Nonlinear Geometric Optics for Weak Solutions of Conservation Laws
NASA Astrophysics Data System (ADS)
Schochet, S.
The O(?) part of solutions obtained via Glimm's scheme of strictly hyperbolic conservation laws with O(?) periodic BV initial data is shown to tend as ? ? 0 to the unique entropy solution of the modulation equations of weakly nonlinear geometric optics derived by Majda and Rosales.
User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures
NASA Technical Reports Server (NTRS)
Whitcomb, J. D.; Dattaguru, B.
1984-01-01
GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.
Auto-focusing accelerating hyper-geometric laser beams
NASA Astrophysics Data System (ADS)
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-02-01
We derive a new solution to the paraxial wave equation that defines a two-parameter family of three-dimensional structurally stable vortex annular auto-focusing hyper-geometric (AH) beams, with their complex amplitude expressed via a degenerate hyper-geometric function. The AH beams are found to carry an orbital angular momentum and be auto-focusing, propagating on an accelerating path toward a focus, where the annular intensity pattern is â€˜sharplyâ€™ reduced in diameter. An explicit expression for the complex amplitude of vortex annular auto-focusing hyper-geometric-Gaussian beams is derived. The experiment has been shown to be in good agreement with theory.
NASTRAN nonlinear vibration analysis of beam and frame structures
NASA Technical Reports Server (NTRS)
Mei, C.; Rogers, J. L., Jr.
1975-01-01
A capability for the nonlinear vibration analysis of beam and frame structures suitable for use with NASTRAN level 15.5 is described. The nonlinearity considered is due to the presence of axial loads induced by longitudinal end restraints and lateral displacements that are large compared to the beam height. A brief discussion is included of the mathematical analysis and the geometrical stiffness matrix for a prismatic beam (BAR) element. Also included are a brief discussion of the equivalent linearization iterative process used to determine the nonlinear frequency, the required modifications to subroutines DBAR and XMPLBD of the NASTRAN code, and the appropriate vibration capability, four example problems are presented. Comparisons with existing experimental and analytical results show that excellent accuracy is achieved with NASTRAN in all cases.
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.
Numerical treatment of a geometrically nonlinear planar Cosserat shell model
NASA Astrophysics Data System (ADS)
Sander, Oliver; Neff, Patrizio; BÃ®rsan, Mircea
2016-02-01
We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general six-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements (GFEs), which leads to an objective discrete model which naturally allows arbitrarily large rotations. GFEs of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton's method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkling of thin elastic sheets in shear.
Geometric Nonlinear Finite Element Analysis of Active Fibre Composite Bimorphs
NASA Astrophysics Data System (ADS)
Kernaghan, Robert
Active fibre composite-actuated bimorphic actuators were studied in order to measure deflection performance. The deflection of the actuators was a function of the actuating electric potential applied to the active material as well as the magnitude of the axial preload applied to the bimorphic structure. This problem required the use of geometric nonlinear modeling techniques. Geometric nonlinear finite element analysis was undertaken to determine the deflection performance of Macro Fibre Composite (MFC)- and Hollow Active Fibre (HAFC)-actuated bimorphic structures. A physical prototype MFC-actuated bimorphic structure was manufactured in order to verify the results obtained by the finite element analysis. Theses analyses determined that the bimorphic actuators were capable of significant deflection. The analyses determined that the axial preload of the bimorphic actuators significantly amplified the deflection performance of the bimorphic actuators. The deflection performance of the bimorphic actuators suggest that they could be candidates to act as actuators for the morphing wing of a micro unmanned air vehicle.
A survey of the core-congruential formulation for geometrically nonlinear TL finite elements
NASA Technical Reports Server (NTRS)
Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn
1994-01-01
This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.
Geometrically induced nonlinear dynamics in one-dimensional lattices
NASA Astrophysics Data System (ADS)
Hamilton, Merle D.; de Alcantara Bonfim, O. F.
2006-03-01
We present a lattice model consisting of a single one-dimensional chain, where the masses are interconnected by linear springs and allowed to move in a horizontal direction only, as in a monorail. In the transverse direction each mass is also attached to two other linear springs, one on each side of the mass. The ends of these springs are kept at fixed positions. The nonlinearity in the model arises from the geometric constraints imposed on the motion of the masses, as well as from the configuration of the springs, where in the transverse direction the springs are either in the extended or compressed state depending on the position of the masses. Under these conditions we show that solitary waves are present in the system. In the long wavelength limit an analytic solution for these nonlinear waves is found. Numerical integrations of the equations of motion in the full system are also performed to analyze the conditions for the existence and stability of the nonlinear waves.
Nonlinear flap-lag axial equations of a rotating beam
NASA Technical Reports Server (NTRS)
Kaza, K. R. V.; Kvaternik, R. G.
1977-01-01
It is possible to identify essentially four approaches by which analysts have established either the linear or nonlinear governing equations of motion for a particular problem related to the dynamics of rotating elastic bodies. The approaches include the effective applied load artifice in combination with a variational principle and the use of Newton's second law, written as D'Alembert's principle, applied to the deformed configuration. A third approach is a variational method in which nonlinear strain-displacement relations and a first-degree displacement field are used. The method introduced by Vigneron (1975) for deriving the linear flap-lag equations of a rotating beam constitutes the fourth approach. The reported investigation shows that all four approaches make use of the geometric nonlinear theory of elasticity. An alternative method for deriving the nonlinear coupled flap-lag-axial equations of motion is also discussed.
NASA Astrophysics Data System (ADS)
Wang, Dongwei
Recent research and development of adaptive materials, smart structures and structronic systems have opened a new era to aerospace and structural engineering. Effective control of these intelligent structures and systems using piezoelectric materials can enhance operation precision, accuracy and reliability. This research is to investigate the dynamics, vibration sensing and control of the geometrically nonlinear distributed piezothermoelastic structures subjected to the combined mechanical, electrical, and thermal excitations by the finite element method. Based on the layerwise constant shear angle theory, the curved hexahedral and triangular piezothermoelastic shell elements are proposed. The generic finite element formulations for vibration sensing and control analysis of nonlinear piezothermoelastic shell structures are derived based on the total Lagrangian virtual work principle. Dynamic system equations, equations of electric potential outputs, and feedback control forces are derived and discussed. The modified Newton-Raphson method is used for efficient dynamic analysis of the nonlinear piezothermoelastic structural systems. Different control algorithms are implemented. The feedback control forces generated from the distributed actuator can effectively enhance system damping and suppress system vibration via proper feedback control techniques. Comprehensive case studies are performed to evaluate the accuracy of the newly developed piezothermoelastic shell elements and to validate the finite element code. Dynamics and vibration sensing/control of nonlinear piezothermoelastic beam and plate systems are analyzed. Distributed piezoelectric films placed on the beam and plate structures respectively serving as sensor and actuators are discussed. The effect of geometric nonlinearity is to stiffen the beam and plate structures and the control effect becomes worse when geometric nonlinearity becomes significant. It shows that negative velocity control scheme is effective to dynamically and electrically induced oscillations. However, it is not effective to the vibrations induced by the steady-state thermal field. Accordingly, one additional control voltage is required to control thermally induced offset. The non-constant curvature structures such as conical shells and toroidal shells are also investigated in linear analysis. Various actuator layouts for these shell structures are proposed and the control effectiveness of the actuators is evaluated. It is suggested that an in-depth understanding of shell dynamics and dominating modes is a must in the effective design and layout of distributed actuators to maximize the distributed control effects.
Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections
NASA Technical Reports Server (NTRS)
Atilgan, Ali R.; Hodges, Dewey H.
1991-01-01
A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.
NASA Astrophysics Data System (ADS)
Song, Pengchao
Recent studies of the occurrence of post-flutter limit cycle oscillations (LCO) of the F-16 have provided good support to the long-standing hypothesis that this phenomenon involves a nonlinear structural damping. A potential mechanism for the appearance of nonlinearity in the damping are the nonlinear geometric effects that arise when the deformations become large enough to exceed the linear regime. In this light, the focus of this investigation is first on extending nonlinear reduced order modeling (ROM) methods to include viscoelasticity which is introduced here through a linear Kelvin-Voigt model in the undeformed configuration. Proceeding with a Galerkin approach, the ROM governing equations of motion are obtained and are found to be of a generalized van der Pol-Duffing form with parameters depending on the structure and the chosen basis functions. An identification approach of the nonlinear damping parameters is next proposed which is applicable to structures modeled within commercial finite element software. The effects of this nonlinear damping mechanism on the post-flutter response is next analyzed on the Goland wing through time-marching of the aeroelastic equations comprising a rational fraction approximation of the linear aerodynamic forces. It is indeed found that the nonlinearity in the damping can stabilize the unstable aerodynamics and lead to finite amplitude limit cycle oscillations even when the stiffness related nonlinear geometric effects are neglected. The incorporation of these latter effects in the model is found to further decrease the amplitude of LCO even though the dominant bending motions do not seem to stiffen as the level of displacements is increased in static analyses.
NASA Technical Reports Server (NTRS)
Muravyov, Alexander A.; Turner, Travis L.; Robinson, Jay H.; Rizzi, Stephen A.
1999-01-01
In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.
Hybrid analytical technique for the nonlinear analysis of curved beams
NASA Technical Reports Server (NTRS)
Noor, A. K.; Andersen, C. M.
1992-01-01
The application of a two-step hybrid technique to the geometrically nonlinear analysis of curved beams is used to demonstrate the potential of hybrid analytical techniques in nonlinear structural mechanics. The hybrid technique is based on successive use of the perturbation method and a classical direct variational procedure. The functions associated with the various-order terms in the perturbation expansion of the fundamental unknowns, and their sensitivity derivatives with respect to material and geometric parameters of the beam, are first obtained by using the perturbation method. These functions are selected as coordinate functions (or modes) and the classical direct variational technique is then used to compute their amplitudes. The potential of the proposed hybrid technique for nonlinear analysis of structures is discussed. The effectiveness of the hybrid technique is demonstrated by means of numerical examples. The symbolic computation system Mathematica is used in the present study. The tasks performed on Mathematica include: (1) generation of algebraic expressions for the perturbation functions of the different response quantities and their sensitivity derivatives: and (2) determination of the radius of convergence of the perturbation series.
Nonlinear analysis of a simply-supported composite beam under random excitations
Eslami, H.; Gudmundson, S.
1994-12-31
Nonlinear analysis of composite laminated beams subjected-to random excitation is studied here. The forcing function is a stationary Gaussian type random excitation. The governing partial differential equations of motion are obtained by considering the Von Karman type geometrical nonlinearity. These partial differential equations are transformed into nonlinear Ordinary differential equations of Duffing type by applying the Galerkin`s method. The resulting nonlinear ODE are first solved by using the equivalent linearization method and the numerical integration (Runge Kutta) method. The equations are reduced to that of isotropic beam and results are also compared with the previously published ones.
Effects of Inertial and Geometric Nonlinearities in the Simulation of Flexible Aircraft Dynamics
NASA Astrophysics Data System (ADS)
Bun Tse, Bosco Chun
This thesis examines the relative importance of the inertial and geometric nonlinearities in modelling the dynamics of a flexible aircraft. Inertial nonlinearities are derived by employing an exact definition of the velocity distribution and lead to coupling between the rigid body and elastic motions. The geometric nonlinearities are obtained by applying nonlinear theory of elasticity to the deformations. Peters' finite state unsteady aerodynamic model is used to evaluate the aerodynamic forces. Three approximate models obtained by excluding certain combinations of nonlinear terms are compared with that of the complete dynamics equations to obtain an indication of which terms are required for an accurate representation of the flexible aircraft behavior. A generic business jet model is used for the analysis. The results indicate that the nonlinear terms have a significant effect for more flexible aircraft, especially the geometric nonlinearities which leads to increased damping in the dynamics.
Beams on nonlinear elastic foundation
Lukkassen, Dag; Meidell, Annette
2014-12-10
In order to determination vertical deflections and rail bending moments the Winkler model (1867) is often used. This linear model neglects several conditions. For example, by using experimental results, it has been observed that there is a substantial increase in the maximum rail deflection and rail bending moment when considering the nonlinearity of the track support system. A deeper mathematical analysis of the models is necessary in order to obtain better methods for more accurate numerical solutions in the determination of deflections and rail bending moments. This paper is intended to be a small step in this direction.
Modeling of the vibrating beam accelerometer nonlinearities
NASA Astrophysics Data System (ADS)
Romanowski, P. A.; Knop, R. C.
Successful modeling and processing of the output of a quartz Vibrating Beam Accelerometer (VBA), whose errors are inherently nonlinear with respect to input acceleration, are reported. The VBA output, with two signals that are frequencies of vibrating quartz beams, has inherent higher-order terms. In order to avoid vibration rectification errors, the signal output must be sampled at a rapid rate and the output must be reduced using a nonlinear model. The present model, with acceleration as a function of frequency, is derived by a least-squares process where the covariance matrix is obtained from simulated data. The system performance is found to be acceptable to strategic levels, and it is shown that a vibration rectification error of 400 micrograms/sq g can be reduced to 4 micrograms/sq g by using the processor electronics and a nonlinear model.
Geometrically nonlinear dynamic response of stiffened plates with moving boundary conditions
NASA Astrophysics Data System (ADS)
Ma, NiuJing; Wang, RongHui; Han, Qiang; Lu, YiGang
2014-08-01
An approach is presented to investigate the nonlinear vibration of stiffened plates. A stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as Euler beams. Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system. Besides, the effect caused by boundary movement is transformed into equivalent excitations. The first approximation solution of the non-resonance is obtained by means of the method of multiple scales. The primary parametric resonance and primary resonance of the stiffened plate are studied by using the same method. The accuracy of the method is validated by comparing the results with those of finite element analysis via ANSYS. Numerical examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary resonance. In addition, the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried out. Some nonlinear vibration characteristics of stiffened plates are obtained, which are useful for engineering design.
Spiraling elliptic beam in nonlocal nonlinear media.
Liang, Guo; Guo, Qi; Cheng, Wenjing; Yin, Naiqiang; Wu, Ping; Cao, Hongmin
2015-09-21
Analytically discussed is the dynamical properties of the spiraling elliptic beams in nonlocal nonlinear media. This class of spiraling elliptic beams carry the orbital angular momentum (OAM), and can rotate on the cross section perpendicular to the propagation direction during the propagations. The optical intensity, the beam width, and specially the angular velocity are both analytically and numerically discussed in details. We shown that both the deviations from the critical power and the deviations from the critical OAM can make the spiraling elliptic beams breathe. The decrease (increase) of the OAM or the increase (decrease) of the power can both make the spiraling elliptic breathers contract (diffract), however, there still exist differences between them. The rotating speed can be changed by the input optical power or the input OAM, which may have potential applications in the controlling of the optical beams. PMID:26406663
Nonlinear evolution of the auroral electron beam
NASA Technical Reports Server (NTRS)
Maggs, James E.
1989-01-01
The nonlinear spatial evolution, from the source to the atmosphere, of the auroral electron beam and the beam-generated electrostatic whistler noise was studied, calculating changes in beam parameters from equations for the conservation of total particle and wave energy and momentum flux density. Wave power fluxes were calculated by numerically integrating the wave kinetic equations, and the levels of beam-generated noise were determined by using thermal levels of Cerenkov radiation as a source. It was found that beam parameters evolve on ionospheric scale lengths, and their positive slope feature in velocity space is maintained over altitudes measured in thousands of kilometers of altitude, even though they can generate wave energy density fluxes sufficient to modify the ionospheric density profile.
A geometric calibration method for cone beam CT systems
Yang, Kai; Kwan, Alexander L. C.; Miller, DeWitt F.; Boone, John M.
2006-06-15
Cone beam CT systems are being deployed in large numbers for small animal imaging, dental imaging, and other specialty applications. A new high-precision method for cone beam CT system calibration is presented in this paper. It uses multiple projection images acquired from rotating point-like objects (metal ball bearings) and the angle information generated from the rotating gantry system is also used. It is assumed that the whole system has a mechanically stable rotation center and that the detector does not have severe out-of-plane rotation (<2 deg.). Simple geometrical relationships between the orbital paths of individual BBs and five system parameters were derived. Computer simulations were employed to validate the accuracy of this method in the presence of noise. Equal or higher accuracy was achieved compared with previous methods. This method was implemented for the geometrical calibration of both a micro CT scanner and a breast CT scanner. The reconstructed tomographic images demonstrated that the proposed method is robust and easy to implement with high precision.
Active suppression of nonlinear composite beam vibrations by selected control algorithms
NASA Astrophysics Data System (ADS)
Warminski, Jerzy; Bochenski, Marcin; Jarzyna, Wojciech; Filipek, Piotr; Augustyniak, Michal
2011-05-01
This paper is focused on application of different control algorithms for a flexible, geometrically nonlinear beam-like structure with Macro Fiber Composite (MFC) actuator. Based on the mathematical model of a geometrically nonlinear beam, analytical solutions for Nonlinear Saturation Controller (NSC) are obtained using Multiple Scale Method. Effectiveness of different control strategies is evaluated by numerical simulations in Matlab-Simulink software. Then, the Digital Signal Processing (DSP) controller and selected control algorithms are implemented to the physical system to compare numerical and experimental results. Detailed analysis for the NSC system is carried out, especially for high level of amplitude and wide range of frequencies of excitation. Finally, the efficiency of the considered controllers is tested experimentally for a more complex autoparametric " L-shape" beam system.
Effect of transverse shears on complex nonlinear vibrations of elastic beams
NASA Astrophysics Data System (ADS)
Krysko, V. A.; Zhigalov, M. V.; Saltykova, O. A.; Krysko, A. V.
2011-09-01
Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h2) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness ? ? 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.
Beam-Plasma Interaction and Nonlinear Effects
Yoon, Peter H.
2009-11-10
This paper presents a survey of perturbative nonlinear plasma theory known as the weak turbulence theory. After the basic concepts and methodology of the weak turbulence theory are outlined in sufficient detail, numerical solutions of the weak turbulence theory obtained in the context of the beam-plasma interaction are compared against particle-in-cell (PIC) numerical simulations. It is demonstrated that theory and PIC simulation are in excellent agreement.
Nonlinear bending models for beams and plates.
Antipov, Y A
2014-10-01
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
Geometric beam coupling impedance of LHC secondary collimators
NASA Astrophysics Data System (ADS)
Frasciello, Oscar; Tomassini, Sandro; Zobov, Mikhail; Salvant, Benoit; Grudiev, Alexej; Mounet, Nicolas
2016-02-01
The High Luminosity LHC project is aimed at increasing the LHC luminosity by an order of magnitude. One of the key ingredients to achieve the luminosity goal is the beam intensity increase. In order to keep beam instabilities under control and to avoid excessive power losses a careful design of new vacuum chamber components and an improvement of the present LHC impedance model are required. Collimators are among the major impedance contributors. Measurements with beam have revealed that the betatron coherent tune shifts were higher by about a factor of 2 with respect to the theoretical predictions based on the LHC impedance model up to 2012. In that model the resistive wall impedance has been considered as the dominating impedance contribution for collimators. By carefully simulating also their geometric impedance we have contributed to the update of the LHC impedance model, reaching also a better agreement between the measured and simulated betatron tune shifts. During the just ended LHC Long Shutdown I (LSI), TCS/TCT collimators were replaced by new devices embedding BPMs and TT2-111R ferrite blocks. We present here preliminary estimations of their broad-band impedance, showing that an increase of about 20% is expected in the kick factors with respect to previous collimators without BPMs.
Geometric misalignment and calibration in cone-beam tomography
Smekal, Lorenz von; Kachelriess, Marc; Stepina, Elizaveta; Kalender, Willi A.
2004-12-01
We present a new high-precision method for the geometric calibration in cone-beam computed tomography. It is based on a Fourier analysis of the projection-orbit data, recorded with a flat-panel area detector, of individual point-like objects. For circular scan trajectories the complete set of misalignment parameters which determine the deviation of the detector alignment from the ideal scan geometry are obtained from explicit analytic expressions. To derive these expressions we show how to disentangle the problems of calculating misalignment parameters and point coordinates. The calculation of the coordinates of the point objects inside the scanned volume, in units of the distance from the focal spot to the center of rotation, is then possible analytically likewise. We simulate point-projection data on a misaligned detector with various amounts of randomness added to mimic measurement uncertainties. This data is then employed in our calibration to validate the method by comparing the resulting misalignment parameters and point coordinates to the known true ones. We also present our implementation and results for the geometric calibration of micro-CT systems. The effectiveness of the corresponding misalignment correction in reducing image artifacts is exemplified by reconstructed micro-CT images.
Multiple-mode nonlinear free and forced vibrations of beams using finite element method
NASA Technical Reports Server (NTRS)
Mei, Chuh; Decha-Umphai, Kamolphan
1987-01-01
Effects of large deflection geometric nonlinearity and multiple modes for free and forced vibrations of beams are investigated. Inplane displacement and inplane inertia are included in the formulation. The finite element method is employed. A harmonic force matrix is derived for forced vibration analysis. The relations of amplitude, frequency ratio and forcing intensity for beams of different boundary conditions and various load conditions are presented.
Geometric structure of multiple time-scale nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Bharadwaj, Sanjay
A new methodology to analyze time-scale structure of smooth finite-dimensional nonlinear dynamical systems is developed. This approach does not assume apriori knowledge of slow and fast variables for special coordinates that simplify the form of the nonlinear dynamics. Conventional approaches to analyze time-scale structure of nonlinear dynamics such as singular perturbation theory proceed from such specialized apriori knowledge which is often not obtainable. Our approach proceeds from spectral analysis of the linear variational dynamics associated with the nonlinear system. The variational dynamics govern the flow on the tangent bundle to the state-space. We decompose the tangent space at each point into spectral subspaces which separate tangent vectors that evolve at different spectral rates. The existence of such measures of spectral rates and corresponding subspaces is established by Sacker and Sell. We have developed a scheme to computationally determine these spectral measures using finite-time Lyapunov exponents and associated direction fields. In the asymptotic limit, the infinite-time Lyapunov direction fields are shown to satisfy useful invariance properties. As a consequence they are shown to uniquely define an invariant spectral filtration, i.e., a collection of nested distributions which are invariant under the nonlinear flow. Using these results, we establish the consistency of these spectral measures with well known results in special cases such as linear time-invariant systems and periodic linear time-varying systems. Differential equations that govern the propagation of Lyapunov directions along orbits of the nonlinear flow are derived using the invariance properties. Methods to apply these spectral analysis tools to construct coordinate transformations that decompose the variational flow are developed. When the Frobenius theorem is applicable, we also show methods to construct a nonlinear transformation of coordinates from the Lyapunov direction fields to decompose the nonlinear dynamics into slow and fast subsystems. In fact, this procedure can be used to transform the two time-scale nonlinear dynamics into a singularly perturbed standard form. Application of these methods for reducing the order of nonlinear dynamics, locating the slow manifold in the state-space and solving boundary value problems arising from hypersensitive optimal control problems is discussed. Several simple examples are used to demonstrate the methods and elucidate the main concepts.
Nonlinear Analysis of a Functionally Graded Beam Resting on the Elastic Nonlinear Foundation
NASA Astrophysics Data System (ADS)
Arefi, M.
2014-06-01
This paper evaluates the nonlinear responses of a function- ally graded (FG) beam resting on a nonlinear foundation. After derivation of fundamental nonlinear differential equation using the Euler-Bernouli beam theory, a semi analytical method has been used to study the response of the problem. The responses can be evaluated for both linear and nonlinear isotropic and FG beams individually. Adomians Decomposition and successive approximation methods have been used for solution of nonlinear differential equation. As numerical investigation, the beams with simply supported ends and linear and nonlinear foundations have been analyzed using this method.
A finite element method for nonlinear forced vibrations of beams
NASA Technical Reports Server (NTRS)
Mei, C.; Decha-Umphai, K.
1984-01-01
Techniques for defining a finite element model (FEM) for analysis of nonlinear vibrations in beam structures subjected to harmonic excitation are presented. The resulting model covers longitudinal deformation and inertial effects. The nonlinear oscillations of a beam element under forced excitation are modeled by a harmonic force matrix based on first order approximations of the Jacobian elliptic forcing function. Harmonic force and nonlinear stiffness matrices are derived and the nonlinear forced responses of beams are calculated under various boundary conditions. The results of FEM computations for simply-supported and clamped beams show that midplane stretching caused by large deflections increases the nonlinearity. Axially-restrained beams experience only hardening nonlinearity, while axially-free beams have reduced nonlinearity in deformation and inertia and an increase in linearity due to large deflection.
NASA Astrophysics Data System (ADS)
Ansari, R.; Faraji Oskouie, M.; Gholami, R.
2016-01-01
In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efï¬cient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.
Beam stability and nonlinear dynamics. Summary report
Parsa, Z.
1996-12-31
A {open_quotes}Beam Stability and Nonlinear Dynamics{close_quotes} Symposium was held October 3-5, 1996 at the Institute for Theoretical Physics (ITP) in Santa Barbara. This was one of the 3 symposia hosted by the ITP and supported by its sponsor, the National Science Foundation, as part of our {open_quotes}New Ideas for Particle Accelerators{close_quotes} program. The symposia was organized and chaired by Dr. Zohreh Parsa of ITP/ Brookhaven National Laboratory. The purpose of this symposium was to deal with some of the fundamental theoretical problems of accelerator physics by bringing together leaders from accelerator physics communities, mathematics, and other fields of physics. The focus was on nonlinear dynamics and beam stability. The symposium began with some defining talks on relevant mathematical topics such as single-particle Hamiltonian dynamics, chaos, and new ideas in symplectic integrators. The physics topics included single-particle and many-particle dynamics. These topics concern circular accelerators in which particles circulate for a very large number of turns as well as linear accelerators where space charge and wakefields induced in accelerating cavities play a strong role. A major question is to determine the best model for numerical simulations in order to accurately reproduce behavior of beams in real accelerators and to predict long-term or long distance stability. Comparison with experiment is recognized as an important tool in improving models.
A computational framework for polyconvex large strain elasticity for geometrically exact beam theory
NASA Astrophysics Data System (ADS)
Ortigosa, Rogelio; Gil, Antonio J.; Bonet, Javier; Hesch, Christian
2016-02-01
In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55-70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney-Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.
A computational framework for polyconvex large strain elasticity for geometrically exact beam theory
NASA Astrophysics Data System (ADS)
Ortigosa, Rogelio; Gil, Antonio J.; Bonet, Javier; Hesch, Christian
2015-12-01
In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55-70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney-Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.
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.
Beam stability & nonlinear dynamics. Formal report
Parsa, Z.
1996-12-31
his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.
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.
An integrated approach to the synthesis of geometrically non-linear structures
NASA Technical Reports Server (NTRS)
Smaoui, H.; Schmit, L. A.
1988-01-01
An integrated approach to the minimum weight design of geometrically nonlinear three-dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The nonlinear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the constraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically nonlinear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.
NASA Astrophysics Data System (ADS)
Du, Dianlou; Yang, Xiao
2015-02-01
The algebraic-geometrical solutions of three (2 + 1)-dimensional equations (including mKP equation and coupled mKP equation) are discussed by Hamiltonian approach. First, the Poisson structure on CN × RN is introduced to give a Hamiltonian system associated with the derivative nonlinear Schrödinger (DNLS) hierarchy. The Hamiltonian system is proved to be Liouville integrable, accordingly the solutions of three (2 + 1)-dimensional nonlinear equations can be solved by three compatible Hamiltonian flows. Second, the canonical separated variables and Hamilton-Jacobi theory is used to definite action-angle variables for Hamiltonian flows. At last, by Riemann-Jacobi inversion, the algebraic-geometrical solutions of three (2 + 1)-dimensional nonlinear equations are obtained. Besides, the algebraic-geometrical solutions of the first two DNLS equations are also given.
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1985-01-01
The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.
Geometrical Nonlinear Analysis of Composite Structures by Zigzag Theoryâ€”A Review
NASA Astrophysics Data System (ADS)
Shirbhate, N. J.; Tungikar, V. B.
2010-10-01
Advances in manufacturing technologies of composites leads to its uses as main load carrying structures which essentially need to be thick structures. Thus it is becoming increasingly important to predict accurately interlaminar variations of stresses and displacements along thickness of the composites. A review of the recent development of finite element methods for geometrical nonlinear analysis of composite structures specifically using zigzag theory is presented in this paper. The literature review is devoted to the recently developed finite elements, theories based on zigzag function for carrying out geometrical nonlinear analysis of composite structures. The future research is summarized finally.
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.
NASA Technical Reports Server (NTRS)
Raju, K. K.; Rao, G. V.; Raju, I. S.
1978-01-01
The effect of geometric nonlinearity on the free flexural vibrations of moderately thick rectangular plates is studied in this paper. Finite element formulation is employed to obtain the non-linear to linear period ratios for some rectangular plates. A conforming finite element of rectangular shape wherein the effects of shear deformation and rotatory inertia are included, is developed and used for the analysis. Results are presented for both simply supported and clamped boundary conditions.
A Global Geometric Framework for Nonlinear Dimensionality Reduction
NASA Astrophysics Data System (ADS)
Tenenbaum, Joshua B.; de Silva, Vin; Langford, John C.
2000-12-01
Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 106 optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.
Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion
NASA Astrophysics Data System (ADS)
McBride, A. T.; Javili, A.; Steinmann, P.; Bargmann, S.
2011-10-01
Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given.
Geometric Nonlinear Computation of Thin Rods and Shells
NASA Astrophysics Data System (ADS)
Grinspun, Eitan
2011-03-01
We develop simple, fast numerical codes for the dynamics of thin elastic rods and shells, by exploiting the connection between physics, geometry, and computation. By building a discrete mechanical picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting, we produce numerical codes that not only are consistent in a classical sense, but also reproduce qualitative, characteristic behavior of a physical system----such as exact preservation of conservation laws----even for very coarse discretizations. As two recent examples, we present discrete computational models of elastic rods and shells, with straightforward extensions to the viscous setting. Even at coarse discretizations, the resulting simulations capture characteristic geometric instabilities. The numerical codes we describe are used in experimental mechanics, cinema, and consumer software products. This is joint work with Miklós Bergou, Basile Audoly, Max Wardetzky, and Etienne Vouga. This research is supported in part by the Sloan Foundation, the NSF, Adobe, Autodesk, Intel, the Walt Disney Company, and Weta Digital.
Multiple-mode nonlinear free and forced vibrations of beams using finite element method
NASA Technical Reports Server (NTRS)
Mei, Chuh; Decha-Umphai, Kamolphan
1987-01-01
Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is derived and explained. Nonlinear free vibration can be simply treated as a special case of the general forced vibration by setting the harmonic force matrix equal to zero. The effect of the higher modes is more pronouced for the clamped supported beam than the simply supported one. Beams without IDI yield more effect of the higher modes than the one with IDI. The effects of IDI are to reduce nonlinearity. For beams with end supports restrained from axial movement (immovable cases), only the hardening type nonlinearity is observed. However, beams of small slenderness ratio (L/R = 20) with movable end supports, the softening type nonlinearity is found. The concentrated force case yields a more severe response than the uniformly distributed force case. Finite element results are in good agreement with the solution of simple elliptic response, harmonic balance method, and Runge-Kutte method and experiment.
NASA Astrophysics Data System (ADS)
Ibrahimbegovic, Adnan; Frey, Francois
1994-11-01
A consistent formulation of the geometrically linear shell theory with drilling rotations is obtained by the consistent linearization of the geometrically nonlinear shell theory considered in Parts 1 and 2 of this work. It was also shown that the same formulation can be recovered by linearizing the governing variational principle for the three-dimensional geometrically nonlinear continuum with independent rotation field. In the finite element implementation of the presented shell theory, relying on the modified method of incompatible modes, we were able to construct a four-node shell element which delivers a very high-level performance. In order to simplify finite element implementation, a shallow reference configuration is assumed over each shell finite element. This approach does not impair the element performance for the present four-node element. The results obtained herein match those obtained with the state-of-the-art implementations based on the classical shell theory, over the complete set of standard benchmark problems.
NASA Astrophysics Data System (ADS)
Mareishi, Soraya; Kalhori, Hamed; Rafiee, Mohammad; Hosseini, Seyedeh Marzieh
2015-01-01
This paper presents an analytical solution for nonlinear free and forced vibration response of smart laminated nano-composite beams resting on nonlinear elastic foundation and under external harmonic excitation. The structure is under a temperature change and an electric excitation through the piezoelectric layers. Different distribution patterns of the single walled aligned and straight carbon nanotubes (SWCNTs) through the thickness of the beam are considered. The beam complies with Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. The nonlinearity is due to the mid-plane stretching of the beam and the nonlinear stiffness of the elastic foundation. The Multiple Time Scales perturbation scheme is used to perform the nonlinear dynamical analysis of functionally graded carbon nanotube-reinforced beams. Analytical expressions of the nonlinear natural frequencies, nonlinear dynamic response and frequency response of the system in the case of primary resonance have been presented. The effects of different parameters including applied voltage, temperature change, beam geometry, the volume fraction and distribution pattern of the carbon nanotubes on the nonlinear natural frequencies and frequency-response curves are presented. It is found that the volume fractions of SWCNTs as well as their distribution pattern significantly change the behavior of the system.
Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials
Li, Nianbei; Ren, Jie
2014-01-01
Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports. PMID:25169668
NASA Technical Reports Server (NTRS)
Mangalgiri, P. D.; Prabhakaran, R.
1986-01-01
An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained.
Nonlinear free vibrations of beams in space due to internal resonance
NASA Astrophysics Data System (ADS)
Stoykov, S.; Ribeiro, P.
2011-08-01
The geometrically nonlinear free vibrations of beams with rectangular cross section are investigated using a p-version finite element method. The beams may vibrate in space, hence they may experience longitudinal, torsional and non-planar bending deformations. The model is based on Timoshenko's theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and is free to warp in the longitudinal direction, as in Saint-Venant's theory. The geometrical nonlinearity is taken into account by considering Green's nonlinear strain tensor. Isotropic and elastic beams are investigated and generalised Hooke's law is used. The equation of motion is derived by the principle of virtual work. Mostly clamped-clamped beams are investigated, although other boundary conditions are considered for validation purposes. Employing the harmonic balance method, the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method. One constant term, odd and even harmonics are assumed in the Fourier series and convergence with the number of harmonics is analysed. The variation of the amplitude of vibration with the frequency of vibration is determined and presented in the form of backbone curves. Coupling between modes is investigated, internal resonances are found and the ensuing multimodal oscillations are described. Some of the couplings discovered lead from planar oscillations to oscillations in the three dimensional space.
NASA Astrophysics Data System (ADS)
Asadi, Hamed; Eynbeygi, Mehdi; Wang, Quan
2014-07-01
The instability of geometrically imperfect shape memory alloy (SMA) fibers reinforced with hybrid laminated composite (SMAHC) plates and subjected to a uniform thermal loading is analytically investigated. The material properties of the SMAHC plates are assumed to be functions of temperature. Nonlinear equations of the plates’ thermal stability are derived based on a higher order shear deformation theory incorporating von Karman geometrical nonlinearity via stationary potential energy. The structural recovery stress, which is generated by martensitic phase transformation of the prestrained SMA fibers, is calculated based on the one-dimensional thermodynamic constitutive model by Brinson. Adopting the Galerkin procedure, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations, in which systems of equations are solved by introducing an analytical approach. Closed-form formulations are presented to determine the load-deflection path and critical buckling temperature of the plate. Based on the developed closed-form solutions, ample numerical results are presented to provide an insight into the effects of the volume fraction, prestrain, location and orientation of the SMA fibers, composite plate geometry, geometrical imperfection and temperature dependence on the stability of the SMAHC plates. It is shown that a proper application of SMA fibers results in a considerable delay of the thermal bifurcation and controllable thermal post-buckling deflection of the SMAHC plate.
Necklace beam generation in nonlinear colloidal engineered media.
Silahli, Salih Z; Walasik, Wiktor; Litchinitser, Natalia M
2015-12-15
Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes as supercontinuum generation, light filamentation, rogue waves, and ring (or necklace) beam formation. To date, a majority of studies of these phenomena have focused on light-matter interactions in self-focusing Kerr media existing in nature. However, a large and tunable nonlinear response of a colloidal suspension can be tailored at will by judiciously engineering the optical polarizability. Here, we analytically and numerically show the possibility of necklace beam generation originating from spatial modulational instability of vortex beams in engineered soft-matter nonlinear media with different types of exponential nonlinearity. PMID:26670494
Nonlinear plasma and beam physics in plasma wake-fields
Rosenzweig, J.B.
1990-02-12
In experimental studies of the Plasma Wake-field Accelerator performed to date at the Argonne Advanced Accelerator Test Facility, significant nonlinearities in both plasma and beam behavior have been observed. The plasma waves driven in the wake of the intense driving beam in these experiments exhibit three-dimensional nonlinear behavior which has as yet no quantitative theoretical explanation. This nonlinearity is due in part to the self-pinching of the driving beam in the plasma, as the denser self-focused beam can excite larger amplitude plasma waves. The self-pinching is a process with interesting nonlinear aspects: the initial evolution of the beam envelope and the subsequent approach to Bennett equilibrium through phase mixing. 35 refs., 10 figs.
NASA Astrophysics Data System (ADS)
Hasanyan, Davresh; Librescu, Liviu; Qin, Zhanming; Ambur, Damodar R.
2005-10-01
A fully coupled magneto-thermo-elastokinetic model of laminated composite, finitely electroconductive plates incorporating geometrical nonlinearities and subjected to a combination of magnetic and thermal fields, as well as carrying an electrical current is developed. In this context, the first-order transversely shearable plate theory in conjunction with von-Kármán geometrically nonlinear strain concept is adopted. Related to the distribution of electric and magnetic field disturbances within the plate, the assumptions proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e. the ones by Faraday, Amp e`re, Ohm, Maxwell and Lorentz), the modified Fourier's law of heat conduction and on the elastokinetic field equations, the 3-D coupled problem is reduced to an equivalent 2-D one. The theory developed herein provides a foundation for the investigation, both analytical and numerical, of the interacting effects among the magnetic, thermal and elastic fields in multi-layered thin plates made of anisotropic materials.
NASA Technical Reports Server (NTRS)
Hasanyan, Davresh; Librescu, Liviu; Qin, Zhanming; Ambur, Damodar R.
2006-01-01
A fully coupled magneto-thermo-elastokinetic model of laminated composite, finitely electroconductive plates incorporating geometrical nonlinearities and subjected to a combination of magnetic and thermal fields, as well as carrying an electrical current is developed, In this context. the first-order transversely shearable plate theory in conjunction with von-Karman geometrically nonlinear strain concept is adopted. Related to the distribution of electric and magnetic field disturbances within the plate, the assumptions proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e. the ones by Faraday, Ampere, Ohm, Maxwell and Lorentz), the modified Fourier's law of heat conduction and on the elastokinetic field equations, the 3-D coupled problem is reduced to an equivalent 2- D one. The theory developed herein provides a foundation for the investigation, both analytical and numerical, of the interacting effects among the magnetic, thermal and elastic fields in multi-layered thin plates made of anisotropic materials.
Nonlinear system identification of frictional effects in a beam with a bolted joint connection
NASA Astrophysics Data System (ADS)
Eriten, Melih; Kurt, Mehmet; Luo, Guanyang; Michael McFarland, D.; Bergman, Lawrence A.; Vakakis, Alexander F.
2013-08-01
We perform nonlinear system identification (NSI) of the effects of frictional connections in the dynamics of a bolted beam assembly. The methodology utilized in this work combines experimental measurements with slow-flow dynamic analysis and empirical mode decomposition, and reconstructs the dynamics through reduced-order models. These are in the form of single-degree-of-freedom linear oscillators (termed intrinsic modal oscillators—IMOs) with forcing terms derived directly from the experimental measurements through slow-flow analysis. The derived reduced order models are capable of reproducing the measured dynamics, whereas the forcing terms provide important information about nonlinear damping effects. The NSI methodology is applied to model nonlinear friction effects in a bolted beam assembly. A 'monolithic' beam with identical geometric and material properties is also tested for comparison. Three different forcing (energy) levels were considered in the tests in order to study the energy-dependencies of the damping nonlinearities induced in the beam from the bolted joint. In all cases, the NSI methodology employed was successful in identifying the damping nonlinearities, their spatial distributions and their effects of the vibration modes of the structural component.
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.; Hodges, Dewey H.
1987-01-01
The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyze 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 deformation. The correlation is excellent in all cases.
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.
NASA Astrophysics Data System (ADS)
Akbari, M. R.; Nimafar, M.; Ganji, D. D.; Akbarzade, M. M.
2014-12-01
The kinematic assumptions upon which the Euler-Bernoulli beam theory is founded allow it to be extended to more advanced analysis. Simple superposition allows for three-dimensional transverse loading. Using alternative constitutive equations can allow for viscoelastic or plastic beam deformation. Euler-Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams and geometrically nonlinear beam deflection. In this study, solving the nonlinear differential equation governing the calculation of the large rotation deviation of the beam (or column) has been discussed. Previously to calculate the rotational deviation of the beam, the assumption is made that the angular deviation of the beam is small. By considering the small slope in the linearization of the governing differential equation, the solving is easy. The result of this simplification in some cases will lead to an excessive error. In this paper nonlinear differential equations governing on this system are solved analytically by Akbari-Ganji's method (AGM). Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration solving. The solution of the problem can be obtained very simply and easily. Furthermore, to enhance the accuracy of the results, the Taylor expansion is not needed in most cases via AGM manner. Also, comparisons are made between AGM and numerical method (Runge-Kutta 4th). The results reveal that this method is very effective and simple, and can be applied for other nonlinear problems.
Nonlinear dynamics of inhomogeneous mismatched charged particle beams
Nunes, R. P.; Rizzato, F. B.
2012-08-13
This work analyzes the transversal dynamics of an inhomogeneous and mismatched charged particle beam. The beam is azimuthally symmetric, initially cold, and evolves in a linear channel permeated by an external constant magnetic field. Based on a Lagrangian approach, a low-dimensional model for the description of the beam dynamics has been obtained. The small set of nonlinear dynamical equations provided results that are in reasonable agreement with that ones observed in full self-consistent N-particle beam numerical simulations.
Nonlinear Self-Similar Beams of Electromagnetic Waves in Vacuum
NASA Astrophysics Data System (ADS)
Vlasov, S. N.
2015-12-01
We study nonlinear beams of electromagnetic waves in vacuum. Within the lowest approximation, their structure is determined by the cubic self-focusing nonlinearity, which manifests itself with the maximum intensity in the presence of counterpropagating waves. It is shown that the fields in the beams have no singularities if their power is less than the critical power of the self-focusing. The dependences of the eigenfrequencies of the modes of the quasioptical resonator on the beam power are found. The structure of the fields of these modes corresponds to self-similar wave beams.
B-spline goal-oriented error estimators for geometrically nonlinear rods
NASA Astrophysics Data System (ADS)
DedÃ¨, L.; Santos, H. A. F. A.
2012-01-01
We consider goal-oriented a posteriori error estimators for the evaluation of the errors on quantities of interest associated with the solution of geometrically nonlinear curved elastic rods. For the numerical solution of these nonlinear one-dimensional problems, we adopt a B-spline based Galerkin method, a particular case of the more general isogeometric analysis. We propose error estimators using higher order "enhanced" solutions, which are based on the concept of enrichment of the original B-spline basis by means of the "pure" k-refinement procedure typical of isogeometric analysis. We provide several numerical examples for linear and nonlinear output functionals, corresponding to the rotation, displacements and strain energy of the rod, and we compare the effectiveness of the proposed error estimators.
NASA Astrophysics Data System (ADS)
Farokhi, Hamed; Ghayesh, Mergen H.
2015-12-01
This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imperfect microplates. Based on the modified couple stress theory, the equations of motion for the in-plane and out-of-plane motions are obtained employing the von KÃ¡rmÃ¡n plate theory as well as Kirchhoff's hypotheses by means of the Lagrange equations. The equations of motions are solved using the pseudo-arclength continuation technique and direct time-integration method. The system parameters are tuned to the values associated with modal interactions, and then nonlinear resonant responses and energy transfer are analysed. Nonlinear motion characteristics are shown in the form of frequency-response and force-response curves, time histories, phase-plane portraits, and fast Fourier transforms.
Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations
NASA Technical Reports Server (NTRS)
Tessler, Alexander; Sleight, David W.
2006-01-01
Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.
Nonlinear frequency conversion of radiation of a focused Gaussian beam
NASA Astrophysics Data System (ADS)
Illarionov, A. I.; Yanchuk, O. V.
2007-12-01
Nonlinear conversion of radiation of a Gaussian beam focused by a lens possessing coma aberration is theoretically analyzed for nonlinear crystals of 6, 4, 4¯ symmetry group. With the help of computer modeling, spatial-angular and energetic structures of fundamental radiation on the crystal face and of the second optical harmonic in a lithium iodate crystal are obtained.
Nonlinear and tangent stiffness of imperfect beam columns
NASA Technical Reports Server (NTRS)
Anderson, M. S.
1982-01-01
A curved member under axial load is analyzed using beam column theory to determine nonlinear response and the tangent stiffness associated with small displacements from the nonlinear state. Such a result is suitable for incorporation into a general nonlinear analysis using a corotational coordinate system to describe the rigid body type motion of individual members. The method is applied to buckling problems. Several examples are given to show the accuracy of the method.
Beam quality measurement of laser pulses by nonlinear optical techniques.
Agnesi, A; Reali, G C; Tomaselli, A
1992-12-15
A novel method for measuring the beam quality of short, powerful laser pulses is presented. The method is based on the Z-scan technique used to investigate the nonlinear susceptibilities of optical materials. It is shown that both two-photon absorption and nonlinear refraction of a nonlinear sample can be used to obtain information about the spatial quality of the pulses. PMID:19798309
Nonlinear beam deflection in photonic lattices with negative defects
Wang Jiandong; Ye Zhuoyi; Lou Cibo; Miller, Alexandra; Zhang Peng; Hu Yi; Chen Zhigang; Yang Jianke
2011-03-15
We demonstrate both theoretically and experimentally that a nonlinear beam can be reflected by a negative defect in a photonic lattice if the incident angle is below a threshold value. Above this threshold angle, the beam simply passes through the defect. This phenomenon occurs in both one- and two-dimensional photonic lattices, and it provides a way to use the incident angle to control beam propagation in a lattice network. If the defect is absent or positive, no evident transition from reflection to transmission occurs. These nonlinear phenomena are also compared with linear nondiffracting-beam propagation in a photonic lattice with a defect, and both similarities and differences are observed. In addition, some important features in linear and nonlinear beam propagations are explained analytically by using a linear model with a delta-function defect.
Hybrid Analytical Technique for Nonlinear Vibration Analysis of Thin-Walled Beams
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Hadian, Jafar M.; Andersen, Carl M.
1993-01-01
A two-step hybrid analytical technique is presented for the nonlinear vibration analysis of thin-walled beams. The first step involves the generation of various-order perturbation functions using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation functions as coordinate (or approximation) functions and then computing both the amplitudes of these functions and the nonlinear frequency of vibration via a direct variational procedure. The analytical formulation is based on a form of the geometrically nonlinear beam theory with the effects of in-plane inertia, rotatory inertia, and transverse shear deformation included. The effectiveness of the proposed technique is demonstrated by means of a numerical example of thin-walled beam with a doubly symmetric I-section. The solutions obtained using a single-spatial mode were compared with those obtained using multiple-spatial modes. The standard of comparison was taken to be the frequencies obtained by the direct integration/fast Fourier transform (FFT) technique. The nonlinear frequencies obtained by the hybrid technique were shown to converge to the corresponding ones obtained by the direct integration/fast Fourier transform (FFT) technique well beyond the range of applicability of the perturbation technique. The frequencies and total strain energy of the beam were overestimated by using a single-spatial mode.
Nonlinear self-collimated sound beams in sonic crystals
NASA Astrophysics Data System (ADS)
Hamham, El Mokhtar; Jiménez, Noé; Picó, Rubén; Sánchez-Morcillo, Víctor J.; García-Raffi, Lluís M.; Staliunas, Kestutis
2015-08-01
We report the propagation of high-intensity sound beams in a sonic crystal, under self-collimation or reduced-divergence conditions. The medium is a fluid with elastic quadratic nonlinearity, where the dominating nonlinear effect is harmonic generation. The conditions for the efficient generation of narrow, nondiverging beam of second harmonic are discussed. Numerical simulations are in agreement with the analytical predictions made, based on the linear dispersion characteristics in modulated media and the nonlinear interaction in a quadratic medium under phase matching conditions.
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
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
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 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.
NASA Technical Reports Server (NTRS)
Robinson, J. C.
1979-01-01
Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.
Non-Linear Vibration of Beams with Internal Resonance by the Hierarchical Finite-Element Method
NASA Astrophysics Data System (ADS)
RIBEIRO, P.; PETYT, M.
1999-07-01
The hierarchical finite-element (HFEM) and the harmonic balance methods (HBM) are used to investigate the geometrically non-linear free and steady-state forced vibrations of uniform, slender beams. The beam analogue of von Kármán's non-linear strain-displacement relationships are employed and the middle plane in-plane displacements are included in the model. The equations of motion are developed by applying the principle of virtual work and are solved by a continuation method, 1:3 and 1:5 internal resonances are discovered and their consequences are discussed. The convergence properties of the HFEM are analyzed and it is demonstrated that the HFEM model requires far fewer degrees of freedom than theh-version of the FEM models presented in the literature.
A boundary element formulation for analysis of elastoplastic plates with geometrical nonlinearity
NASA Astrophysics Data System (ADS)
Waidemam, Leandro; Venturini, Wilson Sergio
2010-03-01
In this paper a new boundary element method formulation for elastoplastic analysis of plates with geometrical nonlinearities is presented. The von Mises criterion with linear isotropic hardening is considered to evaluate the plastic zone. Large deflections are assumed but within the context of small strain. To derive the boundary integral equations the von Kármán’s hypothesis is taken into account. An initial stress field is applied to correct the true stresses according to the adopted criterion. Isoparametric linear elements are used to approximate the boundary unknown values while triangular internal cells with linear shape function are adopted to evaluate the domain value influences. The nonlinear system of equations is solved by using an implicit scheme together with the consistent tangent operator derived along the paper. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.
Geredeli, Pelin G.; Webster, Justin T.
2013-12-15
We analyze the convergence to equilibrium of solutions to the nonlinear Berger plate evolution equation in the presence of localized interior damping (also referred to as geometrically constrained damping). Utilizing the results in (Geredeli et al. in J. Differ. Equ. 254:1193–1229, 2013), we have that any trajectory converges to the set of stationary points N . Employing standard assumptions from the theory of nonlinear unstable dynamics on the set N , we obtain the rate of convergence to an equilibrium. The critical issue in the proof of convergence to equilibria is a unique continuation property (which we prove for the Berger evolution) that provides a gradient structure for the dynamics. We also consider the more involved von Karman evolution, and show that the same results hold assuming a unique continuation property for solutions, which is presently a challenging open problem.
Riemann problem for kinematical conservation laws and geometrical features of nonlinear wavefronts
NASA Astrophysics Data System (ADS)
Baskar, S.; Prasad, Phoolan
2004-08-01
A pair of kinematical conservation laws (KCL) in a ray coordinate system ({xi},t) are the basic equations governing the evolution of a moving curve in two space dimensions. We first study elementary wave solutions and then the Riemann problem for KCL when the metric g, associated with the coordinate {xi} designating different rays, is an arbitrary function of the velocity of propagation m of the moving curve. We assume that m>1 (m is appropriately normalized), for which the system of KCL becomes hyperbolic. We interpret the images of the elementary wave solutions in the ({xi},t)-plane to the (x,y)-plane as elementary shapes of the moving curve (or a nonlinear wavefront when interpreted in a physical system) and then describe their geometrical properties. Solutions of the Riemann problem with different initial data give the shapes of the nonlinear wavefront with different combinations of elementary shapes. Finally, we study all possible interactions of elementary shapes.
Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods.
Calderhead, Ben; Girolami, Mark
2011-12-01
Mechanistic models based on systems of nonlinear differential equations can help provide a quantitative understanding of complex physical or biological phenomena. The use of such models to describe nonlinear interactions in molecular biology has a long history; however, it is only recently that advances in computing have allowed these models to be set within a statistical framework, further increasing their usefulness and binding modelling and experimental approaches more tightly together. A probabilistic approach to modelling allows us to quantify uncertainty in both the model parameters and the model predictions, as well as in the model hypotheses themselves. In this paper, the Bayesian approach to statistical inference is adopted and we examine the significant challenges that arise when performing inference over nonlinear ordinary differential equation models describing cell signalling pathways and enzymatic circadian control; in particular, we address the difficulties arising owing to strong nonlinear correlation structures, high dimensionality and non-identifiability of parameters. We demonstrate how recently introduced differential geometric Markov chain Monte Carlo methodology alleviates many of these issues by making proposals based on local sensitivity information, which ultimately allows us to perform effective statistical analysis. Along the way, we highlight the deep link between the sensitivity analysis of such dynamic system models and the underlying Riemannian geometry of the induced posterior probability distributions. PMID:23226584
Multi-direction vibration isolation with quasi-zero stiffness by employing geometrical nonlinearity
NASA Astrophysics Data System (ADS)
Sun, Xiuting; Jing, Xingjian
2015-10-01
The study proposes a novel vibration isolator with 3D quasi-zero-stiffness (QZS) property. The remarkable feature of the proposed system is to apply symmetrically scissor-like structures (SLS) in the horizontal directions, together with a traditional spring-mass-damper system assembled vertically with positive stiffness. With the mathematical modeling of the proposed system, it is shown that the stiffness and damping properties are nonlinear due to nonlinear geometric relations within the SLSs and both can be adjusted via structural parameters of the system. Theoretical analysis with the harmonic balance method reveals that the system can demonstrate QZS property in 3 directions, and can achieve much better 3D vibration isolation performance, including high-static and quasi-zero-dynamic stiffness, and much larger displacement range around equilibrium, compared with an existing QZS system in the literature. The results provide a novel and significant multi-direction vibration isolation method using structural nonlinearity with noticeable performance but using only passive elements.
Ion beam analysis based on cellular nonlinear networks
NASA Astrophysics Data System (ADS)
Senger, V.; Tetzlaff, R.; Reichau, H.; Ratzinger, U.
2011-07-01
The development of a non- destructive measurement method for ion beam parameters has been treated in various projects. Although results are promising, the high complexity of beam dynamics has made it impossible to implement a real time process control up to now. In this paper we will propose analysing methods based on the dynamics of Cellular Nonlinear Networks (CNN) that can be implemented on pixel parallel CNN based architectures and yield satisfying results even at low resolutions.
A geometrical model for the Monte Carlo simulation of the TrueBeam linac
NASA Astrophysics Data System (ADS)
Rodriguez, M.; Sempau, J.; Fogliata, A.; Cozzi, L.; Sauerwein, W.; Brualla, L.
2015-06-01
Monte Carlo simulation of linear accelerators (linacs) depends on the accurate geometrical description of the linac head. The geometry of the Varian TrueBeam linac is not available to researchers. Instead, the company distributes phase-space files of the flattening-filter-free (FFF) beams tallied at a plane located just upstream of the jaws. Yet, Monte Carlo simulations based on third-party tallied phase spaces are subject to limitations. In this work, an experimentally based geometry developed for the simulation of the FFF beams of the Varian TrueBeam linac is presented. The Monte Carlo geometrical model of the TrueBeam linac uses information provided by Varian that reveals large similarities between the TrueBeam machine and the Clinac 2100 downstream of the jaws. Thus, the upper part of the TrueBeam linac was modeled by introducing modifications to the Varian Clinac 2100 linac geometry. The most important of these modifications is the replacement of the standard flattening filters by ad hoc thin filters. These filters were modeled by comparing dose measurements and simulations. The experimental dose profiles for the 6 MV and 10 MV FFF beams were obtained from the Varian Golden Data Set and from in-house measurements performed with a diode detector for radiation fields ranging from 3??×??3 to 40??×??40 cm2 at depths of maximum dose of 5 and 10 cm. Indicators of agreement between the experimental data and the simulation results obtained with the proposed geometrical model were the dose differences, the root-mean-square error and the gamma index. The same comparisons were performed for dose profiles obtained from Monte Carlo simulations using the phase-space files distributed by Varian for the TrueBeam linac as the sources of particles. Results of comparisons show a good agreement of the dose for the ansatz geometry similar to that obtained for the simulations with the TrueBeam phase-space files for all fields and depths considered, except for the 40??×??40 cm2 field where the ansatz geometry was able to reproduce the measured dose more accurately. Our approach overcomes some of the limitations of using the Varian phase-space files. It makes it possible to: (i) adapt the initial beam parameters to match measured dose profiles; (ii) reduce the statistical uncertainty to arbitrarily low values; and (iii) assess systematic uncertainties (type B) by using different Monte Carlo codes. One limitation of using phase-space files that is retained in our model is the impossibility of performing accurate absolute dosimetry simulations because the geometrical description of the TrueBeam ionization chamber remains unknown.
Propagation of anomalous vortex beams in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Dai, Zhiping; Yang, Zhenjun; Zhang, Shumin; Pang, Zhaoguang
2015-09-01
The propagation properties of anomalous vortex beams in strongly nonlocal nonlinear media are investigated. Two equivalent analytical expressions for the evolution of anomalous vortex beams are obtained. It is found that the input power plays a key role in the beam evolutions. Selecting a proper input power, the beam width can be broadened or be compressed periodically, even it can keep invariant during propagation. The beam order and the topological charge mainly influence the intensity evolution and the phase evolution, respectively. The evolution period, the beam width, the phase distribution and the intensity distribution are discussed in detail. The results can also be generalized to other equivalent physical systems, such as an optical fractional Fourier transform system or a medium with a quadratic graded refractive index distribution.
A nonlinear theory for spinning anisotropic beams using restrained warping functions
NASA Astrophysics Data System (ADS)
Ie, C. A.; Kosmatka, J. B.
1993-04-01
A geometrically nonlinear theory is developed for spinning anisotropic beams having arbitrary cross sections. An assumed displacement field is developed using the standard 3D kinematics relations to describe the global beam behavior supplemented with an additional field that represents the local deformation within the cross section and warping out of the cross section plane. It is assumed that the magnitude of this additional field is directly proportional to the local stress resultants. In order to take into account the effects of boundary conditions, a restraining function is introduced. This function plays the role of reducing the amount of free warping deformation throughout the field due to the restraint of the cross section(s) at the end(s) of the beam, e.g., in the case of a cantilever beam. Using a developed ordering scheme, the nonlinear strains are calculated to the third order. The FEM is developed using the weak form variational formulation. Preliminary interesting numerical results have been obtained that indicate the role of the restraining function in the case of a cantilever beam with circular cross section. These results are for the cases of a tip displacement (static) and free vibration studies for both isotropic and anisotropic materials with varied fiber orientations.
A nonlinear theory for spinning anisotropic beams using restrained warping functions
NASA Technical Reports Server (NTRS)
Ie, C. A.; Kosmatka, J. B.
1993-01-01
A geometrically nonlinear theory is developed for spinning anisotropic beams having arbitrary cross sections. An assumed displacement field is developed using the standard 3D kinematics relations to describe the global beam behavior supplemented with an additional field that represents the local deformation within the cross section and warping out of the cross section plane. It is assumed that the magnitude of this additional field is directly proportional to the local stress resultants. In order to take into account the effects of boundary conditions, a restraining function is introduced. This function plays the role of reducing the amount of free warping deformation throughout the field due to the restraint of the cross section(s) at the end(s) of the beam, e.g., in the case of a cantilever beam. Using a developed ordering scheme, the nonlinear strains are calculated to the third order. The FEM is developed using the weak form variational formulation. Preliminary interesting numerical results have been obtained that indicate the role of the restraining function in the case of a cantilever beam with circular cross section. These results are for the cases of a tip displacement (static) and free vibration studies for both isotropic and anisotropic materials with varied fiber orientations.
Multiscale Reduced Order Models for the Geometrically Nonlinear Response of Complex Structures
NASA Astrophysics Data System (ADS)
Perez, Ricardo Angel
The focus of this investigation includes three aspects. First, the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting "large" deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology, successfully validated in recent years on simpler panel structures, by developing a novel identification strategy of the reduced order model parameters, that enables the consideration of the large number of modes needed for complex structures, and by extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. These novel developments are successfully validated on the nonlinear static and dynamic responses of a 9-bay panel structure modeled within Nastran. In addition, a multi-scale approach based on Component Mode Synthesis methods is explored. Second, an assessment of the predictive capabilities of nonlinear reduced order models for the prediction of the large displacement and stress fields of panels that have a geometric discontinuity; a flat panel with a notch was used for this assessment. It is demonstrated that the reduced order models of both virgin and notched panels provide a close match of the displacement field obtained from full finite element analyses of the notched panel for moderately large static and dynamic responses. In regards to stresses, it is found that the notched panel reduced order model leads to a close prediction of the stress distribution obtained on the notched panel as computed by the finite element model. Two enrichment techniques, based on superposition of the notch effects on the virgin panel stress field, are proposed to permit a close prediction of the stress distribution of the notched panel from the reduced order model of the virgin one. A very good prediction of the full finite element results is achieved with both enrichments for static and dynamic responses. Finally, computational challenges associated with the solution of the reduced order model equations are discussed. Two alternatives to reduce the computational time for the solution of these problems are explored.
Dynamic response analysis of geometrically non-linear structures subjected to high impact.
NASA Technical Reports Server (NTRS)
Gupta, K. K.
1972-01-01
Description of an efficient digital computer method for the determination of the propagation of elastic stresses and deformations in certain geometrically nonlinear structures subjected to high impact loading. The finite-element matrix displacement approach utilizing curved quadrilateral shell elements in conjunction with a nodewise predictor-corrector method employing Runge-Kutta extrapolation techniques has been adopted for the present solution. The related computer program written in FORTRAN V for the UNIVAC 1108 computer has proved to be effective for the solution of a range of practical problems including rectangular and cylindrical panels. Numerical results are presented for a relevant structure, the cell container, and the negative electrode of an impact-resistant battery subjected to high impact, simulating its free landing on a planetary surface.
NASA Astrophysics Data System (ADS)
Passalacqua, Paola; Do Trung, Tien; Foufoula-Georgiou, Efi; Sapiro, Guillermo; Dietrich, William E.
2010-03-01
A geometric framework for the automatic extraction of channels and channel networks from high-resolution digital elevation data is introduced in this paper. The proposed approach incorporates nonlinear diffusion for the preprocessing of the data, both to remove noise and to enhance features that are critical to the network extraction. Following this preprocessing, channels are defined as curves of minimal effort, or geodesics, where the effort is measured on the basis of fundamental geomorphological characteristics such as flow accumulation area and isoheight contours curvature. The merits of the proposed methodology, and especially the computational efficiency and accurate localization of the extracted channels, are demonstrated using light detection and ranging (lidar) data of the Skunk Creek, a tributary of the South Fork Eel River basin in northern California.
A shear-shear torsional beam model for nonlinear aeroelastic analysis of tower buildings
NASA Astrophysics Data System (ADS)
Piccardo, G.; Tubino, F.; Luongo, A.
2015-08-01
In this paper, an equivalent one-dimensional beam model immersed in a three-dimensional space is proposed to study the aeroelastic behavior of tower buildings: linear and nonlinear dynamics are analyzed through a simple but realistic physical modeling of the structure and of the load. The beam is internally constrained, so that it is capable to experience shear strains and torsion only. The elasto-geometric and inertial characteristics of the beam are identified from a discrete model of three-dimensional frame, via a homogenization process. The model accounts for the torsional effect induced by the rotation of the floors around the tower axis; the macroscopic shear strain is produced by bending of the columns, accompanied by negligible rotation of the floors. Nonlinear aerodynamic forces are evaluated through the quasi-steady theory. The first aim is to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions. Furthermore, the role of aerodynamic nonlinearities on the galloping post-critical behavior is analyzed through a perturbation solution which permits to obtain a reduced one-dimensional dynamical system, capable of capturing the essential dynamics of the problem.
Nonlinear transmission line based electron beam driver.
French, David M; Hoff, Brad W; Tang, Wilkin; Heidger, Susan; Allen-Flowers, Jordan; Shiffler, Don
2012-12-01
Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique. PMID:23277977
Nonlinear transmission line based electron beam driver
French, David M.; Hoff, Brad W.; Tang Wilkin; Heidger, Susan; Shiffler, Don; Allen-Flowers, Jordan
2012-12-15
Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique.
Niewodnicza?ski, Wawrzyniec; Bartkowiak, Wojciech
2007-07-01
This paper presents an ab initio quantum chemical investigation of the geometrical structures and the non-linear optical properties (NLO) of three structural isomers of pyridinium N-phenolate betaine dye. The ground state geometrical parameters and the first-order hyperpolarizabilities were calculated using the Hartree-Fock (HF) as well as the second-order perturbation Møller-Pleset (MP2) method with the 6-31G, 6-31G(d), 6-31G(d,p), 6-31+G(d), 6-31++G(d,p), 6-311+G(d), aug-cc-PVDZ and the recently developed Z3PolX basis sets. Moreover, the first-order hyperpolarizability was calculated at the coupled cluster singles and doubles (CCSD/6-31+G(d)) level of theory. The analysis of the results of calculations for the investigated isomers indicates that there are important differences in their NLO activities. Additionally, it was shown that Z3PolX basis set works reasonable well for betaine dyes. PMID:17447089
Nonlinear transient neutralization theory of ion beams with dissipation
NASA Technical Reports Server (NTRS)
Wilhelm, H. E.
1975-01-01
An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions. The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave. This periodic wave structure is damped out by intercomponent momentum transfer, i.e., after a few relaxation lengths a quasi-neutral beam results. The relaxation scale in space agrees with neutralization experiments of rarefied ion beams, if the collective momentum transfer between the electron and ion streams is assumed to be of the Buneman type.
Anisotropic bending-torsion coupling for warping in a non-linear beam
NASA Astrophysics Data System (ADS)
Klinkel, S.; Govindjee, S.
MEMS devices made from single crystal silicon often contain rod-like structures that are operated in bending and/or torsion. The design of these devices usually relies upon simple mechanical theories that ignore the coupling between these two modes of operation. In this paper, we develop a theory that is capable of accounting for the material coupling in the bending and twisting of single crystal beams which arises from anisotropic elastic properties and apply it in selected examples to the case of silicon. The generalized Saint-Venant torsion theory, which is valid for isotropic materials, is extended to arbitrary anisotropic linear elastic materials. The anisotropic material behavior couples the bending and torsion behavior. Thus, for the geometrically linear case, we find two warping functions associated with the bending moments and one warping function which is associated with the torsion moment. These warping patterns or functions are then taken as inputs to a geometrically non-linear formulation. Due to the presence of the additional warping functions, we find the existence of non-standard bi-moment and bi-shears which play an important role under certain conditions of extreme deformations. The final complexity of the non-linear formulation dictates the usage of a numerical solution procedure for practical computations. Here we employ a finite element scheme to solve the governing equations. Example computations elucidate the importance of the coupling effects by examining beams cut from (1 0 0) type silicon wafers.
Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F
2014-11-21
Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane. PMID:25361057
Geometric nonlinear analysis of self-anchored cable-stayed suspension bridges.
Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang
2013-01-01
Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800 m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800 m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed. PMID:24282388
NASA Technical Reports Server (NTRS)
Stoll, Frederick
1993-01-01
The NLPAN computer code uses a finite-strip approach to the analysis of thin-walled prismatic composite structures such as stiffened panels. The code can model in-plane axial loading, transverse pressure loading, and constant through-the-thickness thermal loading, and can account for shape imperfections. The NLPAN code represents an attempt to extend the buckling analysis of the VIPASA computer code into the geometrically nonlinear regime. Buckling mode shapes generated using VIPASA are used in NLPAN as global functions for representing displacements in the nonlinear regime. While the NLPAN analysis is approximate in nature, it is computationally economical in comparison with finite-element analysis, and is thus suitable for use in preliminary design and design optimization. A comprehensive description of the theoretical approach of NLPAN is provided. A discussion of some operational considerations for the NLPAN code is included. NLPAN is applied to several test problems in order to demonstrate new program capabilities, and to assess the accuracy of the code in modeling various types of loading and response. User instructions for the NLPAN computer program are provided, including a detailed description of the input requirements and example input files for two stiffened-panel configurations.
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.
Dynamic response of laminated open deep shells using a geometrically nonlinear theory
Kumar, V.; Singh, A.V.
1995-11-01
In this paper a geometrically nonlinear theory for the analysis of open deep laminated shell panels is presented. The parabolic variation of the transverse shear stresses through the thickness of the shell and the effects of rotary inertia are included in the formulation. The linear and nonlinear stiffness matrices are derived using orthogonal curvilinear coordinate system for a general doubly curved deep laminated shell. The shell`s middle surface displacement and rotation components are modeled using Bezier surface patches and the resulting equation of motion is solved to obtain the transient response, using Beta-m time integration and Newton-Raphson iterations. A very good convergence of the responses is observed by using only the fifth order Bezier surface patches. The dynamic responses of cross-ply laminated circular and noncircular cylindrical panels pinned at the straight edges under a central point load are studied. The effect of the eccentricity on the dynamic response of noncircular cylindrical panels having same plane form as the circular cylindrical panel is also examined.
Geometric Nonlinear Analysis of Self-Anchored Cable-Stayed Suspension Bridges
Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang
2013-01-01
Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800?m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800?m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed. PMID:24282388
Yang, Guang; Lin, Qingyu; Ding, Yu; Tian, Di; Duan, Yixiang
2015-01-01
A new laser induced breakdown spectroscopy (LIBS) based on single-beam-splitting (SBS) and proper optical geometric configuration has been initially explored in this work for effective signal enhancement. In order to improve the interaction efficiency of laser energy with the ablated material, a laser beam operated in pulse mode was divided into two streams to ablate/excite the target sample in different directions instead of the conventional one beam excitation in single pulse LIBS (SP-LIBS). In spatial configuration, the laser beam geometry plays an important role in the emission signal enhancement. Thus, an adjustable geometric configuration with variable incident angle between the two splitted laser beams was constructed for achieving maximum signal enhancement. With the optimized angles of 60° and 70° for Al and Cu atomic emission lines at 396.15?nm and 324.75?nm respectively, about 5.6- and 4.8-folds signal enhancements were achieved for aluminum alloy and copper alloy samples compared to SP-LIBS. Furthermore, the temporal analysis, in which the intensity of atomic lines in SP-LIBS decayed at least ten times faster than the SBS-LIBS, proved that the energy coupling efficiency of SBS-LIBS was significantly higher than that of SP-LIBS. PMID:25557721
Douglas, David R.
2012-01-10
A method of using off-axis particle beam injection in energy-recovering linear accelerators that increases operational efficiency while eliminating the need to merge the high energy re-circulating beam with an injected low energy beam. In this arrangement, the high energy re-circulating beam and the low energy beam are manipulated such that they are within a predetermined distance from one another and then the two immerged beams are injected into the linac and propagated through the system. The configuration permits injection without geometric beam merging as well as decelerated beam extraction without the use of typical beamline elements.
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1986-01-01
The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.
Manipulating nonlinear optical processes with accelerating light beams
Bahabad, Alon; Murnane, Margaret M.; Kapteyn, Henry C.
2011-09-15
We show theoretically that accelerating light beams can be used to manipulate nonlinear optical processes through spatiotemporal quasi-phase-matching, allowing for unprecedented temporal and spectral shaping of the generated light. As a proof of principle, we demonstrate exquisite control over the high-order harmonic frequency conversion process, showing efficient enhancement of an extremely broad range of harmonics emitted during a selected quarter-cycle of the driving laser pulse.
Nonlinear propagation of sinusoidal pulse laser beam in homogeneous plasma
Upadhyay, Ajay K.; Raj, Gaurav; Mishra, Rohit K.; Malviya, Amita; Jha, Pallavi
2007-09-15
The propagation of an intense laser beam, having a sinusoidal pulse profile, in underdense plasma, is analyzed. Applying variational technique and using a standard trial function for the laser pulse amplitude, simultaneous equations describing the evolution of pulse length and spot size are obtained. Relativistic nonlinearity, finite pulse length, and group velocity dispersion effects have been taken into account. Using numerical methods, a graphical analysis of simultaneous evolution of laser spot size and pulse length is presented.
NASA Astrophysics Data System (ADS)
Bekhoucha, Ferhat; Rechak, Said; Duigou, LaÃ«titia; Cadou, Jean-Marc
2015-05-01
This paper deals with the computation of backbone curves bifurcated from a Hopf bifurcation point in the framework of nonlinear free vibrations of a rotating flexible beams. The intrinsic and geometrical equations of motion for anisotropic beams subjected to large displacements are used and transformed with Galerkin and harmonic balance methods to one quadratic algebraic equation involving one parameter, the pulsation. The latter is treated with the asymptotic numerical method using PadÃ© approximants. An algorithm, equivalent to the Lyapunov-Schmidt reduction is proposed, to compute the bifurcated branches accurately from a Hopf bifurcation point, with singularity of co-rank 2, related to a conservative and gyroscopic dynamical system steady state, toward a nonlinear periodic state. Numerical tests dealing with clamped, isotropic and composite, rotating beams show the reliability of the proposed method reinforced by accurate results.
NASA Astrophysics Data System (ADS)
Moroni, Giovanni; Syam, Wahyudin P.; Petrò, Stefano
2014-08-01
Product quality is a main concern today in manufacturing; it drives competition between companies. To ensure high quality, a dimensional inspection to verify the geometric properties of a product must be carried out. High-speed non-contact scanners help with this task, by both speeding up acquisition speed and increasing accuracy through a more complete description of the surface. The algorithms for the management of the measurement data play a critical role in ensuring both the measurement accuracy and speed of the device. One of the most fundamental parts of the algorithm is the procedure for fitting the substitute geometry to a cloud of points. This article addresses this challenge. Three relevant geometries are selected as case studies: a non-linear least-squares fitting of a circle, sphere and cylinder. These geometries are chosen in consideration of their common use in practice; for example the sphere is often adopted as a reference artifact for performance verification of a coordinate measuring machine (CMM) and a cylinder is the most relevant geometry for a pin-hole relation as an assembly feature to construct a complete functioning product. In this article, an improvement of the initial point guess for the Levenberg-Marquardt (LM) algorithm by employing a chaos optimization (CO) method is proposed. This causes a performance improvement in the optimization of a non-linear function fitting the three geometries. The results show that, with this combination, a higher quality of fitting results a smaller norm of the residuals can be obtained while preserving the computational cost. Fitting an ‘incomplete-point-cloud’, which is a situation where the point cloud does not cover a complete feature e.g. from half of the total part surface, is also investigated. Finally, a case study of fitting a hemisphere is presented.
A geometrical model for the Monte Carlo simulation of the TrueBeam linac.
Rodriguez, M; Sempau, J; Fogliata, A; Cozzi, L; Sauerwein, W; Brualla, L
2015-06-01
Monte Carlo simulation of linear accelerators (linacs) depends on the accurate geometrical description of the linac head. The geometry of the Varian TrueBeam linac is not available to researchers. Instead, the company distributes phase-space files of the flattening-filter-free (FFF) beams tallied at a plane located just upstream of the jaws. Yet, Monte Carlo simulations based on third-party tallied phase spaces are subject to limitations. In this work, an experimentally based geometry developed for the simulation of the FFF beams of the Varian TrueBeam linac is presented. The Monte Carlo geometrical model of the TrueBeam linac uses information provided by Varian that reveals large similarities between the TrueBeam machine and the Clinac 2100 downstream of the jaws. Thus, the upper part of the TrueBeam linac was modeled by introducing modifications to the Varian Clinac 2100 linac geometry. The most important of these modifications is the replacement of the standard flattening filters by ad hoc thin filters. These filters were modeled by comparing dose measurements and simulations. The experimental dose profiles for the 6 MV and 10 MV FFF beams were obtained from the Varian Golden Data Set and from in-house measurements performed with a diode detector for radiation fields ranging from 3â€‰â€‰Ã—â€‰â€‰3 to 40â€‰â€‰Ã—â€‰â€‰40 cm(2) at depths of maximum dose of 5 and 10 cm. Indicators of agreement between the experimental data and the simulation results obtained with the proposed geometrical model were the dose differences, the root-mean-square error and the gamma index. The same comparisons were performed for dose profiles obtained from Monte Carlo simulations using the phase-space files distributed by Varian for the TrueBeam linac as the sources of particles. Results of comparisons show a good agreement of the dose for the ansatz geometry similar to that obtained for the simulations with the TrueBeam phase-space files for all fields and depths considered, except for the 40â€‰â€‰Ã—â€‰â€‰40 cm(2) field where the ansatz geometry was able to reproduce the measured dose more accurately. Our approach overcomes some of the limitations of using the Varian phase-space files. It makes it possible to: (i) adapt the initial beam parameters to match measured dose profiles; (ii) reduce the statistical uncertainty to arbitrarily low values; and (iii) assess systematic uncertainties (type B) by using different Monte Carlo codes. One limitation of using phase-space files that is retained in our model is the impossibility of performing accurate absolute dosimetry simulations because the geometrical description of the TrueBeam ionization chamber remains unknown. PMID:25984796
NASA Astrophysics Data System (ADS)
Konoshonkin, Alexander V.; Kustova, Natalia V.; Borovoi, Anatoli G.
2015-10-01
The open-source beam-splitting code is described which implements the geometric-optics approximation to light scattering by convex faceted particles. This code is written in C++ as a library which can be easy applied to a particular light scattering problem. The code uses only standard components, that makes it to be a cross-platform solution and provides its compatibility to popular Integrated Development Environments (IDE's). The included example of solving the light scattering by a randomly oriented ice crystal is written using Qt 5.1, consequently it is a cross-platform solution, too. Both physical and computational aspects of the beam-splitting algorithm are discussed. Computational speed of the beam-splitting code is obviously higher compared to the conventional ray-tracing codes. A comparison of the phase matrix as computed by our code with the ray-tracing code by A. Macke shows excellent agreement.
Investigation of the Geometric Accuracy of Proton Beam Irradiation in the Liver
Fukumitsu, Nobuyoshi; Hashimoto, Takayuki; Okumura, Toshiyuki; Mizumoto, Masashi; Tohno, Eriko; Fukuda, Kuniaki; Abei, Masato; Sakae, Takeji; Sakurai, Hideyuki
2012-02-01
Purpose: To investigate the geometric accuracy of proton beam irradiation to the liver by measuring the change in Hounsfield units (HUs) after irradiation. Methods and Materials: We examined 21 patients with liver tumors who were treated with respiratory-gated proton beam therapy (PBT). The radiation dose was 66 GyE in 12 patients and 72.6 GyE in 9 patients. Image registration and reslicing of the computed tomography (CT) results obtained within 1 month before and 3 months after PBT was performed, referring to the planning CT image. The resliced CT images obtained after PBT were subtracted from the images obtained before PBT. We investigated whether the area of the large HU change was consistent with the high-dose distribution area using the location of the largest change in HU around the tumor (peak) on the subtracted CT image and the 90% dose distribution area of the planning CT image. Results: The number of patients (n = 20) whose left-right peaks were within the 90% dose distribution area was significantly larger than the number of patients whose anterior-posterior peaks and superior-inferior peaks were within the 90% dose distribution area (n = 14, n = 13, p = 0.034, and p = 0.02, respectively). Twelve patients exhibited a peak within the 90% dose distribution area in all directions. Nine of the 11 patients with smaller 90% confidence intervals of the percent normalization of the beam cycle (BC; 90% BC) showed a peak within the 90% dose distribution area in six directions, and this percentage was higher than that among the patients with larger 90% BC (3/10, p = 0.03). Conclusion: The geometric accuracy of proton beam irradiation to the liver was higher in the left-right direction than in the other directions. Patients with an irregular respiratory rhythm have a greater risk of a reduced geometric accuracy of PBT in the liver.
Quality Assurance for the Geometric Accuracy of Cone-Beam CT Guidance in Radiation Therapy
Bissonnette, Jean-Pierre Moseley, Doug; White, Elizabeth; Sharpe, Michael; Purdie, Tom; Jaffray, David A.
2008-05-01
The introduction of volumetric X-ray image-guided radiotherapy systems allows improved management of geometric variations in patient setup and internal organ motion. As these systems become a routine clinical modality, we propose a daily quality assurance (QA) program for cone-beam computed tomography (CBCT) integrated with a linear accelerator. The image-guided system used in this work combines a linear accelerator with conventional X-ray tube and an amorphous silicon flat-panel detector mounted orthogonally from the accelerator central beam axis. This article focuses on daily QA protocols germane to geometric accuracy of the CBCT systems and proposes tolerance levels on the basis of more than 3 years of experience with seven CBCT systems used in our clinic. Monthly geometric calibration tests demonstrate the long-term stability of the flex movements, which are reproducible within {+-}0.5 mm (95% confidence interval). The daily QA procedure demonstrates that, for rigid phantoms, the accuracy of the image-guided process can be within 1 mm on average, with a 99% confidence interval of {+-}2 mm.
NASA Astrophysics Data System (ADS)
He, Qizhi; Kang, Zhan; Wang, Yiqiang
2014-09-01
Based on the element-free Galerkin (EFG) method, an analysis-independent density variable approach is proposed for topology optimization of geometrically nonlinear structures. This method eliminates the mesh distortion problem often encountered in the finite element analysis of large deformations. The topology optimization problem is formulated on the basis of point-wise description of the material density field. This density field is constructed by a physical meaning-preserving interpolation with the density values of the design variable points, which can be freely positioned independently of the field points used in the displacement analysis. An energy criterion of convergence is used to resolve the well-known convergence difficulty, which would be usually encountered in low density regions, where displacements oscillate severely during the optimization process. Numerical examples are given to demonstrate the effectiveness of the developed approach. It is shown that relatively clear optimal solutions can be achieved, without exhibiting numerical instabilities like the so-called "layering" or "islanding" phenomena even in large deformation cases. This study not only confirms the potential of the EFG method in topology optimization involving large deformations, but also provides a novel topology optimization framework based on element-free discretization of displacement and density fields, which can also easily incorporate other meshless analysis methods for specific purposes.
NASA Astrophysics Data System (ADS)
Di Egidio, Angelo; Contento, Alessandro; Vestroni, Fabrizio
2015-12-01
An open-cross section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear open-cross section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.
NASA Astrophysics Data System (ADS)
Gautesen, A. K.; Morris, J. R.
We develop a geometric optics series expansion approximation to a model of phase-compensated whole-beam thermal blooming of high-power laser beams. The model consists of a nonlinear medium whose thermal blooming coupling coefficient decreases exponentially with the propagation distance from the laser and whose motion relative to the laser beam is taken to be unidirectional, a Gaussian high-power intensity profile at the laser, and a collimated beam boundary condition at an exit plane that is many e-folding scale lengths from the laser. The series expansion parameter is directly proportional to Smith's geometric optics distortion parameter. Expansion formulas are derived for both the intensity and phase at all propagation distances. The exit plane intensity profiles obtained from these formulas qualitatively agree with numerical results obtained from the wave-optics thermal blooming code FOURD, except when the FOURD results indicate that caustics are forming; quantitative agreement is also excellent, except for small differences in fine structure near the downwind edge of the beam. FOURD's return-wave phase-compensation iteration provides an estimate that the rms error in the initial phase obtained from our series approximation truncated at third-order is approximately 0.5 percent over the range of values we investigated.
NASA Technical Reports Server (NTRS)
Hrinda, Glenn A.; Nguyen, Duc T.
2008-01-01
A technique for the optimization of stability constrained geometrically nonlinear shallow trusses with snap through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite element formulation. The optimization method uses an iterative scheme that evaluates the design variables' performance and then updates them according to a recursive formula controlled by the arc length method. A minimum weight design is achieved when a uniform nonlinear strain energy density is found in all members. This minimal condition places the design load just below the critical limit load causing snap through of the structure. The optimization scheme is programmed into a nonlinear finite element algorithm to find the large strain energy at critical limit loads. Examples of highly nonlinear trusses found in literature are presented to verify the method.
The wave energy flux of high frequency diffracting beams in complex geometrical optics
Maj, Omar; Poli, Emanuele; Mariani, Alberto; Farina, Daniela
2013-04-15
We consider the construction of asymptotic solutions of Maxwell's equations for a diffracting wave beam in the high frequency limit and address the description of the wave energy flux transported by the beam. With this aim, the complex eikonal method is applied. That is a generalization of the standard geometrical optics method in which the phase function is assumed to be complex valued, with the non-negative imaginary part accounting for the finite width of the beam cross section. In this framework, we propose an argument which simplifies significantly the analysis of the transport equation for the wave field amplitude and allows us to derive the wave energy flux. The theoretical analysis is illustrated numerically for the case of electron cyclotron beams in tokamak plasmas by using the GRAY code [D. Farina, Fusion Sci. Technol. 52, 154 (2007)], which is based upon the complex eikonal theory. The results are compared to those of the paraxial beam tracing code TORBEAM [E. Poli et al., Comput. Phys. Commun. 136, 90 (2001)], which provides an independent calculation of the energy flow.
Davis, M. J.; Skodje, R. T.; Chemistry; Univ. of Colorado
2001-01-01
A geometric approach to the study of multiple-time-scale kinetics is taken here. The approach to equilibrium for kinetic systems is studied via low-dimensional manifolds, with an application to a nonlinear master equation for vibrational relaxation. One of our main concerns is the asymptotic (in time) behavior of the system and whether there is a well-defined rate of approach to equilibrium. One-dimensional slow manifolds provide a good means for studying such behavior in nonlinear systems, because they are the analogue of the eigenvector with least negative eigenvalue for linear kinetics.
A new pre-loaded beam geometric stiffness matrix with full rigid body capabilities
NASA Technical Reports Server (NTRS)
Bosela, P. A.; Fertis, D. G.; Shaker, F. J.
1992-01-01
Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the 'blanket' of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as 'grounding', or false stiffening, of the stiffness matrix occurs during rigid body rotation. The authors have previously shown that the grounding phenomenon is caused by a lack of rigid body rotational capability, and is typical in beam geometric stiffness matrices formulated by others, including those which contain higher order effects. The cause of the problem was identified as the force imbalance inherent in the formulations. In this paper, the authors develop a beam geometric stiffness matrix for a directed force problem, and show that the resultant global stiffness matrix contains complete rigid body mode capabilities, and performs very well in the diagonalization methodology customarily used in dynamic analysis.
Nonlinear Finite Element Analysis of FRP Strengthened Reinforced Concrete Beams
NASA Astrophysics Data System (ADS)
Sasmal, S.; Kalidoss, S.; Srinivas, V.
2012-12-01
This paper focuses on nonlinear analysis of parent and fiber reinforced polymer (FRP) strengthened reinforced concrete (RC) beam using general purpose finite element software, ANSYS. Further, it is aimed to investigate the suitability of different elements available in ANSYS library to represent FRP, epoxy and interface. 3-D structural RC solid element has been used to model concrete and truss element is employed for modeling the reinforcements. FRP has been modelled using 3-D membrane element and layered element with number of layers, epoxy is modelled using eight node brick element, and eight node layered solid shell is used to mathematically represent the concrete-FRP interface behavior. Initially, the validation of the numerical model for the efficacy of different elements (SOLID65 for concrete and LINK8 for reinforcement) and material models is carried out on the experimental beam reported in literature. The validated model, elements and material properties is used to evaluate the load-displacement and load-strain response behavior and crack patterns of the FRP strengthened RC beams. The numerical results indicated that significant improvement in the displacement in the strengthened RC beams with the advancement of cracks. The study shows that FRP with shell elements is recommended when single layer of FRP is used. When multi layered FRP is used, solid layered element can be a reasonably good choice whereas the epoxy matrix with linear solid element does not need further complicated model. Interfacial element makes the analysis minimally improved at the cost of complicated modeling issues and considerable computation time. Hence, for nonlinear analysis of usual strengthened structures, unless it is specifically required for, interface element may not be required and a full contact can be assumed at interface.
Lin, Tai-Chia; Beli?, Milivoj R.; Petrovi?, Milan S.; Chen, Goong; Department of Mathematics and Institute for Quantum Science and Engineering, Texas A and M University, College Station, Texas 77843
2014-01-15
Counterpropagating optical beams in nonlinear media give rise to a host of interesting nonlinear phenomena such as the formation of spatial solitons, spatiotemporal instabilities, self-focusing and self-trapping, etc. Here we study the existence of ground state (the energy minimizer under the L{sup 2}-normalization condition) in two-dimensional (2D) nonlinear Schrödinger (NLS) systems with saturable nonlinearity, which describes paraxial counterpropagating beams in isotropic local media. The nonlinear coefficient of saturable nonlinearity exhibits a threshold which is crucial in determining whether the ground state exists. The threshold can be estimated by the Gagliardo-Nirenberg inequality and the ground state existence can be proved by the energy method, but not the concentration-compactness method. Our results also show the essential difference between 2D NLS equations with cubic and saturable nonlinearities.
Light beams with general direction and polarization: Global description and geometric phase
Nityananda, R.; Sridhar, S.
2014-02-15
We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S{sup 2} of directions, is given through the construction of an orthogonal basis pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S{sup 2}Ã—C{sup 2}âˆ–(0), the (untwisted) Cartesian product of a sphere and a two dimensional complex vector space minus the origin. A Hopf map (i.e. mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S{sup 2}Ã—S{sup 2} which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majoranaâ€™s mapping of the states of a spin one quantum system to an unordered pair of points on a sphere. This is a different manifold, CP{sup 2}, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S{sup 2}Ã—S{sup 2}. We give the U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework. -- Highlights: â€¢ We construct a polarization basis for light which is smooth in all directions. â€¢ Proof that the manifold of all polarizations and directions is S{sup 2}Ã—S{sup 2}. â€¢ Formula for the geometric phase for paths in S{sup 2}Ã—S{sup 2}, generalizing earlier work.
NASA Astrophysics Data System (ADS)
Cesnik, C. E. S.; Opoku, D. G.; Nitzsche, F.; Cheng, T.
2004-06-01
An active aeroelastic and aeroacoustic analysis of helicopter rotor systems is presented in this paper. It is a tightly coupled computational aeroelastic code that interfaces a particle-wake panel method code with an active nonlinear mixed variational intrinsic beam element code. In addition, a Ffowcs-Williams-Hawkings equation-based acoustic component is incorporated to complete the numerical implementation. The theory behind each component is summarized here as well as the method for coupling the aerodynamic and structural components. Sample acoustic and aeroelastic results are given for different model-scale rotors. Comparisons with available (passive) results show very good agreement. Preliminary study with an active twist rotor is also shown.
Modeling of nonlinear combining of multiple laser beams in Kerr medium.
Lushnikov, Pavel M; Vladimirova, Natalia
2015-11-30
We model combining of multiple laser beams into a single near diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. The beams with the total power above critical are combined in the near field and then propagated in the Kerr medium. Nonlinearity results in self-focusing event, combining multiple beams into nearly a diffraction-limited beam that carries the critical power. Beam quality of the combined beam is analyzed as a function of the number of combining beams and the level of random fluctuations of the combining beams phases. PMID:26698740
Evaluation and Correction of the Non-linear Distortion of CEBAF Beam Position Monitors
M. Spata, T.L. Allison, K.E. Cole, J. Musson, J. Yan
2011-09-01
The beam position monitors at CEBAF have four antenna style pickups that are used to measure the location of the beam. There is a strong nonlinear response when the beam is far from the electrical center of the device. In order to conduct beam experiments at large orbit excitation we need to correct for this nonlinearity. The correction algorithm is presented and compared to measurements from our stretched wire BPM test stand.
Geometric Parameters Estimation and Calibration in Cone-Beam Micro-CT
Zhao, Jintao; Hu, Xiaodong; Zou, Jing; Hu, Xiaotang
2015-01-01
The quality of Computed Tomography (CT) images crucially depends on the precise knowledge of the scanner geometry. Therefore, it is necessary to estimate and calibrate the misalignments before image acquisition. In this paper, a Two-Piece-Ball (TPB) phantom is used to estimate a set of parameters that describe the geometry of a cone-beam CT system. Only multiple projections of the TPB phantom at one position are required, which can avoid the rotation errors when acquiring multi-angle projections. Also, a corresponding algorithm is derived. The performance of the method is evaluated through simulation and experimental data. The results demonstrated that the proposed method is valid and easy to implement. Furthermore, the experimental results from the Micro-CT system demonstrate the ability to reduce artifacts and improve image quality through geometric parameter calibration. PMID:26371008
NASA Astrophysics Data System (ADS)
Rafiee, M.; Liu, X. F.; He, X. Q.; Kitipornchai, S.
2014-07-01
The nonlinear free vibration of carbon nanotubes/fiber/polymer composite (CNTFPC) multi-scale plates with surface-bonded piezoelectric actuators is studied in this paper. The governing equations of the piezoelectric nanotubes/fiber/polymer multiscale laminated composite plates are derived based on first-order shear deformation plate theory (FSDT) and von Kármán geometrical nonlinearity. Halpin-Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale composite. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. A perturbation scheme of multiple time scales is employed to determine the nonlinear vibration response and the nonlinear natural frequencies of the plates with immovable simply supported boundary conditions. The effects of the applied constant voltage, plate geometry, volume fraction of fibers and weight percentage of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) on the linear and nonlinear natural frequencies of the piezoelectric nanotubes/fiber/polymer multiscale composite plate are investigated through a detailed parametric study.
Integrability and chaos in nonlinearly coupled optical beams
David, D.
1989-01-01
This paper presents a study, using dynamical systems methods, of the equations describing the polarization behavior of two nonlinearly coupled optical beams counterpropagating in a nonlinear medium. In the travelling-wave regime assumption, this system possesses a Lie-Poisson structure on the manifold C{sup 2} {times} C{sup 2}. In the case where the medium is assumed to be isotropic, this system exhibits invariance under the Hamiltonian action of two copies of the rotation group, S{sup 1}, and actually reduces to a lower-dimensional system on the two-sphere, S{sup 2}. We study the dynamics on the reduced space and examine the structure of the phase portrait by determining the fixed points and infinite-period homoclinic and heteroclinic orbits; we concentrate on presenting some exotic behaviour that occurs when some parameters are varied, and we also show special solutions associated with some of the above-mentioned orbits. Last, we demonstrate the existence of complex dynamics when the system is subject to certain classes of Hamiltonian perturbations. To this end, we make use of the Melnikov method to analytically show the occurrence of either horseshoe chaos, or Arnold diffusion. 19 refs.
NASA Astrophysics Data System (ADS)
Kuang, Zheng; Li, Jiangning; Edwardson, Stuart; Perrie, Walter; Liu, Dun; Dearden, Geoff
2015-07-01
We have demonstrated an original ultrafast laser beam shaping technique for material processing using a spatial light modulator (SLM). Complicated and time-consuming diffraction far-field phase hologram calculations based on Fourier transformations are avoided, while simple and direct geometric masks are used to shape the incident beam at diffraction near-field. Various beam intensity shapes, such as square, triangle, ring and star, are obtained and then reconstructed at the imaging plane of an f-theta lens. The size of the shaped beam is approximately 20 ?m, which is comparable to the beam waist at the focal plane. A polished stainless steel sample is machined by the shaped beam at the imaging plane. The shape of the ablation footprint well matches the beam shape.
NASA Astrophysics Data System (ADS)
Rauter, N.; Lammering, R.
2015-04-01
In order to detect micro-structural damages accurately new methods are currently developed. A promising tool is the generation of higher harmonic wave modes caused by the nonlinear Lamb wave propagation in plate like structures. Due to the very small amplitudes a cumulative effect is used. To get a better overview of this inspection method numerical simulations are essential. Previous studies have developed the analytical description of this phenomenon which is based on the five-constant nonlinear elastic theory. The analytical solution has been approved by numerical simulations. In this work first the nonlinear cumulative wave propagation is simulated and analyzed considering micro-structural cracks in thin linear elastic isotropic plates. It is shown that there is a cumulative effect considering the S1-S2 mode pair. Furthermore the sensitivity of the relative acoustical nonlinearity parameter regarding those damages is validated. Furthermore, an influence of the crack size and orientation on the nonlinear wave propagation behavior is observed. In a second step the micro-structural cracks are replaced by a nonlinear material model. Instead of the five-constant nonlinear elastic theory hyperelastic material models that are implemented in commonly used FEM software are used to simulate the cumulative effect of the higher harmonic Lamb wave generation. The cumulative effect as well as the different nonlinear behavior of the S1-S2 and S2-S4 mode pairs are found by using these hyperelastic material models. It is shown that, both numerical simulations, which take into account micro-structural cracks on the one hand and nonlinear material on the other hand, lead to comparable results. Furthermore, in comparison to the five-constant nonlinear elastic theory the use of the well established hyperelastic material models like Neo-Hooke and Mooney-Rivlin are a suitable alternative to simulate the cumulative higher harmonic generation.
Geometric calibration of a mobile C-arm for intraoperative cone-beam CT
Daly, M. J.; Siewerdsen, J. H.; Cho, Y. B.; Jaffray, D. A.; Irish, J. C.
2008-01-01
A geometric calibration method that determines a complete description of source-detector geometry was adapted to a mobile C-arm for cone-beam computed tomography (CBCT). The non-iterative calibration algorithm calculates a unique solution for the positions of the source (Xs,Ys,Zs), detector (Xd,Yd,Zd), piercing point (Uo,Vo), and detector rotation angles (?,?,?) based on projections of a phantom consisting of two plane-parallel circles of ball bearings encased in a cylindrical acrylic tube. The prototype C-arm system was based on a Siemens PowerMobil modified to provide flat-panel CBCT for image-guided interventions. The magnitude of geometric nonidealities in the source-detector orbit was measured, and the short-term (?4 h) and long-term (?6 months) reproducibility of the calibration was evaluated. The C-arm exhibits large geometric nonidealities due to mechanical flex, with maximum departures from the average semicircular orbit of ?Uo=15.8 mm and ?Vo=9.8 mm (for the piercing point), ?X and ?Y=6–8 mm and ?Z=1 mm (for the source and detector), and ???2.9°, ???1.9°, and ???0.8° (for the detector tilt?rotation). Despite such significant departures from a semicircular orbit, these system parameters were found to be reproducible, and therefore correctable by geometric calibration. Short-term reproducibility was <0.16 mm (subpixel) for the piercing point coordinates, <0.25 mm for the source-detector X and Y, <0.035 mm for the source-detector Z, and <0.02° for the detector angles. Long-term reproducibility was similarly high, demonstrated by image quality and spatial resolution measurements over a period of 6 months. For example, the full-width at half-maximum (FWHM) in axial images of a thin steel wire increased slightly as a function of the time (?) between calibration and image acquisition: FWHM=0.62, 0.63, 0.66, 0.71, and 0.72 mm at ?=0 s, 1 h, 1 day, 1 month, and 6 months, respectively. For ongoing clinical trials in CBCT-guided surgery at our institution, geometric calibration is conducted monthly to provide sufficient three-dimensional (3D) image quality while managing time and workflow considerations of the calibration and quality assurance process. The sensitivity of 3D image quality to each of the system parameters was investigated, as was the tolerance to systematic and random errors in the geometric parameters, showing the most sensitive parameters to be the piercing point coordinates (Uo,Vo) and in-plane positions of the source (Xs,Ys) and detector (Xd,Yd). Errors in the out-of-plane position of the source (Zs) and detector (Zd) and the detector angles (?,?,?) were shown to have subtler effects on 3D image quality. PMID:18561688
Nonlinear Interaction of Elliptical Laser Beam with Collisional Plasma: Effect of Linear Absorption
NASA Astrophysics Data System (ADS)
Keshav, Walia; Sarabjit, Kaur
2016-01-01
In the present work, nonlinear interaction of elliptical laser beam with collisional plasma is studied by using paraxial ray approximation. Nonlinear differential equations for the beam width parameters of semi-major axis and semi-minor axis of elliptical laser beam have been set up and solved numerically to study the variation of beam width parameters with normalized distance of propagation. Effects of variation in absorption coefficient and plasma density on the beam width parameters are also analyzed. It is observed from the analysis that extent of self-focusing of beam increases with increase/decrease in plasma density/absorption coefficient.
Non-linear optical measurements using a scanned, Bessel beam
NASA Astrophysics Data System (ADS)
Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.
2015-03-01
Oftentimes cells are removed from the body for disease diagnosis or cellular research. This typically requires fluorescent labeling followed by sorting with a flow cytometer; however, possible disruption of cellular function or even cell death due to the presence of the label can occur. This may be acceptable for ex vivo applications, but as cells are more frequently moving from the lab to the body, label-free methods of cell sorting are needed to eliminate these issues. This is especially true of the growing field of stem cell research where specialized cells are needed for treatments. Because differentiation processes are not completely efficient, cells must be sorted to eliminate any unwanted cells (i.e. un-differentiated or differentiated into an unwanted cell type). In order to perform label-free measurements, non-linear optics (NLO) have been increasingly utilized for single cell analysis because of their ability to not disrupt cellular function. An optical system was developed for the measurement of NLO in a microfluidic channel similar to a flow cytometer. In order to improve the excitation efficiency of NLO, a scanned Bessel beam was utilized to create a light-sheet across the channel. The system was tested by monitoring twophoton fluorescence from polystyrene microbeads of different sizes. Fluorescence intensity obtained from light-sheet measurements were significantly greater than measurements made using a static Gaussian beam. In addition, the increase in intensity from larger sized beads was more evident for the light-sheet system.
A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation
NASA Technical Reports Server (NTRS)
Crivelli, Luis A.; Felippa, Carlos A.
1992-01-01
A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.
Geometrically nonlinear static and dynamic analysis of functionally graded skew plates
NASA Astrophysics Data System (ADS)
Upadhyay, A. K.; Shukla, K. K.
2013-08-01
The present paper deals with nonlinear static and dynamic behavior of functionally graded skew plates. The equations of motion are derived using higher order shear deformation theory in conjunction with von-Karman's nonlinear kinematics. The physical domain is mapped into computational domain using linear mapping and chain rule of differentiation. The spatial and temporal discretization is based on fast converging finite double Chebyshev series and Houbolt's method. Quadratic extrapolation technique is employed to linearize the governing nonlinear equations. The spatial and temporal convergence and validation studies have been carried out to establish the efficacy of the present solution methodology. In case of dynamic analysis, the results are obtained for uniform step, sine, half sine, triangular and exponential type of loadings. The effect of volume fraction index, skew angle and boundary conditions on nonlinear displacement and moment response are presented.
Ronald C. Davidson; W. Wei-li Lee; Hong Qin; Edward Startsev
2001-11-08
This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed.
NASA Astrophysics Data System (ADS)
Liu, Peipei; Sohn, Hoon; Park, Byeongjin
2015-06-01
Damage often causes a structural system to exhibit severe nonlinear behaviors, and the resulting nonlinear features are often much more sensitive to the damage than their linear counterparts. This study develops a laser nonlinear wave modulation spectroscopy (LNWMS) so that certain types of damage can be detected without any sensor placement. The proposed LNWMS utilizes a pulse laser to generate ultrasonic waves and a laser vibrometer for ultrasonic measurement. Under the broadband excitation of the pulse laser, a nonlinear source generates modulations at various frequency values due to interactions among various input frequency components. State space attractors are reconstructed from the ultrasonic responses measured by LNWMS, and a damage feature called Bhattacharyya distance (BD) is computed from the state space attractors to quantify the degree of damage-induced nonlinearity. By computing the BD values over the entire target surface using laser scanning, damage can be localized and visualized without relying on the baseline data obtained from the pristine condition of a target structure. The proposed technique has been successfully used for visualizing fatigue crack in an aluminum plate and delamination and debonding in a glass fiber reinforced polymer wind turbine blade.
Effects of Geometric Azimuthal Asymmetries of the PPM Stack on Electron Beam Characteristics
NASA Technical Reports Server (NTRS)
Kory, Carol L.
2000-01-01
The effects of geometric azimuthally asymmetric properties of a periodic permanent magnet (PPM) focusing stack on electron beam characteristics obtained using a fully three dimensional (3D) particle-in-cell (PIC) code will be presented. The simulation model, using MAFIA (Solution of MAxwell's equations by the Finite-Integration-Algorithm), incorporates 3D behavior of the beam immersed in static fields calculated directly from the exact geometry and material properties of the 3D magnetic focusing structure. The Hughes 8916H, 18-40 GHz helical TWT for the millimeter-wave power module (MMPM) was used as a prototype. Firstly, the effects of C-magnets used at the input and output of the TWT to allow for coupling of the RF signal into and out of the tube are considered. The 8916H input and output C-magnets differ because coaxial couplers are used at the input and waveguide couplers are used at the output The repositioning of the beam from its central axis due to the inclusion of the output C-magnet was found to be most significant. The modeled output C-magnet and its orientation in the Cartesian coordinate system is shown, and a two-dimensional beam profile including the output C-magnet is also shown. A table presents the shift of the beam center off the central axis relative to the average radius of the beam at the longitudinal points A, B and C designated on an enclosed figure. Secondly, the addition of shunts, or rectangular iron pieces applied manually by a skilled technician in order to improve beam transmission, is considered. The shunts are applied to the top of the tube; thus, azimuthal symmetry of the focusing stack is interrupted. Although shunts are typically added during RF focusing, they are also typically added at the input section of the tube where RF forces are minimal, making an electron optics analysis meaningful. Because several shunts are usually applied to one pole piece, the simulations have been simplified by modeling a half washer with the same radius and longitudinal length as a shunt over the entire x, positive-y half of the transverse plane. A modeled pole piece and shunt as described are shown. Lastly, in order to study the effects of magnet misalignments, a magnet in the PPM stack was arbitrarily chosen and adjusted so that its central axis was shifted both 0.7 percent and 1.0 percent of the magnet outer diameter in the positive-y direction. In practice, positioning the magnets so that their central axis is accurately aligned with the central axis of the tube is challenging. Thus, it is a strong possibility that one or more magnets will be misaligned relative to the tube central axis.
Cornacchia, M.; Evans, L.
1982-10-07
In this report we describe an experiment which was conducted at the SPS to observe the combined effects of a single isolated high-order nonlinear resonance, nonlinear detuning, and tune modulation. The nonlinear resonance, as well as the nonlinear detuning, was driven by a nonlinear lens, which had been previously used at the SPS for the study of the beam-beam interactions. The nonlinear motion of a particle in the field of the lens is discussed.
Suppression of space charge induced beam halo in nonlinear focusing channel
NASA Astrophysics Data System (ADS)
Batygin, Yuri K.; Scheinker, Alexander; Kurennoy, Sergey; Li, Chao
2016-04-01
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.
Fedele, Renato; Jovanovic, Dusan
2004-12-01
Charged-particle beams are employed for a number of scientific and technological applications. The conventional description of their collective behavior is usually given in terms of the Vlasov equation. In the last 15 years some alternative descriptions have been developed in terms of a nonlinear Schroedinger equation governing the collective dynamics of the beam while interacting with the surrounding medium. This approach gives new insights, providing an alternative 'key of reading' of the charged-particle beam dynamics, and have been applied to a number of physical problems concerning conventional particle accelerating machines as well as plasma-based accelerator schemes. Remarkably, it is based on a mathematical formalism fully similar to those used for the propagation of e.m. radiation beams in nonlinear media a well as the nonlinear dynamics of the Bose-Einsten condensates.In this paper, a presentation of some significant nonlinear collective effects of a charged-particle beam in particle accelerators, that have been recently investigated in the framework of the above Schroedinger-like descriptions, is given.
Propagation of an asymmetric Gaussian beam in a nonlinear absorbing medium
NASA Astrophysics Data System (ADS)
Ianetz, D.; Kaganovskii, Yu.; Wilson-Gordon, A. D.; Rosenbluh, M.
2010-05-01
Propagation of an asymmetric Gaussian beam in a cubic-quintic absorbing medium is analyzed and compared with that of a symmetric beam in both lossless and lossy media. A “collective variable approach” technique, based on trial functions, is used for solution of the general nonlinear Schrödinger equation. Using this variational approach, we investigate the self-focusing and breathing of an intense asymmetric Gaussian beam, taking into account both linear and nonlinear absorption. For a lossless medium, we define regions of oscillatory and diffractive beam propagation, for both symmetric and asymmetric beams. In particular, for an asymmetric beam, we find that there is no sharp boundary between the oscillatory self-focusing and oscillatory diffractive regimes of propagation. In the oscillatory region, we detect an interesting phenomenon—“beats” of the amplitude and perpendicular widths of the beam. For a lossy medium, significant differences between the amplitudes, widths, and phases of the symmetric and asymmetric beams have been predicted.
Feola, Andrew; Pal, Siladitya; Moalli, Pamela; Maiti, Spandan; Abramowitch, Steven
2014-08-22
Synthetic polypropylene meshes were designed to restore pelvic organ support for women suffering from pelvic organ prolapse; however, the FDA released two notifications regarding potential complications associated with mesh implantation. Our aim was to characterize the structural properties of Restorelle and UltraPro subjected to uniaxial tension along perpendicular directions, and then model the tensile behavior of these meshes utilizing a co-rotational finite element model, with an imbedded linear or fiber-recruitment local stress-strain relationship. Both meshes exhibited a highly nonlinear stress-strain behavior; Restorelle had no significant differences between the two perpendicular directions, while UltraPro had a 93% difference in the low (initial) stiffness (p=0.009) between loading directions. Our model predicted that early alignment of the mesh segments in the loading direction and subsequent stretching could explain the observed nonlinear tensile behavior. However, a nonlinear stress-strain response in the stretching regime, that may be inherent to the mesh segment, was required to better capture experimental results. Utilizing a nonlinear fiber recruitment model with two parameters A and B, we observed improved agreement between the simulations and the experimental results. An inverse analysis found A=120 MPa and B=1.75 for Restorelle (RMSE=0.36). This approach yielded A=30 MPa and B=3.5 for UltraPro along one direction (RMSE=0.652), while the perpendicular orientation resulted in A=130 MPa and B=4.75 (RMSE=4.36). From the uniaxial protocol, Restorelle was found to have little variance in structural properties along these two perpendicular directions; however, UltraPro was found to behave anisotropically. PMID:25011619
Feola, Andrew; Pal, Siladitya; Moalli, Pamela; Maiti, Spandan; Abramowitch, Steven
2014-01-01
Synthetic polypropylene meshes were designed to restore pelvic organ support for women suffering from pelvic organ prolapse; however, the FDA released two notifications regarding the potential complications associated with mesh implantation. Our aim was to characterize the structural properties of Restorelle and UltraPro subjected to uniaxial tension along perpendicular directions, and then model the tensile behavior of these meshes utilizing a co-rotational finite element model, with an imbedded linear or fiber-recruitment local stress-strain relationship. Both meshes exhibited highly nonlinear stress-strain behavior; Restorelle had no significant differences between the two perpendicular directions, while UltraPro had a 93% difference in the low (initial) stiffness (p=0.009) between loading directions. Our model predicted that early alignment of the mesh segments in the loading direction and subsequent stretching could explain the observed nonlinear tensile behavior. However, a nonlinear stress-strain response in the stretching regime, that may be inherent to the mesh segment, was required to better capture experimental results. Utilizing a nonlinear fiber recruitment model with two parameters A and B, we observed improved agreement between the simulations and the experimental results. An inverse analysis found A=120 MPa and B=1.75 for Restorelle (RMSE=0.36). This approach yielded A=30 MPa and B=3.5 for UltraPro along one direction (RMSE=0.652), while the perpendicular orientation resulted in A=130 MPa and B=4.75 (RMSE=4.36). From the uniaxial protocol, Restorelle was found to have little variance in structural properties along these two perpendicular directions; however, UltraPro was found to behave anisotropically. PMID:25011619
Geometrically nonlinear design sensitivity analysis on parallel-vector high-performance computers
NASA Technical Reports Server (NTRS)
Baddourah, Majdi A.; Nguyen, Duc T.
1993-01-01
Parallel-vector solution strategies for generation and assembly of element matrices, solution of the resulted system of linear equations, calculations of the unbalanced loads, displacements, stresses, and design sensitivity analysis (DSA) are all incorporated into the Newton Raphson (NR) procedure for nonlinear finite element analysis and DSA. Numerical results are included to show the performance of the proposed method for structural analysis and DSA in a parallel-vector computer environment.
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.
2003-01-01
The use of stress predictions from equivalent linearization analyses in the computation of high-cycle fatigue life is examined. Stresses so obtained differ in behavior from the fully nonlinear analysis in both spectral shape and amplitude. Consequently, fatigue life predictions made using this data will be affected. Comparisons of fatigue life predictions based upon the stress response obtained from equivalent linear and numerical simulation analyses are made to determine the range over which the equivalent linear analysis is applicable.
Self-focusing of Hermite-Gaussian laser beam with relativistic nonlinearity
NASA Astrophysics Data System (ADS)
Sharma, Prerana
2015-07-01
This paper presents an investigation of self-focusing of Hermite-Gaussian laser beams in plasma considering relativistic nonlinearity. The differential equations for beam width parameters are obtained using the usual Wentzel-Kramers-Brillouin and paraxial approximations. The nonlinearity in the dielectric constant is assumed to be aroused mainly due to the relativistic mass correction of electron. To highlight the nature of focusing, graphical results of the behavior of beam-width parameters with the dimensionless distance of propagation is presented. The numerical computation is completed by using Taylor series method. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments.
Sensitivity of nonlinear harmonic generation to electron beam quality in free-electron lasers
Biedron, Sandra G.; Huang, Zhirong; Kim, Kwange-Je; Milton, Stephen; Dattoli, Giuseppe; Ottavani, Pier Luigi; Renieri, Alberto; Fawley, William M.; Freund, Henry P.; Huhn, Heinz-Dieter
2002-03-01
The generation of harmonics through a nonlinear mechanism driven by bunching at the fundamental has sparked interest as a path toward enhancing and extending the usefulness of an x-ray free-electron laser (FEL) facility. The sensitivity of the nonlinear harmonic generation to undulator imperfections, electron beam energy spread, peak current, and emittance is important in an evaluation of the process. Typically, linear instabilities in FELs are characterized by increased sensitivity to both electron beam and undulator quality with increasing harmonic number. However, since the nonlinear harmonic generation mechanism is driven by the growth of the fundamental, the sensitivity of the nonlinear harmonic mechanism is not expected to be significantly greater than that of the fundamental. In this paper, they study the effects of electron beam quality, more specifically, emittance, energy spread, and peak current, on the nonlinear harmonics in a 1.5-{angstrom} FEL, and show that the decline in the harmonic emission roughly follows that of the fundamental.
Horizontal geometrical reaction time model for two-beam nacelle LiDARs
NASA Astrophysics Data System (ADS)
Beuth, Thorsten; Fox, Maik; Stork, Wilhelm
2015-06-01
Wind energy is one of the leading sustainable energies. To attract further private and state investment in this technology, a broad scaled drop of the cost of energy has to be enforced. There is a trend towards using Laser Doppler Velocimetry LiDAR systems for enhancing power output and minimizing downtimes, fatigue and extreme forces. Since most used LiDARs are horizontally setup on a nacelle and work with two beams, it is important to understand the geometrical configuration which is crucial to estimate reaction times for the actuators to compensate wind gusts. In the beginning of this article, the basic operating modes of wind turbines are explained and the literature on wind behavior is analyzed to derive specific wind speed and wind angle conditions in relation to the yaw angle of the hub. A short introduction to the requirements for the reconstruction of the wind vector length and wind angle leads to the problem of wind shear detection of angled but horizontal homogeneous wind fronts due to the spatial separation of the measuring points. A distance is defined in which the wind shear of such homogeneous wind fronts is not present which is used as a base to estimate further distance calculations. The reaction time of the controller and the actuators are having a negative effect on the effective overall reaction time for wind regulation as well. In the end, exemplary calculations estimate benefits and disadvantages of system parameters for wind gust regulating LiDARs for a wind turbine of typical size. An outlook shows possible future improvements concerning the vertical wind behavior.
NASA Astrophysics Data System (ADS)
Kanwar, V.; Singh, Sukhjit; Bakshi, S.
2008-01-01
In this paper, we derive one-parameter families of Newton, Halley, Chebyshev, Chebyshev-Halley type methods, super-Halley, C-methods, osculating circle and ellipse methods respectively for finding simple zeros of nonlinear equations, permitting f???(x)?=?0 at some points in the vicinity of the required root. Halley, Chebyshev, super-Halley methods and, as an exceptional case, Newton method are seen as the special cases of the family. All the methods of the family and various others are cubically convergent to simple roots except Newton?s or a family of Newton?s method.
Nonlinear beam clean-up using resonantly enhanced sum-frequency mixing
NASA Astrophysics Data System (ADS)
Karamehmedovi?, E.; Pedersen, C.; Jensen, O. B.; Tidemand-Lichtenberg, P.
2009-08-01
We investigate the possibility of improving the beam quality and obtaining high conversion efficiency in nonlinear sum-frequency generation. A 765 nm beam from an external cavity tapered diode laser is single-passed through a nonlinear crystal situated in the high intracavity field of a 1342 nm Nd:YVO4 laser, generating a SFG beam at 488 nm. The ECDL have M {/H 2}=1.9 and M {/V 2}=2.4 and the solid-state laser has M 2<1.05. Varying the focusing of the 765 nm beam, the conversion efficiency and the beam quality of the generated 488 nm beam change correspondingly. We show that it is possible to improve the M 2 of the 488 nm beam to less than 1.3 while preserving a high conversion efficiency of the SFG process.
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Feng, Bin-Lu; Rui, Wen-Juan; Zhang, Xiang-Zhi
2015-07-01
With the help of a simple Lie algebra, an isospectral Lax pair, whose feature presents decomposition of element (1, 2) into a linear combination in the temporal Lax matrix, is introduced for which a new integrable hierarchy of evolution equations is obtained, whose Hamiltonian structure is also derived from the trace identity in which contains a constant ? to be determined. In the paper, we obtain a general formula for computing the constant ?. The reduced equations of the obtained hierarchy are the generalized nonlinear heat equation containing three-potential functions, the mKdV equation and a generalized linear KdV equation. The algebro-geometric solutions (also called finite band solutions) of the generalized nonlinear heat equation are obtained by the use of theory on algebraic curves. Finally, two kinds of gauge transformations of the spatial isospectral problem are produced. Supported by the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014) and the National Natural Science Foundation of China under Grant No. 11371361, the Fundamental Research Funds for the Central Universities (2013XK03) as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016
NASA Astrophysics Data System (ADS)
Sahmani, S.; Bahrami, M.; Ansari, R.
2014-12-01
This investigation deals with the free vibration characteristics of circular higher-order shear deformable nanoplates around the postbuckling configuration incorporating surface effects. Using the Gurtin-Murdoch elasticity theory, a size-dependent higher-order shear deformable plate model is developed which takes account all surface effects including surface elasticity, surface stress and surface density. Geometrical nonlinearity is considered based on the von Karman type nonlinear strain-displacement relationships. Also, in order to satisfy the balance conditions between bulk and surfaces of nanoplate, it is assumed that the normal stress is distributed cubically through the thickness of nanoplate. Hamilton's principle is utilized to derive non-classical governing differential equations of motion and related boundary conditions. Afterwards, an efficient numerical methodology based on a generalized differential quadrature (GDQ) method is employed to solve numerically the problem so as to discretize the governing partial differential equations along various edge supports using Chebyshev-Gauss-Lobatto grid points and pseudo arc-length continuation technique. A comparison between the results of present non-classical model and those of the classical plate theory is conducted. It is demonstrated that in contrast to the prebuckling domain, for a specified value of axial load in the postbuckling domain, increasing the plate thickness leads to higher frequencies.
Propagation property of a Lorentz-Gauss vortex beam in a strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Zhou, Guoquan
2014-11-01
An analytical expression of a Lorentz-Gauss vortex beam with one topological charge propagating in a strongly nonlocal nonlinear media is derived. The analytical expressions of the beam width, the curvature radius, and the orbital angular momentum density for the Lorentz-Gauss vortex beam with one topological charge have been also presented. The normalized intensity distribution, the relative beam width, the curvature radius, and the orbital angular momentum density distribution of the Lorentz-Gauss vortex beam with one topological charge are demonstrated in the strongly nonlocal nonlinear media, respectively. The normalized intensity, the beam width, the curvature radius, and the orbital angular momentum density versus the axial propagation distance are all periodic and the period is T=?z0/?. The evolution of the propagation property of the Lorentz-Gauss vortex beam with one topological charge has been exhibited in the strongly nonlocal nonlinear media. When the parameter ? reaches the critical value, the beam width keeps invariant upon propagation, and the corresponding curvature radius is infinite. The propagation of Lorentz-Gauss vortex beams with larger topological charge propagating in the strongly nonlocal nonlinear media can be analyzed by the same procedure as here.
Davidson, Ronald C.; Qin, Hong
2015-09-21
This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius r w . The average axial electric field is expressed as < E_{z} >=–(?/?z)=–e_{b}g???_{b}/?z – e_{b}g_{2}r^{2}_{w}?^{3}?_{b}/?z^{3}, where g_{0} and g_{2} are constant geometric factors, ?_{b}(z,t)=?dp_{z} F_{b} (z,p_{z},t) is the line density of beam particles, and F _{b} (z,p_{z},t) satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (soliton) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (i) the nonlinear waterbag distribution, where F_{b} = const in a bounded region of p_{z}-space; and (ii) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field.
Davidson, Ronald C.; Qin, Hong
2015-09-21
This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius r w . The average axial electric field is expressed as z >=–(?/?z)=–ebg???b/?z – ebg2r2w?3?b/?z3, where g0 and g2 are constant geometric factors, ?b(z,t)=?dpz Fb (z,pz,t) is the line density of beam particles, and F b (z,pz,t) satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (soliton) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations ofmore »the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (i) the nonlinear waterbag distribution, where Fb = const in a bounded region of pz-space; and (ii) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field.« less
A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches
NASA Astrophysics Data System (ADS)
Sedighi, Hamid M.; Shirazi, Kourosh H.; Attarzadeh, Mohammad A.
2013-10-01
This paper intends to promote the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams. Four new studied methods are Stiffness analytical approximation method, Homotopy Perturbation Method with an Auxiliary Term, Max-Min Approach (MMA) and Iteration Perturbation Method (IPM). The powerful analytical approaches are used to obtain the nonlinear frequency-amplitude relationship for dynamic behavior of vibrating beams with quintic nonlinearity. It is demonstrated that the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the integrity of the asymptotic methods.
Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment
Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.; Obayashi, T.
1986-01-01
A rocket-borne experiment called MINIX was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction Experiment and was carried out on August 29, 1983. The objectives of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere such as the Ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no Ohmic heating effects were detected. 4 figures.
HAMMERAND,DANIEL C.; KAPANIA,RAKESH K.
2000-05-01
A triangular flat shell element for large deformation analysis of linear viscoelastic laminated composites is presented. Hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Recurrence relations are developed and implemented for the evaluation of the viscoelastic memory loads. The nonlinear deformation process is computed using an incremental/iterative approach with the Newton-Raphson Method used to find the incremental displacements in each step. The presented numerical examples consider the large deformation and stability of linear viscoelastic structures under deformation-independent mechanical loads, deformation-dependent pressure loads, and thermal loads. Unlike elastic structures that have a single critical load value associated with a given snapping of buckling instability phenomenon, viscoelastic structures will usually exhibit a particular instability for a range of applied loads over a range of critical times. Both creep buckling and snap-through examples are presented here. In some cases, viscoelastic results are also obtained using the quasielastic method in which load-history effects are ignored, and time-varying viscoelastic properties are simply used in a series of elastic problems. The presented numerical examples demonstrate the capability and accuracy of the formulation.
Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads
Kong, Y. S.; Omar, M. Z.; Chua, L. B.; Abdullah, S.
2013-01-01
This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209
Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads.
Kong, Y S; Omar, M Z; Chua, L B; Abdullah, S
2013-01-01
This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209
Shen, Ming; Gao, Jinsong; Ge, Lijuan
2015-01-01
We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media. PMID:25900878
NASA Technical Reports Server (NTRS)
Rosen, A.; Friedmann, P.
1979-01-01
The nonlinear behavior of slender and initially straight beams is investigated. A set of equilibrium equations for a beam undergoing moderate rotations and small strains is derived. The derivation includes several assumptions which are clearly stated and explained. These equations are used to investigate the deformations of a cantilevered beam which is loaded by a concentrated transverse load at the free end. The numerical results are in very good agreement with the experimental results.
Nonlinear Phase Imaging Using Two-Beam Interferometry in Stimulated Parametric Emission Microscopy
NASA Astrophysics Data System (ADS)
Yamagiwa, Masatomo; Ozeki, Yasuyuki; Omura, Gen; Suzuki, Takeshi; Kajiyama, Shin'ichiro; Fukui, Kiichi; Itoh, Kazuyoshi
2009-06-01
We demonstrate that two-beam interferometry is applicable to phase detection of nonlinear susceptibility of biological samples in the stimulated parametric emission (SPE) microscopy, which is one of the coherent nonlinear optical microscopy techniques. We experimentally observed stained mouse kidney cells and successfully confirmed nonlinear phase shift associated with an electronic resonance at stained nuclei. In addition, phase blurring was found to be almost completely eliminated in a nonlinear differential interferometric contrast image, which can be produced through a simple post-processing procedure.
Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams
NASA Astrophysics Data System (ADS)
Porras, Miguel A.; Ruiz-Jiménez, Carlos; Losada, Juan Carlos
2015-12-01
In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NLUBB) whose inward Hänkel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines the NLUBB attractor is given. Steady or unsteady propagation depends on whether the attracting NLUBB has a small, exponentially growing, unstable mode. In the case of unsteady propagation, periodic, quasiperiodic, or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.
NASA Astrophysics Data System (ADS)
Nili Ahmadabadi, Z.; Khadem, S. E.
2014-09-01
This paper presents an optimal design for a system comprising a nonlinear energy sink (NES) and a piezoelectric-based vibration energy harvester attached to a free-free beam under shock excitation. The energy harvester is used for scavenging vibration energy dissipated by the NES. Grounded and ungrounded configurations are examined and the systems parameters are optimized globally to both maximize the dissipated energy by the NES and increase the harvested energy by piezoelectric element. A satisfactory amount of energy has been harvested as electric power in both configurations. The realization of nonlinear vibration control through one-way irreversible nonlinear energy pumping and optimizing the system parameters result in acquiring up to 78 percent dissipation of the grounded system energy.
Extension of non-linear beam models with deformable cross sections
NASA Astrophysics Data System (ADS)
Sokolov, I.; Krylov, S.; Harari, I.
2015-12-01
Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.
Effect of Geometric Azimuthal Asymmetries of PPM Stack on Electron Beam Characteristics
NASA Technical Reports Server (NTRS)
Kory, Carol L.; Heinen, Vernon (Technical Monitor)
2000-01-01
A three-dimensional (3D) beam optics model has been developed using the electromagnetic particle-in-cell (PIC) code MAFIA. The model includes an electron beam with initial transverse velocity distribution focused by a periodic permanent magnet (PPM) stack. All components of the model are simulated in three dimensions allowing several azimuthally asymmetric traveling wave tube (TWT) characteristics to be investigated for the first time. These include C-magnets, shunts, and magnet misalignment and their effects on electron beam behavior. The development of the model is presented and 3D TWT electron beam characteristics are compared in the absence of and under the influence of the azimuthally asymmetric characteristics described.
Effect of Geometric Azimuthal Asymmetrics of PPM Stack on Electron Beam Characteristics
NASA Technical Reports Server (NTRS)
Kory, Carol L.
2000-01-01
A three-dimensional (3D) beam optics model has been developed using the electromagnetic particle-in-cell (PIC) code MAFIA. The model includes an electron beam with initial transverse velocity distribution focused by a periodic permanent magnet (PPM) stack. All components of the model are simulated in three dimensions allowing several azimuthally asymmetric traveling wave tube (TWT) characteristics to be investigated for the first time. These include C-magnets, shunts and magnet misalignment and their effects on electron beam behavior. The development of the model is presented and 3D TWT electron beam characteristics are compared in the absence of and under the influence of the azimuthally asymmetric characteristics described.
Nonlinear energy flow in a beam-plasma system
NASA Technical Reports Server (NTRS)
Whelan, D. A.; Stenzel, R. L.
1983-01-01
The three-dimensional character of the beam-plasma instability is investigated. The true beam-electron distribution function is resolved with a novel directional energy analyzer. The electron plasma waves are observed to develop a large spread in perpendicular wave numbers and damp in a relatively short distance producing an energetic electron tail on the background distribution. The damping is believed to be due to strong ion fluctuations which produce an anomalous resistivity.
Nonlinear beam kinematics by decomposition of the rotation tensor
NASA Technical Reports Server (NTRS)
Danielson, D. A.; Hodges, D. H.
1987-01-01
A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion, extension, shear deformation, and warping of an initially curved and twisted beam.
Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor
NASA Technical Reports Server (NTRS)
Danielson, D. A.; Hodges, D. H.
1987-01-01
A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion extension, shear deformation, and warping of an initially curved and twisted beam.
Vibrations in an elastic beam with nonlinear supports at both ends
NASA Astrophysics Data System (ADS)
Wang, Yi-Ren; Fang, Zhi-Wei
2015-03-01
Vibrations in an elastic beam supported by nonlinear supports at both ends under the influence of harmonic forces are analyzed in this study. It is hypothesized that the elastic Bernoulli-Euler beam is supported by cubic springs to simulate nonlinear boundary conditions. The dynamic behavior of the beam is described by using the Fourier expansion and the Bessel functions. The Hankel transform is then applied to obtain particular (nonhomogeneous) solutions. This study succeeds in describing the "jump" phenomenon (instantaneous transition of the system from one position to another) of the vibrating system at certain frequencies. Models based on linear boundary conditions are unable to capture this phenomenon. A larger modulus of elasticity in nonlinear supports increases the frequency of unstable vibrations in the first mode and also widens the frequency region of system instability. This influence is less prominent in the second mode, in which the largest amplitude is smaller than those observed in the first mode.
a Perturbation Approach to the Nonlinear Vibration of a Damaged Beam
NASA Astrophysics Data System (ADS)
Mendelsohn, D. A.; Vedachalam, S.; Mokashi, P. S.; Pecorari, C.
2008-02-01
The vibration characteristics of a cohesively cracked Euler-Bernoulli beam are investigated using the modified line-spring method. The crack plane is statically loaded in bending into the nonlinear region and small amplitude vibrations are superposed about this state. The deflection solution form is then separated into the zeroth order linear and first order nonlinear components. Several vibration characteristics such as deflection, slope and modal amplitude are studied as a function of the applied static moment.
Enhanced sensitivity beam emission spectroscopy system for nonlinear turbulence measurements
Gupta, Deepak K.; Fonck, Raymond J.; McKee, George R.; Schlossberg, David J.; Shafer, Morgan W.
2004-10-01
An upgraded beam emission spectroscopy (BES) system has been deployed to access low amplitude turbulence regions near internal transport barriers on the DIII-D tokamak. Sixteen high sensitivity channels are being installed. A significant increase in total signal to noise is achieved by: (1) Increased spatial volume sampling tailored to known turbulence characteristics; (2) An increased throughput spectrometer assembly to isolate the local beam fluorescence, coupled to new large area photoconductive photodiodes; (3) A new sharp edge interference filter designed to optimize detection of the beam emission plus a significant fraction of the thermal deuterium charge exchange. A new data acquisition system has been installed, providing an eight times increase in integration time or an increased sample rate. Preliminary results from the upgraded system show a signal enhancement of greater than an order of magnitude. A clear broadband density fluctuation signal is observed in H-mode discharges with the upgraded BES system, demonstrating the significant performance enhancement.
Light localization and nonlinear beam transmission in specular amorphous photonic lattices.
Ni, Peigen; Zhang, Peng; Qi, Xinyuan; Yang, Jianke; Chen, Zhigang; Man, Weining
2016-02-01
We demonstrate specular photonic "lattices" with random index variations at disordered positions of lattice sites. These amorphous lattice structures, optically induced in a bulk nonlinear crystal, remain invariant during propagation since they are constructed from random components residing on a fixed ring in momentum space. We observe linear spatial localization of a light beam when probing through different "defect" points in such specular lattices, as well as the nonlinear destruction of localized modes. In addition, we illustrate the possibility of image transmission through the disordered lattices, when a self-defocusing nonlinearity is employed. PMID:26906817
Feng, Zexin; Froese, Brittany D; Huang, Chih-Yu; Ma, Donglin; Liang, Rongguang
2015-07-10
We consider here creation of an unconventional flattop beam with a large depth of field by employing double freeform optical surfaces. The output beam is designed with continuous variations from the flattop to almost zero near the edges to resist the influence of diffraction on its propagation. We solve this challenging problem by naturally incorporating an optimal transport map computation scheme for unconventional boundary conditions with a simultaneous point-by-point double surface construction procedure. We demonstrate experimentally the generation of a long-range propagated triangular beam through a plano-freeform lens pair fabricated by a diamond-tuning machine. PMID:26193404
NASA Astrophysics Data System (ADS)
Müller, Kei W.; Meier, Christoph; Wall, Wolfgang A.
2015-12-01
Networks of crosslinked biopolymer filaments such as the cytoskeleton are the subject of intense research. Oftentimes, mechanics on the scale of single monomers (? 5 nm) govern the mechanics of the entire network (? 10 ?m). Until now, one either resolved the small scales and lost the big (network) picture or focused on mechanics above the single-filament scale and neglected the molecular architecture. Therefore, the study of network mechanics influenced by the entire spectrum of relevant length scales has been infeasible so far. We propose a method that reconciles both small and large length scales without the otherwise inevitable loss in either numerical efficiency or geometrical (molecular) detail. Both explicitly modeled species, filaments and their crosslinkers, are discretized with geometrically exact beam finite elements of Simo-Reissner type. Through specific coupling conditions between the elements of the two species, mechanical joints can be established anywhere along a beam's centerline, enabling arbitrary densities of chemical binding sites. These binding sites can be oriented to model the monomeric architecture of polymers. First, we carefully discuss the method and then demonstrate its capabilities by means of a series of numerical examples.
Numerical simulation of nonlinear processes in a beam-plasma system
NASA Astrophysics Data System (ADS)
Efimova, A. A.; Berendeev, E. A.; Dudnikova, G. I.; Vshivkov, V. A.
2015-10-01
In the present paper we consider the efficiency of the electromagnetic radiation generation due to various nonlinear processes in the beam-plasma system. The beam and plasma parameters were chosen close to the parameters in the experiment on the GOL-3 facility (BINP SB RAS). The model of the collisionless plasma is described by system of the Vlasov-Maxwell equations with periodic boundary conditions. The parallel numerical algorithm is based on the particles-in-cell method (PIC) with mixed Euler-Lagrangian domain decomposition. Various scenarios of nonlinear evolution in the beam-plasma system under the influence of an external magnetic field in case of a low density beam were studied. The energy transfer from one unstable mode to the others modes was observed.
The influence of nonlinear terms to external focusing on beam halo formation.
NASA Astrophysics Data System (ADS)
Sonnad, Kiran; Cary, John R.
2000-10-01
Halo formation is an important issue in intensely charged particle beams because the loss of halo particles can lead to radio activation of the accelerator. Halo formation can be shown to occur in a continuous, linear focusing channel. In this paper we investigate the influence of a cubic term in the external focusing. The resulting equilibrium particle distribution will then be modified. Deviations from this equilibrium distribution will lead to non-linear oscillations of the beam envelope and the core particles. This in turn will lead to heating of the beam core. We study the effect of this non-linear focusing term on beam halo formation by calculation of test particle trajectories and from simulations using the object-oriented particle-in-cell code OOPIC.
Effects of Transverse Physics on Nonlinear Evolution of Longitudinal Space-Charge Waves in Beams
K. Tian, I. Haber, R.A. Kishek, P.G. O'Shea, M. Reiser, D. Stratakis
2009-05-01
Longitudinal space-charge waves can introduce energy perturbations into charge particle beams and degrade the beam quality, which is critical to many modern applications of particle accelerators. Although many longitudinal phenomena arising from small perturbations can be explained by a one-dimensional cold fluid theory, nonlinear behavior of space-charge waves observed in experiments has not been well understood. In this paper, we summarize our recent investigation by means of more detailed measurements and self-consistent simulations. Combining the numerical capability of a PIC code, WARP, with the detailed initial conditions measured by our newly developed time resolved 6-D phase space mapping technique, we are able to construct a self consistent model for studying the complex physics of longitudinal dynamics of space-charge dominated beams. Results from simulation studies suggest that the unexplained nonlinear behavior of space-charge waves may be due to transverse mismatch or misalignment of beams.
Nonlinear delta(f) Simulations of Collective Effects in Intense Charged Particle Beams
Hong Qin
2003-01-21
A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, et al., in Proc. of the Particle Accelerator Conference, Chicago, 2001 (IEEE, Piscataway, NJ, 2001), Vol. 1, p. 688.] at the Los Alamos National Laboratory agree well with experimental observations. Large-scale parallel simulations have also been carried out for the ion-electron two-stream instability in the very-high-intensity heavy ion beams envisioned for heavy ion fusion applications. In both cases, the simulation results indicate that the dominant two-stream instability has a dipole-mode (hose-like) structure and can be stabilized by a modest axial momentum spread of the beam particles.
Random vibration of nonlinear beams by the new stochastic linearization technique
NASA Technical Reports Server (NTRS)
Fang, J.
1994-01-01
In this paper, the beam under general time dependent stationary random excitation is investigated, when exact solution is unavailable. Numerical simulations are carried out to compare its results with those yielded by the conventional linearization techniques. It is found that the modified version of the stochastic linearization technique yields considerably more accurate results for the mean square displacement of the beam than the conventional equivalent linearization technique, especially in the case of large nonlinearity.
Experimental damage detection of cracked beams by using nonlinear characteristics of forced response
NASA Astrophysics Data System (ADS)
Andreaus, U.; Baragatti, P.
2012-08-01
Experimental evaluation of the flexural forced vibrations of a steel cantilever beam having a transverse surface crack extending uniformly along the width of the beam was performed, where an actual fatigue crack was introduced instead - as usual - of a narrow slot. The nonlinear aspects of the dynamic response of the beam under harmonic excitation were considered and the relevant quantitative parameters were evaluated, in order to relate the nonlinear resonances to the presence and size of the crack. To this end, the existence of sub- and super-harmonic components in the Fourier spectra of the acceleration signals was evidenced, and their amplitudes were quantified. In particular, the acceleration signals were measured in different positions along the beam axis and under different forcing levels at the beam tip. The remarkable relevance of the above mentioned nonlinear characteristics, and their substantial independence on force magnitude and measurement point were worthily noted in comparison with the behavior of the intact beam. Thus, a reliable method of damage detection was proposed which was based on simple tests requiring only harmonically forcing and acceleration measuring in any point non-necessarily near the crack. Then, the time-history of the acceleration recorded at the beam tip was numerically processed in order to obtain the time-histories of velocity and displacement. The nonlinear features of the forced response were described and given a physical interpretation in order to define parameters suitable for damage detection. The efficiency of such parameters was discussed with respect to the their capability of detecting damage and a procedure for damage detection was proposed which was able to detect even small cracks by using simple instruments. A finite element model of the cantilever beam was finally assembled and tuned in order to numerically simulate the results of the experimental tests.
NASA Astrophysics Data System (ADS)
Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline
2001-12-01
Discrete geometric conservation laws (DGCLs) govern the geometric parameters of numerical schemes designed for the solution of unsteady flow problems on moving grids. A DGCL requires that these geometric parameters, which include among others grid positions and velocities, be computed so that the corresponding numerical scheme reproduces exactly a constant solution. Sometimes, this requirement affects the intrinsic design of an arbitrary Lagrangian Eulerian (ALE) solution method. In this paper, we show for sample ALE schemes that satisfying the corresponding DGCL is a necessary and sufficient condition for a numerical scheme to preserve the nonlinear stability of its fixed grid counterpart. We also highlight the impact of this theoretical result on practical applications of computational fluid dynamics.
Nonlinear hybrid simulation of internal kink with beam ion effects in DIII-D
Shen, Wei; Sheng, Zheng-Mao; Fu, G. Y.; Tobias, Benjamin; Zeeland, Michael Van; Wang, Feng
2015-04-15
In DIII-D sawteething plasmas, long-lived (1,1) kink modes are often observed between sawtooth crashes. The saturated kink modes have two distinct frequencies. The mode with higher frequency transits to a fishbone-like mode with sufficient on-axis neutral beam power. In this work, hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of the nâ€‰=â€‰1 mode with effects of energetic beam ions for a typical DIII-D discharge where both saturated kink mode and fishbone were observed. Linear simulation results show that the nâ€‰=â€‰1 internal kink mode is unstable in MHD limit. However, with kinetic effects of beam ions, a fishbone-like mode is excited with mode frequency about a few kHz depending on beam pressure profile. The mode frequency is higher at higher beam power and/or narrower radial profile consistent with the experimental observation. Nonlinear simulations have been performed to investigate mode saturation as well as energetic particle transport. The nonlinear MHD simulations show that the unstable kink mode becomes a saturated kink mode after a sawtooth crash. With beam ion effects, the fishbone-like mode can also transit to a saturated kink mode with a small but finite mode frequency. These results are consistent with the experimental observation of saturated kink mode between sawtooth crashes.
Nonlinear hybrid simulation of internal kink with beam ion effects in DIII-D
NASA Astrophysics Data System (ADS)
Shen, Wei; Fu, G. Y.; Tobias, Benjamin; Van Zeeland, Michael; Wang, Feng; Sheng, Zheng-Mao
2015-04-01
In DIII-D sawteething plasmas, long-lived (1,1) kink modes are often observed between sawtooth crashes. The saturated kink modes have two distinct frequencies. The mode with higher frequency transits to a fishbone-like mode with sufficient on-axis neutral beam power. In this work, hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of the n = 1 mode with effects of energetic beam ions for a typical DIII-D discharge where both saturated kink mode and fishbone were observed. Linear simulation results show that the n = 1 internal kink mode is unstable in MHD limit. However, with kinetic effects of beam ions, a fishbone-like mode is excited with mode frequency about a few kHz depending on beam pressure profile. The mode frequency is higher at higher beam power and/or narrower radial profile consistent with the experimental observation. Nonlinear simulations have been performed to investigate mode saturation as well as energetic particle transport. The nonlinear MHD simulations show that the unstable kink mode becomes a saturated kink mode after a sawtooth crash. With beam ion effects, the fishbone-like mode can also transit to a saturated kink mode with a small but finite mode frequency. These results are consistent with the experimental observation of saturated kink mode between sawtooth crashes.
Ella, Lior Yuvaraj, D.; Suchoi, Oren; Shtempluk, Oleg; Buks, Eyal
2015-01-07
We present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the bias current and applied flux of the SQUID. We detect the position of the beam by placing it in an optical cavity, which sets free the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a Duffing oscillator behavior which is periodic in the applied magnetic flux. To account for this, we develop a model based on the standard theory for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the responsivity of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.
Jiang, Zhen; Zhu, Quing; Piao, Daqing
2007-12-01
This paper discusses a dispersion effect in a grating-based time-domain delay line that is different from the second- or higher-order dispersion in a grating-based Fourier-domain delay line. When the lateral broadening of the beam profile after grating dispersion exceeds the collection aperture of the reference fiber, the peripheral spectrum is decoupled by the fiber. The loss of reference spectral bandwidth by this geometric-beam broadening thus degrades the axial resolution. The polarizing-beam reflector used in the Fourier-domain delay line for suppression of lateral beam walk-off is implemented in this grating-based time-domain delay line to minimize geometric-beam broadening. Theoretical analysis and experiments are given to validate the axial resolution improvement after geometric-beam broadening is minimized. In vitro and in vivo imaging results are presented to demonstrate the improvement. It is also shown that geometric-beam broadening may exist in other optical coherence tomography reference arm configurations. PMID:18059934
NASA Astrophysics Data System (ADS)
Yildirim, Tanju; Ghayesh, Mergen H.; Li, Weihua; Alici, Gursel
2016-01-01
An experimental investigation has been carried out on the nonlinear dynamics of a clamped–clamped Magneto-Rheological Elastomer (MRE) sandwich beam with a point mass when subjected to a point excitation. Three sets of experiments have been conducted namely for (i) an aluminium beam, (ii) a MRE sandwich beam in the absence of a magnetic field and (iii) a MRE sandwich beam in the presence of a magnetic field. An electrodynamic shaker was used to excite each system and the corresponding displacement of the point mass was measured: for the third experiment (iii), an array of magnets has been placed at various distances away from the centre of the point mass to investigate the effect of changing stiffness and damping properties on the nonlinear dynamical behaviour. An interesting feature for the third group is the beam point mass displacement was no longer symmetric as the stiffness and damping of the system are increased when moving towards the magnets. Both the first and second groups exhibited distinct nonlinear behaviour; however, for the third group this work shows that for a low magnetic field the sandwich beam exhibits two distinct resonance peaks, one occurring above and the other below the fundamental natural frequency of the transverse motion, with the right one larger. For a larger magnetic field, these peaks even out until the magnetic force was large enough that the hardening-type nonlinear behaviour changes to a softening-type; a significant qualitative change in the nonlinear dynamical behaviour of the system, due to the presence of the magnetic field, was observed.
Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
Bliokh, Konstantin Yu.
2006-07-28
We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.
Michael Spata
2012-08-01
An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a beam-based technique for characterizing the extent of the nonlinearity of the magnetic fields of a beam transport system. Horizontally and vertically oriented pairs of air-core kicker magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the beam orbit relative to the unperturbed reference orbit. Fourier decomposition of the position data at eight different points along the beamline was then used to measure the amplitude of these frequencies. For a purely linear transport system one expects to find solely the frequencies that were applied to the kickers with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was then applied to a pair of Arc 1 dipoles and then to the magnets in the Transport Recombiner beamline to measure their multipole content as a function of transverse position within the magnets.
NASA Astrophysics Data System (ADS)
Malekzadeh, P.; Vosoughi, A. R.
2009-03-01
This paper presents an efficient and accurate differential quadrature (DQ) large amplitude free vibration analysis of laminated composite thin beams on nonlinear elastic foundation. Beams under consideration have elastically restrained against rotation and in-plane immovable edges. Elastic foundation has cubic nonlinearity with shearing layer. We impose the boundary conditions directly into the governing equations in spite of the conventional DQ method and without any extra efforts. A direct iterative method is used to solve the nonlinear eigenvalue system of equations after transforming the governing equations into the frequency domain. The fast rate of convergence of the method is shown and their accuracy is demonstrated by comparing the results with those for limit cases, i.e. beams with classical boundary conditions, available in the literature. Besides, we develop a finite element program to verify the results of the presented DQ approach and to show its high computational efficiency. The effects of different parameters on the ratio of nonlinear to linear natural frequency of beams are studied.
Beam Loading in the Nonlinear Regime of Plasma-Based Acceleration
Tzoufras, M.; Lu, W.; Tsung, F. S.; Huang, C.; Mori, W. B.; Katsouleas, T.; Vieira, J.; Fonseca, R. A.; Silva, L. O.
2008-10-03
A theory that describes how to load negative charge into a nonlinear, three-dimensional plasma wakefield is presented. In this regime, a laser or an electron beam blows out the plasma electrons and creates a nearly spherical ion channel, which is modified by the presence of the beam load. Analytical solutions for the fields and the shape of the ion channel are derived. It is shown that very high beam-loading efficiency can be achieved, while the energy spread of the bunch is conserved. The theoretical results are verified with the particle-in-cell code OSIRIS.
Nariyuki, Y.; Hada, T.; Tsubouchi, K.
2012-08-15
In the present study, the dissipation processes of circularly polarized Alfven waves in solar wind plasmas including beam components are numerically discussed by using a 2-D hybrid simulation code. Numerical results suggest that the parent Alfven waves are rapidly dissipated due to the presence of the beam-induced obliquely propagating waves, such as kinetic Alfven waves. The nonlinear wave-wave coupling is directly evaluated by using the induction equation for the parent wave. It is also observed both in the 1-D and 2-D simulations that the presence of large amplitude Alfven waves strongly suppresses the beam instabilities.
Nonlinear-resonance line shapes: Dependence on the transverse intensity distribution of a light beam
Taichenachev, A.V.; Yudin, V.I.; Wynands, R.; Kitching, J.; Hollberg, L.
2004-02-01
We analyze the line shape and width of atomic coherent-population-trapping (CPT) resonances excited by laser beams with different transverse intensity profiles. A dramatic difference in the resonance line shape is found when comparing a beam with a 'steplike' profile to a beam with a Gaussian profile. In particular, for nonuniform profiles, a non-Lorentzian functional form is given that is more appropriate for describing the nonlinear resonance line shape than is a conventional Lorentzian. Our analysis is supported by measurements of CPT line shapes in a thermal vapor of {sup 85}Rb.
Mimicking the cochlear amplifier in a cantilever beam using nonlinear velocity feedback control
NASA Astrophysics Data System (ADS)
Joyce, Bryan S.; Tarazaga, Pablo A.
2014-07-01
The mammalian cochlea exhibits a nonlinear amplification which allows mammals to detect a large range of sound pressure levels while maintaining high frequency sensitivity. This work seeks to mimic the cochlea’s nonlinear amplification in a mechanical system. A nonlinear, velocity-based feedback control law is applied to a cantilever beam with piezoelectric actuators. The control law reduces the linear viscous damping of the system while introducing a cubic damping term. The result is a system which is positioned close to a Hopf bifurcation. Modelling and experimental results show that the beam with this control law undergoes a one-third amplitude scaling near the resonance frequency and an amplitude-dependent bandwidth. Both behaviors are characteristic of data obtained from the mammalian cochlea. This work could provide insight on the biological cochlea while producing bio-inspired sensors with a large dynamic range and sharp frequency sensitivity.
Thermodynamic Bounds on Nonlinear Electrostatic Perturbations in Intense Charged Particle Beams
Nikolas C. Logan and Ronald C. Davidson
2012-07-18
This paper places a lowest upper bound on the field energy in electrostatic perturbations in single-species charged particle beams with initial temperature anisotropy (TllTâŠ¥ < 1). The result applies to all electrostatic perturbations driven by the natural anisotropies that develop in accelerated particle beams, including Harris-type electrostatic instabilities, known to limit the luminosity and minimum spot size attainable in experiments. The thermodynamic bound on the field perturbation energy of the instabilities is obtained from the nonlinear Vlasov-Poisson equations for an arbitrary initial distribution function, including the effects of intense self-fields, finite geometry and nonlinear processes. This paper also includes analytical estimates of the nonlinear bounds for space-charge-dominated and emittance-dominated anisotropic bi-Maxwellian distributions.
Nonlinear Charge and Current Neutralization of an Ion Beam Pulse in a Pre-formed Plasma
Igor D. Kaganovich; Gennady Shvets; Edward Startsev; Ronald C. Davidson
2001-01-30
The propagation of a high-current finite-length ion beam in a cold pre-formed plasma is investigated. The outcome of the calculation is the quantitative prediction of the degree of charge and current neutralization of the ion beam pulse by the background plasma. The electric magnetic fields generated by the ion beam are studied analytically for the nonlinear case where the plasma density is comparable in size with the beam density. Particle-in-cell simulations and fluid calculations of current and charge neutralization have been performed for parameters relevant to heavy ion fusion assuming long, dense beams with el >> V(subscript b)/omega(subscript b), where V(subscript b) is the beam velocity and omega subscript b is the electron plasma frequency evaluated with the ion beam density. An important conclusion is that for long, nonrelativistic ion beams, charge neutralization is, for all practical purposes, complete even for very tenuous background plasmas. As a result, the self-magnetic force dominates the electric force and the beam ions are always pinched during beam propagation in a background plasma.
THE EFFECT OF NONLINEAR LANDAU DAMPING ON ULTRARELATIVISTIC BEAM PLASMA INSTABILITIES
Chang, Philip; Lamberts, Astrid; Broderick, Avery E.; Shalaby, Mohamad; Pfrommer, Christoph; Puchwein, Ewald
2014-12-20
Very high energy gamma-rays from extragalactic sources produce pairs from the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the ''oblique'' instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here we show with numerical calculations that the effective damping rate is 8 Ã— 10{sup â€“4} the growth rate of the linear instability, which is sufficient for the ''oblique'' instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wave numbers and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to approximate equipartition with the beam by increasingly depositing energy into long-wavelength modes. As we have not included the effect of nonlinear wave-wave interactions on these long-wavelength modes, this scenario represents the ''worst case'' scenario for the oblique instability. As it continues to drain energy from the beam at a faster rate than other processes, we conclude that the ''oblique'' instability is sufficiently strong to make it the physically dominant cooling mechanism for high-energy pair beams in the intergalactic medium.
Geometrical study on two tilting arcs based exact cone-beam CT for breast imaging
NASA Astrophysics Data System (ADS)
Zeng, Kai; Yu, Hengyong; Fajardo, Laurie L.; Wang, Ge
2006-08-01
Breast cancer is the second leading cause of cancer death in women in the United States. Currently, X-ray mammography is the method of choice for screening and diagnosing breast cancer. However, this 2D projective modality is far from perfect; with up to 17% breast cancer going unidentified. Over past several years, there has been an increasing interest in cone-beam CT for breast imaging. However, previous methods utilizing cone-beam CT only produce approximate reconstructions. Following Katsevich's recent work, we propose a new scanning mode and associated exact cone-beam CT method for breast imaging. In our design, cone-beam scans are performed along two tilting arcs for collection of a sufficient amount of data for exact reconstruction. In our Katsevich-type algorithm, conebeam data is filtered in a shift-invariant fashion and then backprojected in 3D for the final reconstruction. This approach has several desirable features. First, it allows data truncation unavoidable in practice. Second, it optimizes image quality for quantitative analysis. Third, it is efficient for sequential/parallel computation. Furthermore, we analyze the reconstruction region and the detection window in detail, which are important for numerical implementation.
Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids
NASA Astrophysics Data System (ADS)
Aureli, M.; Basaran, M. E.; Porfiri, M.
2012-03-01
In this paper, we study flexural vibrations of a cantilever beam with thin rectangular cross section submerged in a quiescent viscous fluid and undergoing oscillations whose amplitude is comparable with its width. The structure is modeled using Euler-Bernoulli beam theory and the distributed hydrodynamic loading is described by a single complex-valued hydrodynamic function which accounts for added mass and fluid damping experienced by the structure. We perform a parametric 2D computational fluid dynamics analysis of an oscillating rigid lamina, representative of a generic beam cross section, to understand the dependence of the hydrodynamic function on the governing flow parameters. We find that increasing the frequency and amplitude of the vibration elicits vortex shedding and convection phenomena which are, in turn, responsible for nonlinear hydrodynamic damping. We establish a manageable nonlinear correction to the classical hydrodynamic function developed for small amplitude vibration and we derive a computationally efficient reduced order modal model for the beam nonlinear oscillations. Numerical and theoretical results are validated by comparison with ad hoc designed experiments on tapered beams and multimodal vibrations and with data available in the literature. Findings from this work are expected to find applications in the design of slender structures of interest in marine applications, such as biomimetic propulsion systems and energy harvesting devices.
General Nonlinear Mechanics of AN Electron Beam Driven Multimode Plasma System
NASA Astrophysics Data System (ADS)
McCowan, Robert Bruce
The general nonlinear behavior of the beam driven multimode system is examined. The linearized dispersion for a beam plasma is reviewed and the new features of linear theory needed to explain the behavior for the plasma with two oppositely directed beams are derived. The dispersion relation and an extension of van der Pol theory are used to develop nonlinear amplitude rate equations for the plasma. Where quantitative comparison is possible agreement between the model and the experimental behavior is within the expected ranges. Important qualitative features of the nonlinear multimode system, mode locking and entrainment are observed in the model and in the experiment. An apparatus for experimental test of the model was built. The components of the system included a vacuum vessel, magnets to guide the electron beam and confine the plasma and an electron gun to provide the electron beam. Diagnostics used in the experiment were also built and include probes, a microwave resonance shift cavity and a retarding field energy analyzer. Data were collected and recorded by single channel superheterodyne receivers, spectrum analyzers and a Data Precision D6000, a digital waveform acquisition and analysis system. An Apple Macintosh computer is used to communicate with the D6000 and details of the communication between the D6000 and the Macintosh are also presented.
Energy harvesting of cantilever beam system with linear and nonlinear piezoelectric model
NASA Astrophysics Data System (ADS)
Borowiec, Marek
2015-11-01
The nonlinear beam with vertical combined excitations is proposed as an energy harvester. The nonlinearities are included both, in the beam model and also in the electrical subsystem. The system is modelled as a cantilever beam with included a tip mass and piezoelectric patches which convert the bending strains induced by both, the harmonic and the additive stochastic forces. The excitation affects in vertical directions by kinematic forcing into electrical charge. The first main goal is to analyse the dynamics of the electro-mechanical beam system and the influence of the mixed excitation forces into an effectiveness of the energy harvesting. Overcoming the potential barrier by the beam system is also analysed, where large output amplitudes occur. Such region of the vibration affects more power generation, which is crucial in terms of load resistors sensitivities. By increasing the additive noise level with fixed harmonic force it is observed the transition from single well oscillations to inter-well stochastic jumps. The second mail goal is analysing the influence of the piezoelectric nonlinear characteristic and compare the results to the linear piezoelectric cases. The output power is measured during different system behaviours provided by different piezoelectric characteristic as well as introduced stochastic components by modulated tip mass of the system.
Understanding the nonlinear beam dynamics of the Advanced Light Source
Robin, D.; Laskar, J.
1996-09-18
Frequency map analysis is used to study the single particle transverse beam dynamics in ALS. The maps, which provide details about the diffusion of orbits and limits on long term stability, are generated by a postprocessor attached to a tracking code. This paper describes the method and shows how the map is changed when the 12- fold symmetry of the linear lattice is perturbed by including measured magnetic field imperfections. Also the long term stability of orbits that reside in regions of large diffusion is studied.
Nonlinear static and dynamic finite element analysis of an eccentrically loaded graphite-epoxy beam
NASA Technical Reports Server (NTRS)
Fasanella, Edwin L.; Jackson, Karen E.; Jones, Lisa E.
1991-01-01
The Dynamic Crash Analysis of Structures (DYCAT) and NIKE3D nonlinear finite element codes were used to model the static and implulsive response of an eccentrically loaded graphite-epoxy beam. A 48-ply unidirectional composite beam was tested under an eccentric axial compressive load until failure. This loading configuration was chosen to highlight the capabilities of two finite element codes for modeling a highly nonlinear, large deflection structural problem which has an exact solution. These codes are currently used to perform dynamic analyses of aircraft structures under impact loads to study crashworthiness and energy absorbing capabilities. Both beam and plate element models were developed to compare with the experimental data using the DYCAST and NIKE3D codes.
Huang, J. L.; Chen, S. H.; Su, R. K. L.; Lee, Y. Y.
2010-05-21
This paper analyzes nonlinear vibration of an axially moving beam subject to periodic lateral forces by Incremental Harmonic Balance (IHB) method. Attention is paid to the fundamental resonance as the force frequency is close to the first frequencies omega{sub 1} of the system. Galerkin method is used to discretize the governing equations and the IHB method is used to illustrate the nonlinear dynamic behavior of the axially moving beam. The stable and unstable periodic solutions for given parameters are determined by the multivariable Floquet theory. Hsu's method is applied for computing the transition matrix at the end of one period. The effects of internal resonance on the beam responses are discussed. The periodic solutions obtained from the IHB method are in good agreement with the results obtained from numerical integration.
High Current Electron Beam Emission Driven by a Nonlinear Transmission Line
NASA Astrophysics Data System (ADS)
French, David; Hoff, Brad; Heidger, Susan
2014-10-01
Simulations of an electron beam diode driven by a modulated voltage pulse provided by a nonlinear transmission line (NLTL) will be presented. Based on a previous low voltage experiment the new design operates at 250 kV and provides a multi-kA modulated electron beam based on the modulated drive signal from a ferrite based NLTL. The NLTL driver has been demonstrated experimentally and is tunable from 900-1400 MHz with pulse durations from 4-17 ns. Particle-In-Cell simulations in ICEPIC show the modulated voltage signal results in a modulated electron beam current emitted directly from the cathode in a few cm annular beam. Expected results and the experimental design for the electron beam diode and diagnostics will also be presented.
Nonlinear tracking control of vibration amplitude for a parametrically excited microcantilever beam
NASA Astrophysics Data System (ADS)
Nguyen, Quoc Chi; Krylov, Slava
2015-03-01
In this paper, a feedback control algorithm to regulate oscillation amplitude of a microelectromechanical (MEMS) cantilever beam operated at parametric resonances is developed. The control objective is to drive the oscillation amplitude of the micro-beam, which is amplified using parametric excitation, to the desired values. The principle of the control algorithm is to establish an output tracking control based on the nonlinear dynamic model of the micro-beam, where the supply voltage is considered as a control input. The tracking control algorithm is designed to solve the singularities resulting from the zero-deflection state of the micro-beam. The Galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the beam into a set of ordinary differential equations (ODEs). Uniformly ultimate boundedness stability of the control system is proved using Lyapunov method. The effectiveness of the proposed control algorithm is illustrated via numerical simulations.
Nonlinear modes of an intense laser beam interacting with a periodic lattice of nanoparticle
NASA Astrophysics Data System (ADS)
Sepehri Javan, N.; Homami, S. H. H.
2015-08-01
Self-guided nonlinear propagation of an intense laser beam through a periodic lattice of nanoparticle is studied. Using a perturbative method, a cubic nonlinear wave equation describing the laser-nanoparticle interaction in the weakly relativistic regime is derived. Transverse Eigen modes of the laser, nonlinear dispersion relation and its related group velocity are obtained. It is shown that the best fitted function to the transverse profile is Gaussian. Effect of the laser amplitude and also the ratio of nanoparticles radius to their separation on the nonlinear dispersion and amplitude profiles are investigated. It is found that the increase in the just mentioned parameters leads to the localization of transverse profile around the propagation axis.
Reichert, Matthew; Zhao, Peng; Reed, Jennifer M; Ensley, Trenton R; Hagan, David J; Van Stryland, Eric W
2015-08-24
A polarization-resolved beam deflection technique is used to separate the bound-electronic and molecular rotational components of nonlinear refractive transients of molecular gases. Coherent rotational revivals from N(2), O(2), and two isotopologues of carbon disulfide (CS(2)), are identified in gaseous mixtures. Dephasing rates, rotational and centrifugal distortion constants of each species are measured. Polarization at the magic angle allows unambiguous measurement of the bound-electronic nonlinear refractive index of air and second hyperpolarizability of CS(2). Agreement between gas and liquid phase second hyperpolarizability measurements is found using the Lorentz-Lorenz local field correction. PMID:26368195
A time delay control for a nonlinear dynamic beam under moving load
NASA Astrophysics Data System (ADS)
Qian, C. Z.; Tang, J. S.
2008-01-01
The bifurcation resulted from moving force may lead to instability for the system. Based on time delay feedback controller, a nonlinear beam under moving load is discussed in the case of the primary resonance and the 1/3 subharmonic resonance. The bifurcation may be eliminated or the bifurcation point's position may be changed. The perturbation method is used to obtain the bifurcation equation of the nonlinear dynamic system. The result indicates time delay feedback controller may work well on this system, but the selection of a proper time delay and its coefficient may depend on the engineering condition. This paper presents some theoretical results.
High-contrast artifact reduction in cone beam computed tomography by using geometric techniques
NASA Astrophysics Data System (ADS)
Noël, Peter B.; Xu, Jinhui; Hoffmann, Kenneth R.; Corso, Jason J.; Schafer, Sebastian; Walczak, Alan M.
2009-02-01
The use of cone beam computed tomography (CBCT) is growing in the clinical arena, due to its ability to provide 3-D information during interventions, its high diagnostic quality (sub-millimeter resolution), and its short scanning times (10 seconds). In many situations, the reconstructions suffer from artifacts from high contrast objects (due mainly to angular sampling by the projections or by beam hardening) which can reduce image quality. In this study, we propose a novel algorithm to reduce these artifacts. In our approach, these objects are identified and then removed in the sinogram space by using computational geometry techniques. In particular, the object is identified in a reconstruction from a few views. Then, the rays (projection lines) intersecting the high contrast objects are identified using the technique of topological walk in a dual space which effectively models the problem as a visibility problem and provides a solution in optimal time and space complexity. As a result, the corrections can be performed in real time, independent of the projection image size. Subsequently, a full reconstruction is performed by leaving out the high contrast objects in the reconstructions. Evaluations were performed using simulations and animal studies. The artifacts are significantly reduced when using our approach. This optimal time and space complexity and relative simple implementation makes our approach attractive for artifact reduction.
Instability and dynamics of two nonlinearly coupled intense laser beams in a quantum plasma
NASA Astrophysics Data System (ADS)
Wang, Yunliang; Shukla, P. K.; Eliasson, B.
2013-01-01
We consider nonlinear interactions between two relativistically strong laser beams and a quantum plasma composed of degenerate electron fluids and immobile ions. The collective behavior of degenerate electrons is modeled by quantum hydrodynamic equations composed of the electron continuity, quantum electron momentum (QEM) equation, as well as the Poisson and Maxwell equations. The QEM equation accounts the quantum statistical electron pressure, the quantum electron recoil due to electron tunneling through the quantum Bohm potential, electron-exchange, and electron-correlation effects caused by electron spin, and relativistic ponderomotive forces (RPFs) of two circularly polarized electromagnetic (CPEM) beams. The dynamics of the latter are governed by nonlinear wave equations that include nonlinear currents arising from the relativistic electron mass increase in the CPEM wave fields, as well as from the beating of the electron quiver velocity and electron density variations reinforced by the RPFs of the two CPEM waves. Furthermore, nonlinear electron density variations associated with the driven (by the RPFs) quantum electron plasma oscillations obey a coupled nonlinear Schrödinger and Poisson equations. The nonlinearly coupled equations for our purposes are then used to obtain a general dispersion relation (GDR) for studying the parametric instabilities and the localization of CPEM wave packets in a quantum plasma. Numerical analyses of the GDR reveal that the growth rate of a fastest growing parametrically unstable mode is in agreement with the result that has been deduced from numerical simulations of the governing nonlinear equations. Explicit numerical results for two-dimensional (2D) localized CPEM wave packets at nanoscales are also presented. Possible applications of our investigation to intense laser-solid density compressed plasma experiments are highlighted.
Instability and dynamics of two nonlinearly coupled intense laser beams in a quantum plasma
Wang Yunliang; Shukla, P. K.; Eliasson, B.
2013-01-15
We consider nonlinear interactions between two relativistically strong laser beams and a quantum plasma composed of degenerate electron fluids and immobile ions. The collective behavior of degenerate electrons is modeled by quantum hydrodynamic equations composed of the electron continuity, quantum electron momentum (QEM) equation, as well as the Poisson and Maxwell equations. The QEM equation accounts the quantum statistical electron pressure, the quantum electron recoil due to electron tunneling through the quantum Bohm potential, electron-exchange, and electron-correlation effects caused by electron spin, and relativistic ponderomotive forces (RPFs) of two circularly polarized electromagnetic (CPEM) beams. The dynamics of the latter are governed by nonlinear wave equations that include nonlinear currents arising from the relativistic electron mass increase in the CPEM wave fields, as well as from the beating of the electron quiver velocity and electron density variations reinforced by the RPFs of the two CPEM waves. Furthermore, nonlinear electron density variations associated with the driven (by the RPFs) quantum electron plasma oscillations obey a coupled nonlinear Schroedinger and Poisson equations. The nonlinearly coupled equations for our purposes are then used to obtain a general dispersion relation (GDR) for studying the parametric instabilities and the localization of CPEM wave packets in a quantum plasma. Numerical analyses of the GDR reveal that the growth rate of a fastest growing parametrically unstable mode is in agreement with the result that has been deduced from numerical simulations of the governing nonlinear equations. Explicit numerical results for two-dimensional (2D) localized CPEM wave packets at nanoscales are also presented. Possible applications of our investigation to intense laser-solid density compressed plasma experiments are highlighted.
Parameterization of a geometrical reaction time model for two beam nacelle lidars
NASA Astrophysics Data System (ADS)
Beuth, Thorsten; Fox, Maik; Stork, Wilhelm
2015-09-01
The reaction time model is briefly reintroduced as published in a previous publication to explain the restrictions of detecting a horizontal homogenous wind field by two beams of a LiDAR placed on a wind turbine's nacelle. The model is parameterized to get more general statements for a beneficial system design concept. This approach is based on a parameterization towards the rotor disc radius R. All other parameters, whether they are distances like the measuring length or velocities like the cut-out wind speed, can be expressed by the rotor disc radius R. A review of state-of-the-art commercially available wind turbines and their size and rotor diameter is given to estimate the minimum measuring distances that will benefit most wind turbine systems in present as well as in the near future. In the end, the requirements are matched against commercially available LiDARs to show the necessity to advance such systems.
Lee, S. Y.
2014-04-07
We had carried out a design of an ultimate storage ring with beam emittance less than 10 picometer for the feasibility of coherent light source at X-ray wavelength. The accelerator has an inherent small dynamic aperture. We study method to improve the dynamic aperture and collective instability for an ultimate storage ring. Beam measurement and accelerator modeling are an integral part of accelerator physics. We develop the independent component analysis (ICA) and the orbit response matrix method for improving accelerator reliability and performance. In collaboration with scientists in National Laboratories, we also carry out experimental and theoretical studies on beam dynamics. Our proposed research topics are relevant to nuclear and particle physics using high brightness particle and photon beams.
Influence of non-linear index on coherent passive beam combining of fiber lasers
NASA Astrophysics Data System (ADS)
Napartovich, A. P.; Elkin, N. N.; Vysotsky, D. V.
2011-02-01
Coherent laser beam combining is potentially attractive way to increase the output beam brightness beyond the limits imposed on single-mode lasers by technological problems. Passive phase locking does not need complex external management. A specific feature of fiber amplifiers and lasers is that they possess optical path differences of many wavelengths magnitude. Cold-cavity theory of coherent laser beam combining predicts in this case rather low efficiency of beam combining even for an array of 8 lasers. Experiments, in contrast, demonstrated in such systems that high degree of phasing takes place for up to 20 lasers in an array. Possible explanation of this discrepancy may be associated with a number of factors. These factors are: gain saturation, intensity-dependent index, laser wavelength self-adjustment within the gain bandwidth. Besides, high degree of phase-locking can be established in self-sustained pulse periodic or spiky regime. Our approach takes injection controlled laser as a base unit of an ensemble. Beams from the neighboring lasers are injected into the reference laser in the array. Then a relationship between reference laser characteristics and whole wave field parameters can be found. As an example, fiber laser array with global coupling is numerically simulated with laser wavelength scanned within the gain bandwidth. Non-linear index is found to improve essentially passive phasing efficiency independent of the non-linearity sign.
Egorov, E. N. Koronovskii, A. A.; Kurkin, S. A.; Hramov, A. E.
2013-11-15
Results of numerical simulations and analysis of the formation and nonlinear dynamics of the squeezed state of a helical electron beam in a vircator with a magnetron injection gun as an electron source and with additional electron deceleration are presented. The ranges of control parameters where the squeezed state can form in such a system are revealed, and specific features of the system dynamics are analyzed. It is shown that the formation of a squeezed state of a nonrelativistic helical electron beam in a system with electron deceleration is accompanied by low-frequency longitudinal dynamics of the space charge.
NASA Astrophysics Data System (ADS)
Egorov, E. N.; Koronovskii, A. A.; Kurkin, S. A.; Hramov, A. E.
2013-11-01
Results of numerical simulations and analysis of the formation and nonlinear dynamics of the squeezed state of a helical electron beam in a vircator with a magnetron injection gun as an electron source and with additional electron deceleration are presented. The ranges of control parameters where the squeezed state can form in such a system are revealed, and specific features of the system dynamics are analyzed. It is shown that the formation of a squeezed state of a nonrelativistic helical electron beam in a system with electron deceleration is accompanied by low-frequency longitudinal dynamics of the space charge.
Nonlinear gyrofluid models of shear Alfven instabilities in ignited and beam heated toroidal plasmas
Spong, D.A.; Hedrick, C.L.; Carreras, B.A.
1993-07-01
Shear Alfven instabilities driven by energetic beams and alpha populations are investigated using a reduced MHD-gyrofluid model with Landau closure. The moment equations for the fast ions are truncated in a way which incorporates the wave particle resonances that are required to destabilize the shear Alfven mode. These are coupled to an Ohm`s law and vorticity equations which have been generalized to include ion FLR, electron and ion Landau damping. This model has been applied to experimentally observed regimes in a number of tokamak and stellarator devices. Both linearized growth rates and the nonlinear evolution are obtained. The saturated nonlinear regimes indicate mode number and frequency spectra which are generally consistent with experiment. A detailed examination of one typical nonlinear state has allowed identification of the dominant saturation mechanisms. This indicates that generation of n = 0, m = 0 sheared poloidal velocity flows and quasi linear modification of the q(r) profile can be important factors in reaching saturation.
Stimulated Raman scattering and nonlinear focusing of high-power laser beams propagating in water.
Hafizi, B; Palastro, J P; Peñano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D
2015-04-01
The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown, and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. The phenomenon of gain-focusing discussed here for propagation in water is expected to be of general occurrence applicable to any medium supporting nonlinear focusing and stimulated Raman scattering. PMID:25831383
Nonlinear self-focus of pulsed-wave beams in Kerr media
Judkins, J.B.
1992-12-31
A modified finite-difference time-domain method for solving Maxwell`s equations in nonlinear media is presented. This method allows for a finite response time to be incorporated in the medium, physically creating dispersion and absorption mechanisms. The technique models electromagnetic fields in two space dimensions and time and encompasses both the TE{sub z} and TM{sub z} set of decoupled field equations. Aspects of an ultra-short pulsed Gaussian beam are studied in a variety of linear and nonlinear environments to demonstrate that the methods developed here can be used efficaciously in the modeling of pulses in complex problem space geometries even when nonlinearities are present.
Nonlinear control via approximate input-output linearization - The ball and beam example
NASA Technical Reports Server (NTRS)
Hauser, John; Sastry, Shankar; Kokotovic, Petar
1992-01-01
A study is made of approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree. For such systems, a method is provided for constructing approximate systems that are input-output linearizable. The analysis presented in this note is motivated through its application to a common undergraduate control laboratory experiment, the ball and beam system, where it is shown to be more effective for trajectory tracking than the standard Jacobian linearization.
Nonlinear dust-plasma interactions of a cross-beam system in interplanetary space
Jammalamadaka, S.; Araneda, J.; McKenzie, J. F.; Gruenwaldt, H.
1998-10-21
Dust plasma interaction has been considered. The present work is an extension of the paper of Mann and McKenzie [Mann and McKenzie, 1997]. Using the cross-beam configuration we investigate the dust plasma interaction taking into account the inhomogeneity of density. The dust interacts in our case with an inhomogeneous collisionless multi-ion plasma. Linear and nonlinear behaviour of the system has been examined and its impact on the dust dynamics is pointed out.
Nonlinear beam dynamics studies at Indiana University. Final report, August 1, 1993--July 31, 1997
Lee, S.Y.
1998-03-31
During the three-year funding period the author`s achievements can be summarized as follows: (1) The author has systematically studied the effect of phase modulation on bunch distribution. (2) The author has found that a frequently observed proton beam instability when the velocity of cooling electrons differs from that of protons is due to Hopf bifurcation. The equilibrium proton beam distribution becomes a limiting cycle attractor. This technique can be used to measure the temperature of cooling electrons. (3) The author has studied mechanisms of controlled bunch dilution. Evolution of beam bunch profile is measured while the beam is perturbed by the modulation of a secondary rf system. The experimental data reveal that mean square bunch length {sigma}{sup 2}(t) exhibits two characteristic time scales. He finds that overlapping parametric resonances plays an important role in beam diffusion. (4) He has studied the effects of global chaos on the halo formation of space charge dominated beams. He has analyzed the halo produced by a modulating mismatched space charge dominated beam in a uniform focusing channel. He found that the halo formation is determined by a single scaling parameter, the space charge perveance parameter divided by the phase advance per unit length. The condition of global chaos can thus be predicted. In June 1994, Indiana University has served as the host of the USPAS (United States Particle Accelerator School). In July 1994, IUCF has also served as the host site of the workshop on the future direction of hadron facilities. In October 1994, the author organized a successful workshop on space charge dominated beams and application of high brightness beams. During this period of this funding, he has had many visitors from SSC, SLAC, Fermilab, and Brookhaven National Laboratory. He has carried out many nonlinear beam dynamics experiments at the IUCF Cooler Ring. He has published about 30 refereed journal papers related to this project. These papers are listed in Sec. 3.
NASA Astrophysics Data System (ADS)
Reaungamornrat, S.; Otake, Y.; Uneri, A.; Schafer, S.; Mirota, D. J.; Nithiananthan, S.; Stayman, J. W.; Khanna, A. J.; Reh, D. D.; Gallia, G. L.; Taylor, R. H.; Siewerdsen, J. H.
2012-02-01
Conventional surgical tracking configurations carry a variety of limitations in line-of-sight, geometric accuracy, and mismatch with the surgeon's perspective (for video augmentation). With increasing utilization of mobile C-arms, particularly those allowing cone-beam CT (CBCT), there is opportunity to better integrate surgical trackers at bedside to address such limitations. This paper describes a tracker configuration in which the tracker is mounted directly on the Carm. To maintain registration within a dynamic coordinate system, a reference marker visible across the full C-arm rotation is implemented, and the "Tracker-on-C" configuration is shown to provide improved target registration error (TRE) over a conventional in-room setup - (0.9+/-0.4) mm vs (1.9+/-0.7) mm, respectively. The system also can generate digitally reconstructed radiographs (DRRs) from the perspective of a tracked tool ("x-ray flashlight"), the tracker, or the C-arm ("virtual fluoroscopy"), with geometric accuracy in virtual fluoroscopy of (0.4+/-0.2) mm. Using a video-based tracker, planning data and DRRs can be superimposed on the video scene from a natural perspective over the surgical field, with geometric accuracy (0.8+/-0.3) pixels for planning data overlay and (0.6+/-0.4) pixels for DRR overlay across all C-arm angles. The field-of-view of fluoroscopy or CBCT can also be overlaid on real-time video ("Virtual Field Light") to assist C-arm positioning. The fixed transformation between the x-ray image and tracker facilitated quick, accurate intraoperative registration. The workflow and precision associated with a variety of realistic surgical tasks were significantly improved using the Tracker-on-C - for example, nearly a factor of 2 reduction in time required for C-arm positioning, reduction or elimination of dose in "hunting" for a specific fluoroscopic view, and confident placement of the x-ray FOV on the surgical target. The proposed configuration streamlines the integration of C-arm CBCT with realtime tracking and demonstrated utility in a spectrum of image-guided interventions (e.g., spine surgery) benefiting from improved accuracy, enhanced visualization, and reduced radiation exposure.
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
NASA Astrophysics Data System (ADS)
Tokluoglu, Erinc K.
Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged fields generated by beam-plasma instabilities can be responsible for defocusing and distorting beams propagating in background plasma. This can be problematic in inertial fusion applications where the beam is intended to propagate ballistically as the background plasma neutralizes the beam space charge and current. We used particle-in-cell (PIC) code LSP to numerically investigate the defocusing effects in an ion beam propagating in background plasma experiences as it is exposed to the non-linear fields generated by Two-Stream instability between beam ions and plasma electrons. Supported by theory and benchmarked by the numerical solutions of governing E&M equations, the simulations were used to find and check scaling laws for the defocusing forces in the parameter space of beam and plasma density as well as the beam ion mass. A transition region where the defocusing fields peak has been identified, which should be avoided in the design of experimental devices. We further proposed a diagnostic tool to identify the presence of the two-stream instability in a system with parameters similar to the National Drift Compression Experiment II (NDCX-II) and conducted proof-of concept simulations. In the case of electron beam propagating in background plasma instability driven collisionless scattering and plasma heating is observed. 1-D simulations conducted in EDIPIC were benchmarked in LSP to study the excitation and time-evolution of electron-electron Two-Stream instability. Coupling of electron dynamics via non-linear ponderomotive force created by instability generated fields with ion cavities and Ion-Acoustic mode excitation was observed. Furthermore 2-D simulations of an electron-beam in a background plasma was performed. Many of the effects in observed in 1-D simulations were replicated. Morever generation of oblique modes with transverse wave numbers were observed in the simulations, which resulted in significant transverse scattering of beam electrons and the time evolution of the turbulent spectrum was studied via Fourier techniques. It is plausible that the modes excited might be interacting non-linearly via mode-coupling, however further theoretical and numerical investigation of the turbulent spectrum is needed. The study of the more realistic 2-D system and the spectrum is important for the understanding of collisionless heating of plasmas by beams and the underlying energy delivery which can have important applications in especially low temperature plasma systems used primarily in etching and materials processing.
Engaging new dimensions in nonlinear optical spectroscopy using auxiliary beams of light
NASA Astrophysics Data System (ADS)
Ford, Jack S.; Bradshaw, David S.; Andrews, David L.
2014-05-01
By applying a sufficiently intense beam of off-resonant light, simultaneously with a conventional excitation source beam, the efficiencies of one- and two-photon absorption processes may be significantly modified. The nonlinear mechanism that is responsible, known as laser modified absorption, is fully described by a quantum electrodynamical analysis. The origin of the process, which involves stimulated forward Rayleigh-scattering of the auxiliary beam, relates to higher order terms which are secured by a time-dependent perturbation treatment. These terms, usually inconsequential when a single beam of light is present, become prominent under the secondary optical stimulus - even with levels of intensity that are moderate by today's standards. Distinctive kinds of behaviour may be observed for chromophores fixed in a static arrangement, or for solution- or gas-phase molecules whose response is tempered by a rotational average of orientations. In each case the results exhibit an interplay of factors involving the beam polarisations and the molecular electronic response. Special attention is given to interesting metastable states that are symmetry forbidden by one- or two-photon absorption. Such states may be accessible, and thus become populated, on input of the auxiliary beam. For example, in the one-photon absorption case, terms arise that are more usually associated with three-photon processes, corresponding to very different selection rules. Other kinds of metastable state also arise in the two-photon process, and measuring the effect of applying the stimulus beam to absorbances of such character adds a new dimension to the information content of the associated spectroscopy. Finally, based on these novel forms of optical nonlinearity, there may be new possibilities for quantum non-demolition measurements.
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.
NASA Astrophysics Data System (ADS)
Akbari, M. R.; Ganji, D. D.; Rostami, A. K.; Nimafar, M.
2015-03-01
In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji's method (AGM). AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method (Runk45) and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration ( A), the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure. Therefore, AGM can be considered as a significant progress in nonlinear sciences.
NASA Astrophysics Data System (ADS)
Andreaus, Ugo; Baragatti, Paolo
2011-02-01
Numerical evaluation of the flexural forced vibration of a cantilever beam having a transverse surface crack extending uniformly along the width of the beam was performed to relate the nonlinear resonances to the crack presence, location, and depth. To this end, the qualitative characteristics, namely phase portrait distortions, sub- and super-harmonic components in the Fourier spectrum, and curved shape of the modal line were considered. Furthermore, quantitative parameters, such as the eccentricity and the excursion of the orbit, and the harmonic amplitude in the spectrum were measured. Then, an identification procedure was proposed which was based on the intersection of constructed surfaces which allowed to identify the structural damage. The acceleration record of the beam tip was sufficient to detect the existence of the crack and to identify crack depth and site.
On the Nonlinear Effects in Focused Ultrasound Beams with Frequency Power Law Attenuation
NASA Astrophysics Data System (ADS)
Jiménez, N.; Redondo, J.; Sánchez-Morcillo, V.; Iglesias, P. C.; Camarena, F.
When finite amplitude ultrasound propagation is considered, changes in spatial features of focused ultrasound beams can be observed. These nonlinear effects typically appear in thermoviscous fluids as focal displacements, beam-width variations or gain changes. However, in soft-tissue media, the frequency dependence of the attenuation doesn't obey a squared law. In this way, these complex media response leads to weak dispersion that prevents the cumulative processes of energy transfer to higher harmonics. In this work we explore the influence of different frequency power law attenuation responses and its influence on the self-defocusing effects in focused ultrasound beams. Thus, we numerically explore the spatial field distributions produced by low-Fresnel number devices and High Intensity Focused Ultrasound (HIFU) radiating trough different soft-tissue media.
Nonlinear resonance and envelope instability of intense beam in axial symmetric periodic channel
NASA Astrophysics Data System (ADS)
Li, Chao; Liu, Zhicong; Zhao, Yaliang; Qin, Qing
2016-03-01
When an intense charged particle beam propagates through a given periodic focusing channel, it will experience the phenomena of nonlinear resonance, collective instability or chaotic motion with different conditions. In this paper, the collective envelope instability mechanisms are studied for symmetric beam propagation in an axially symmetric periodic channel. The beam is characterized as collectively stable if there exists a stable fixed point (SFP) located at the matched beam condition (rm , 0) in (r ,pr) phase space. It is found that the well-known collective envelope instability is dynamically related to the period-two orbits bifurcation of the matched SFP, meanwhile the unique stable SFP turns into an unstable saddle-node, surrounded by 1/2 resonance islands. However, higher orders of resonance (l / n, n > 2) coming from period-n bifurcation will not lead to collective beam instability because a new SFP emerges immediately upon the bifurcation process. The orders of SFP bifurcation is numerically depicted by the envelope tune Î½=Ï•/360, where Ï• is the eigenphase of the Poincar e Â´ tangent map T(s) in one focusing period at SFP, as functions of depressed phase advance. With strong space charge, due to these resonances from SFP bifurcation could be overlapped, mismatched beam would even show chaotic motion. For specific parameters, regular orbits, resonance islands, chaotic regions formed by resonance overlapping are clearly depicted with frequency analysis and Lyapunov spectral exponents, a method that may prove useful when extended to higher phase-space dimensions.
Geometric Effects on Electron Cloud
Wang, L
2007-07-06
The development of an electron cloud in the vacuum chambers of high intensity positron and proton storage rings may limit the machine performances by inducing beam instabilities, beam emittance increase, beam loss, vacuum pressure increases and increased heat load on the vacuum chamber wall. The electron multipacting is a kind of geometric resonance phenomenon and thus is sensitive to the geometric parameters such as the aperture of the beam pipe, beam shape and beam bunch fill pattern, etc. This paper discusses the geometric effects on the electron cloud build-up in a beam chamber and examples are given for different beams and accelerators.
Yin, L.; Albright, B. J.; Rose, H. A.; Bowers, K. J.; Bergen, B.; Montgomery, D. S.; Kline, J. L.; Kirkwood, R. K.; Hinkel, D. E.; Langdon, A. B.; Michel, P.
2012-05-15
In inertial confinement fusion experiments, stimulated Raman scattering (SRS) occurs when electron density fluctuations are amplified resonantly by the incident laser beams and scattered light. These beams comprise several thousands of individual laser speckles. We have found in single-speckle studies that electron trapping lowers the threshold intensity for SRS onset to a value below that from linear theory and enhances scattering. The trapping-induced plasma-wave frequency shift leads to wave-front bowing and filamentation processes that saturate SRS and limit scattering within a speckle. With large-scale simulations, we have now examined how laser speckles interact with one another through three-dimensional (3D) particle-in-cell (PIC) simulations of two interacting speckles and 2D PIC simulations of ensembles of laser speckles (hundreds of speckles). Our work shows that kinetic trapping physics also governs the onset and saturation of SRS in ensembles of speckles. Speckles interact in a manner that is nonlinear and nonlocal: An intense speckle can destabilize its neighbors through transport of hot electrons and SRS waves, resulting in enhanced emission of particles and waves that, in turn, act upon the original speckle. In this manner, speckles below threshold when in isolation can be above the threshold in multi-speckled beams under conditions for laser-driven fusion experiments at the National Ignition Facility (NIF) and ensembles of speckles are thus found to collectively lower the SRS onset threshold. Simulations of the hohlraum interior where laser beams overlap show that multi-speckled laser beams at low average intensity (a few times 10{sup 14} W/cm{sup 2}) have correspondingly lower thresholds for enhanced SRS and that the sub-ps bursts of SRS saturate through trapping induced nonlinearities. Because of electron trapping effects, SRS reflectivity grows slowly with average laser intensity. While SRS reflectivity saturates under NIF conditions, SRS hot electron energy increases with increasing laser intensity and may contribute to capsule preheat.
Nonlinear optics and liquid crystal light valve for laser beam control
NASA Astrophysics Data System (ADS)
Huignard, Jean Pierre; Brignon, Arnaud; Steinhausser, Bastien
2008-11-01
The recent advances in solid state laser technology now permit to achieve high energy and efficiency sources for a wide range of applications extending from laser physics to material processing, biophotonics, remote sensing and coherent lidar systems. In particular the progress of fibre laser exploiting the double clading diode pumping structure are impressive: they are compact and emit single mode beams. However optical damage and nonlinear effects limit the output peak power emitted by a single mode fiber laser. Also limitations arise in bulk laser materials due to the thermal loading which induces strong wavefront distortions on the beams. We develop in this paper original concepts adapted to power-energy scaling of bulk or fibre lasers. The final objective is to emit high brightness and high energy beams whose quality is close to the diffraction limit. For this purpose we present new technics to be inspired from from Fourier optics and allowing the wavefront processing either through nonlinear interactions or with adaptive optical components such as electro optic phase modulators or liquid crystal light valves.
Nariyuki, Y.; Hada, T.; Tsubouchi, K.
2014-10-01
The damping process of field-aligned, low-frequency right-handed polarized nonlinear Alfvén waves (NAWs) in solar wind plasmas with and without proton beams is studied by using a two-dimensional ion hybrid code. The numerical results show that the obliquely propagating kinetic Alfvén waves (KAWs) excited by beam protons affect the damping of the low-frequency NAW in low beta plasmas, while the nonlinear wave-wave interaction between parallel propagating waves and nonlinear Landau damping due to the envelope modulation are the dominant damping process in high beta plasmas. The nonlinear interaction between the NAWs and KAWs does not cause effective energy transfer to the perpendicular direction. Numerical results suggest that while the collisionless damping due to the compressibility of the envelope-modulated NAW plays an important role in the damping of the field-aligned NAW, the effect of the beam instabilities may not be negligible in low beta solar wind plasmas.
Nonlinear Mechanisms of Light Beam Absorption in Transparent Materials under High Power Laser Action
Eliseev, Peter G.; Kozlovskaya, Natalia A.; Krokhin, Oleg N.; Zavestovskaya, Irina N.
2010-10-08
Analysis of nonlinear mechanisms of light beam absorption in transparent materials under high power and ultrashort pulses laser action is presented. The processes of nonlinear absorption and ablation of transparent materials (such as nitride semiconductor, sapphire and others) under terawatt/cm{sup 2}-laser irradiation with ultrashort pulses are considered. The values of ablation thresholds for different dielectrics are discussed. The threshold appears to grow approximately in proportion to the third power of the material energy bandgap. The model is based on the tunneling absorption under the irradiation by high-intensity ultrashort pulses. The theory of ionization of solids in a field of strong electromagnetic wave is used. The effect of the material energy bandgap on the laser ablation threshold s adequately explained.
Sonnad, Kiran G.; Cary, John R.
2015-04-15
A procedure to obtain a near equilibrium phase space distribution function has been derived for beams with space charge effects in a generalized periodic focusing transport channel. The method utilizes the Lie transform perturbation theory to canonically transform to slowly oscillating phase space coordinates. The procedure results in transforming the periodic focusing system to a constant focusing one, where equilibrium distributions can be found. Transforming back to the original phase space coordinates yields an equilibrium distribution function corresponding to a constant focusing system along with perturbations resulting from the periodicity in the focusing. Examples used here include linear and nonlinear alternating gradient focusing systems. It is shown that the nonlinear focusing components can be chosen such that the system is close to integrability. The equilibrium distribution functions are numerically calculated, and their properties associated with the corresponding focusing system are discussed.
Nonlinear theory of electron neutralization waves in ions beams with dissipation
NASA Technical Reports Server (NTRS)
Wilhelm, H. E.
1974-01-01
An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer - i.e., after a few relaxation lengths a quasi-neutral plasma results.
Kong, Ling-Bao; Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 ; Wang, Hong-Yu; Hou, Zhi-Ling; Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 ; Jin, Hai-Bo; Du, Chao-Hai
2013-12-15
The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained.
Larciprete, M.C.; Passeri, D.; Michelotti, F.; Paoloni, S.; Sibilia, C.; Bertolotti, M.; Belardini, A.; Sarto, F.; Somma, F.; Lo Mastro, S.
2005-01-15
We investigated second order optical nonlinearity of zinc oxide thin films, grown on glass substrates by the dual ion beam sputtering technique under different deposition conditions. Linear optical characterization of the films was carried out by spectrophotometric optical transmittance and reflectance measurements, giving the complex refractive index dispersion. Resistivity of the films was determined using the four-point probe sheet resistance method. Second harmonic generation measurements were performed by means of the Maker fringes technique where the fundamental beam was originated by nanosecond laser at {lambda}=1064 nm. We found a relatively high nonlinear optical response, and evidence of a dependence of the nonlinear coefficient on the deposition parameters for each sample. Moreover, the crystalline properties of the films were investigated by x-ray diffraction measurements and correlation with second order nonlinearity were analyzed. Finally, we investigated the influence of the oxygen flow rate during the deposition process on both the second order nonlinearity and the structural properties of the samples.
NASA Astrophysics Data System (ADS)
Gupta, Naveen; Singh, Navpreet; Singh, Arvinder
2015-11-01
This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on a numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.
Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies
Chang, Jing; Gao, Yixian Li, Yong
2015-05-15
Consider the one dimensional nonlinear beam equation u{sub tt} + u{sub xxxx} + mu + u{sup 3} = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form.â€‰.
Nonlinear Elastic J-Integral Measurements in Mode I Using a Tapered Double Cantilever Beam Geometry
NASA Technical Reports Server (NTRS)
Macon, David J.
2006-01-01
An expression for the J-integral of a nonlinear elastic material is derived for an advancing crack in a tapered double cantilever beam fracture specimen. The elastic and plastic fracture energies related to the test geometry and how these energies correlates to the crack position are discussed. The dimensionless shape factors eta(sub el and eta(sub p) are shown to be equivalent and the deformation J-integral is analyzed in terms of the eta(sub el) function. The fracture results from a structural epoxy are interpreted using the discussed approach. The magnitude of the plastic dissipation is found to strongly depend upon the initial crack shape.
Korte, Dorota; Franko, Mladen
2015-01-01
In this work, complex geometrical optics is, for what we believe is the first time, applied instead of geometrical or wave optics to describe the probe beam interaction with the field of the thermal wave in photothermal beam deflection (photothermal deflection spectroscopy) experiments on thin films. On the basis of this approach the thermal (thermal diffusivity and conductivity), optical (energy band gap), and transport (carrier lifetime) parameters of the semiconductor thin films (pure TiO2, N- and C-doped TiO2, or TiO2/SiO2 composites deposited on a glass or aluminum support) were determined with better accuracy and simultaneously during one measurement. The results are in good agreement with results obtained by the use of other methods and reported in the literature. PMID:26366490
NASA Astrophysics Data System (ADS)
Makov, Y. N.; Espinosa, V.; Sánchez-Morcillo, V. J.; Ramis, J.; Cruañes, J.; Camarena, F.
2006-05-01
On the basis of theoretical concepts, an accurate and complete experimental and numerical examination of the on-axis distribution and the corresponding temporal profiles for low-Fresnel-number focused ultrasound beams under increasing transducer input voltage has been performed. For a real focusing transducer with sufficiently small Fresnel number, a strong initial (linear) shift of the main on-axis pressure maximum from geometrical focal point towards the transducer, and its following displacement towards the focal point and backward motion as the driving transducer voltage increase until highly nonlinear regimes were fixed. The simultaneous monitoring of the temporal waveform modifications determines the real roles and interplay between different nonlinear effects (refraction and attenuation) in the observed dynamics of on-axis pressure maximum. The experimental results are in good agreement with numerical solutions of KZK equation, confirming that the observed dynamic shift of the maximum pressure point is related only to the interplay between diffraction, dissipation and nonlinearity of the acoustic wave.
Non-linear optical flow cytometry using a scanned, Bessel beam light-sheet.
Collier, Bradley B; Awasthi, Samir; Lieu, Deborah K; Chan, James W
2015-01-01
Modern flow cytometry instruments have become vital tools for high-throughput analysis of single cells. However, as issues with the cellular labeling techniques often used in flow cytometry have become more of a concern, the development of label-free modalities for cellular analysis is increasingly desired. Non-linear optical phenomena (NLO) are of growing interest for label-free analysis because of the ability to measure the intrinsic optical response of biomolecules found in cells. We demonstrate that a light-sheet consisting of a scanned Bessel beam is an optimal excitation geometry for efficiently generating NLO signals in a microfluidic environment. The balance of photon density and cross-sectional area provided by the light-sheet allowed significantly larger two-photon fluorescence intensities to be measured in a model polystyrene microparticle system compared to measurements made using other excitation focal geometries, including a relaxed Gaussian excitation beam often used in conventional flow cytometers. PMID:26021750
Non-Linear Optical Flow Cytometry Using a Scanned, Bessel Beam Light-Sheet
Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.
2015-01-01
Modern flow cytometry instruments have become vital tools for high-throughput analysis of single cells. However, as issues with the cellular labeling techniques often used in flow cytometry have become more of a concern, the development of label-free modalities for cellular analysis is increasingly desired. Non-linear optical phenomena (NLO) are of growing interest for label-free analysis because of the ability to measure the intrinsic optical response of biomolecules found in cells. We demonstrate that a light-sheet consisting of a scanned Bessel beam is an optimal excitation geometry for efficiently generating NLO signals in a microfluidic environment. The balance of photon density and cross-sectional area provided by the light-sheet allowed significantly larger two-photon fluorescence intensities to be measured in a model polystyrene microparticle system compared to measurements made using other excitation focal geometries, including a relaxed Gaussian excitation beam often used in conventional flow cytometers. PMID:26021750
Beam quality from self and ionization induced trapping in the nonlinear LWFA regime
NASA Astrophysics Data System (ADS)
Davidson, Asher; Lu, Wei; Joshi, Chan; Silva, Luis; Martins, Joana; Fonseca, Ricardo; Mori, Warren
2011-10-01
In plasma based accelerators (LWFA and PWFA), the methods of injecting high quality electron bunches into the accelerating wakefield is of utmost importance for various applications. Understanding how injection occurs in both self and controlled scenarios is therefore important. We present results from high fidelity OSIRIS simulations on the beam quality that can be obtained from self and ionized induced trapping in the nonlinear LWFA regime. We compare trapping thresholds from the simulations to analytical expressions. We also quantify how the beam quality of 1.5-5 GeV beams can be improved through angle and energy selection as well as quantify the slice energy spread and emittance. We also study the effect of ion motion and the axial density profile. Preliminary results on inputting beams from OSIRS into the FEL code GENESIS will be presented. This work was supported by UC Lab Fees Research Award No. 09-LR-05-118764-DOUW, DOE grants DOE DE-FC02-07ER41500 and DE-FG02-92ER40727 and by NSF grants NSF PHY-0904039 and NSF PHY-0936266. The simulations were performed on Jaguar under an INCITE award.
NASA Technical Reports Server (NTRS)
Noor, A. K.; Peters, J. M.
1981-01-01
Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.
Vibration of vehicle-pavement coupled system based on a Timoshenko beam on a nonlinear foundation
NASA Astrophysics Data System (ADS)
Ding, Hu; Yang, Yan; Chen, Li-Qun; Yang, Shao-Pu
2014-12-01
This paper focuses on the coupled nonlinear vibration of vehicle-pavement system. The pavement is modeled as a Timoshenko beam resting on a six-parameter foundation. The vehicle is simplified as a spring-mass-damper oscillator. For the first time, the dynamic response of vehicle-pavement coupled system is studied by modeling the pavement as a Timoshenko beam resting on a nonlinear foundation. Consequently, the shear effects and the rotational inertia of the pavement are included in the modeling process. The pavement model is assumed to be a linear-plus-cubic Pasternak-type foundation. Furthermore, the convergent Galerkin truncation is used to obtain approximate solutions to the coupled vibratory response of the vehicle-pavement coupled system. The dynamic responses of the vehicle-pavement system with the asphalt pavement on soft soil foundation are investigated via the numerical examples. The numerical results show that the calculation for the coupled vibratory response needs high-order modes. Moreover, the coupling effects between the pavement and the vehicle are numerically examined by using the convergent modal truncation. The physical parameters of the vehicle-pavement system such as the shear modulus are compared for determining their influences on the coupled vibratory response.
NASA Technical Reports Server (NTRS)
Dowell, E. H.; Traybar, J.; Hodges, D. H.
1977-01-01
An experimental study of the large deformation of a cantilevered beam under a gravity tip load has been made. The beam root is rotated so that the tip load is oriented at various angles with respect to the beam principal axes. Static twist and bending deflections of the tip and bending natural frequencies have been measured as a function of tip load magnitude and orientation. The experimental data are compared with the results of a recently developed non-linear structural theory. Agreement is reasonably good when bending deflections are small compared to the beam span, but systematic differences occur for larger deflections.
NASA Astrophysics Data System (ADS)
Sasmal, Saptarshi; Kalidoss, S.
2015-05-01
In the present study, investigations on fiber-reinforced plastic (FRP) plated-reinforced concrete (RC) beam are carried out. Numerical investigations are performed by using a nonlinear finite element analysis by incorporating cracking and crushing of concrete. The numerical models developed in the present study are validated with the results obtained from the experiment under monotonic load using the servo-hydraulic actuator in displacement control mode. Further, the validated numerical models are used to evaluate the influence of different parameters. It is found from the investigations that increase in the elastic modulus of adhesive layer and CFRP laminate increases the interfacial stresses whereas increase in laminate modulus decreases the displacement and reinforcement strain of the beam. It is also observed that increase in the adhesive layer can largely reduce the interfacial stresses, whereas increase in laminate thickness increases it. However, increase in laminate thickness decreases the displacement and reinforcement strain of the beam significantly. It is mention worthy that increase in laminate length reduces the interfacial stresses, whereas CFRP width change does not affect the interfacial stresses. The study will be useful for the design and practicing engineers for arriving at the FRP-based strengthening schemes for RC structures judiciously.
Effect of nonlinear radiofrequency electromagnetic fields on the emittance of bunched beams
NASA Astrophysics Data System (ADS)
Phadte, D. S.; Patidar, C. B.
2013-07-01
Gap transformations are frequently used in ion Linac codes, to efficiently describe the particle dynamics. Using similar approach, we analyze the uniformly bunched beam passing through an axis-symmetric radiofrequency (RF) cavity. The method can be used for other distributions as well using a similar six dimensional analysis. The effect of non-linear RF field in radial and axial directions in an RF cavity and the finite phase width of the bunch, on the transverse and longitudinal emittance growth have been studied. The expressions obtained have been verified for the two types of cavity cells namely the zero mode DTL and pi mode CCL type used frequently in ion linacs. The results are seen to be valid for the entire maximum phase acceptance up to 360 degrees. Simulations with the equivalent beams of non-uniform distributions namely Waterbag and Gaussian show that at synchronous phases closer to the wave crest, the results give a good approximation of emittance growth in both planes for non-uniform beams.
The coaxial gyrotron with two electron beams. I. Linear theory and nonlinear theory
Liu Shenggang; Yuan Xuesong; Fu Wengjie; Yan Yang; Zhang Yaxin; Li Hongfu; Zhong Renbin
2007-10-15
The coaxial gyrotron with two electron beams (CGTB) is proposed and investigated in this paper. This paper consists of two parts: the linear theory and nonlinear theory of CGTB are presented in part I and the investigation on the dual frequency operation, a special operation state of CGTB, is given in part II. The magnetron injection gun with two electron beams has been developed, and simulations show that it may work well. It may guarantee that both the electric potential and the ratio of vertical to longitudinal velocities of two electron beams are equal. The results of the calculation show that CGTB has some distinguished advantages: mode competition is improved and output power is enhanced. Thus CGTB may be capable of providing 2-4 MW continuous-wave (CW) at 170 GHz to meet the demand of very high radio frequency CW power 1-2 MW in the ITER [ITER EDA Agreement and Protocol 2 (IAEA, Vienna, 1994)] program and other applications.
NASA Astrophysics Data System (ADS)
Elwakil, S. A.; El-hanbaly, A. M.; Elgarayh, A.; El-Shewy, E. K.; Kassem, A. I.
2014-11-01
The properties of nonlinear electron-acoustic rogue waves have been investigated in an unmagnetized collisionless four-component plasma system consisting of a cold electron fluid, non-thermal hot electrons obeying a non-thermal distribution, an electron beam and stationary ions. It is found that the basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of rogue wave profiles on the electron beam and energetic population parameter are discussed. The results of the present investigation may be applicable in auroral zone plasma.
He, Qingbo Xu, Yanyan; Lu, Siliang; Dai, Daoyi
2014-04-28
This Letter reports an out-of-resonance vibro-acoustic modulation (VAM) effect in nonlinear ultrasonic evaluation of a microcracked cantilever beam. We design a model to involve the microcracked cantilever beam in a nonlinear oscillator system whose dynamics is introduced to extend the operating vibration excitation band of the VAM out of resonance. The prototype model exhibits an effective bandwidth four times that of the traditional linear model. The reported VAM effect allows efficiently enhancing the detection, localization, and imaging of various types of microcracks in solid materials at out-of-resonance vibration excitation frequencies.
NASA Astrophysics Data System (ADS)
Abdi, Mohamad; Hajihasani, Mojtaba; Gharibzadeh, Shahriar; Tavakkoli, Jahan
2012-12-01
Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is presented.
Papon, G.; Marquestaut, N.; Royon, A.; Canioni, L.; Petit, Y.; Dussauze, M.; Rodriguez, V.; Cardinal, T.
2014-03-21
We depict a new approach for the localized creation in three dimensions (3D) of a highly demanded nonlinear optical function for integrated optics, namely second harmonic generation. We report on the nonlinear optical characteristics induced by single-beam femtosecond direct laser writing in a tailored silver-containing phosphate glass. The original spatial distribution of the nonlinear pattern, composed of four lines after one single laser writing translation, is observed and modeled with success, demonstrating the electric field induced origin of the second harmonic generation. These efficient second-order nonlinear structures (with Ï‡{sub eff}{sup (2)}â€‰âˆ¼â€‰0.6â€‰pm V{sup âˆ’1}) with sub-micron scale are impressively stable under thermal constraint up to glass transition temperature, which makes them very promising for new photonic applications, especially when 3D nonlinear architectures are desired.
NASA Technical Reports Server (NTRS)
Crespo Da Silva, M. R. M.; Hodges, D. H.
1986-01-01
The dynamic response and aeroelastic stability of rotating beams such as helicopter blades is investigated analytically. The Hamilton principle is used to formulate the equations of motion for extensional and inextensional beams with precone angles and variable pitch angles, taking higher-order nonlinearities into account. The derivation of the equations and their approximate solution by a Galerkin procedure are explained in detail, and numerical results of equilibrium solutions and stability analyses are presented graphically.
Fast spatial beam shaping by acousto-optic diffraction for 3D non-linear microscopy.
Akemann, Walther; Léger, Jean-François; Ventalon, Cathie; Mathieu, Benjamin; Dieudonné, Stéphane; Bourdieu, Laurent
2015-11-01
Acousto-optic deflection (AOD) devices offer unprecedented fast control of the entire spatial structure of light beams, most notably their phase. AOD light modulation of ultra-short laser pulses, however, is not straightforward to implement because of intrinsic chromatic dispersion and non-stationarity of acousto-optic diffraction. While schemes exist to compensate chromatic dispersion, non-stationarity remains an obstacle. In this work we demonstrate an efficient AOD light modulator for stable phase modulation using time-locked generation of frequency-modulated acoustic waves at the full repetition rate of a high power laser pulse amplifier of 80 kHz. We establish the non-local relationship between the optical phase and the generating acoustic frequency function and verify the system for temporal stability, phase accuracy and generation of non-linear two-dimensional phase functions. PMID:26561090
Nonlinear optical properties of bulk cuprous oxide using single beam Z-scan at 790 nm
NASA Astrophysics Data System (ADS)
Serna, J.; Rueda, E.; García, H.
2014-11-01
The two-photon absorption (TPA) coefficient ? and the nonlinear index of refraction n2 for bulk cuprous oxide (Cu2O) direct gap semiconductor single crystal have been measured by using a balance-detection Z-scan single beam technique, with an excellent signal to noise ratio. Both coefficients were measured at 790 nm using a 65 fs laser pulse at a repetition rate of 90.9 MHz, generated by a Ti:Sapphire laser oscillator. The experimental values for ? were explained by using a model that includes allowed-allowed, forbidden-allowed, and forbidden-forbidden transitions. It was found that the forbidden-forbidden transition is the dominant mechanism, which is consistent with the band structure of Cu2O. The low value for ? found in bulk, as compared with respect to thin film, is explained in terms of the structural change in thin films that result in opposite parities of the conduction and valence band. The n2 is also theoretically calculated by using the TPA dispersion curve and the Kramers-Kronig relations for nonlinear optics.
Lagrange-type formulation for finite element analysis of non-linear beam vibrations
NASA Astrophysics Data System (ADS)
Sarma, B. S.; Varadan, T. K.
1983-01-01
A Lagrange-type formulation for finite element analysis of non-linear vibrations of immovably supported beams is presented. Two equations of motion coupled in axial and transverse displacements are derived by using Lagrange's equations. By neglecting the in-plane inertial effects, these equations are written in terms of the transverse displacement alone. Upon defining certain properties for the non-linear oscillatory behaviour of the transverse displacement, the governing equation is reduced to an equation in space alone from which the eigenvalue-like quantity is computed. The governing equation is solved in two ways. A direct iteration technique is used in the first method to compute a numerically exact mode shape and the corresponding frequency. A Rayleigh quotient type of formulation, similar to linear vibration analysis, is used in the second approach to evaluate the frequency of vibration for a fundamental mode which is determined from a linear FEM model and is maintained constant at all amplitudes. Numerical results are compared with available results and they corroborate the observations of earlier research workers.
Time-domain modeling of nonlinear distortion of pulsed finite amplitude sound beams.
Remenieras, J P; Bou Matar, O; Labat, V; Patat, F
2000-03-01
This work aims to validate a time domain numerical model for the nonlinear propagation of a short pulse of finite amplitude sound beam propagation in a tissue-mimicking liquid. The complete evolution equation is simply derived by a superposition of elementary operators corresponding to the 'one effect equation'. Diffraction LD, absorption and dispersion LAD, and nonlinear distortion LNL effects are treated independently using a first order operator-splitting algorithm. Using the method of fractional steps, the normal particle velocity and the acoustical pressure are calculated plane by plane, at each point of a two-dimensional spatial grid, from the surface of the plane circular transducer to a specified distance. The LA operator is a time convolution between the particle velocity and the causal attenuation filter built after the Kramers-Kroning relations. The LNL operator is a time-based transformation obtained by following an implicit Poisson analytic solution. The LD operator is the usual Rayleigh integral. We present a comparison between theoretical and experimental temporal pressure waveform and axial pressure curves for fundamental (2.25 MHz), second, third and fourth harmonics, obtained after spectral analysis. PMID:10829679
NASA Astrophysics Data System (ADS)
Chrysochoidis, Nikolaos A.; Barouni, Antigoni K.; Saravanos, Dimitris A.
2009-03-01
This paper investigates the potential of a novel SHM method for the detection of delamination cracks in composites which exploits the nonlinear ultrasonic response with in-situ d31 piezoceramic actuators and sensors. Composite beam specimens with artificially created delamination cracks are tested, entailing two piezoceramic actuator patches, the first to generate a low frequency, high power modal excitation and the second a high frequency acoustical wave, as well as a piezoceramic sensor. Nonlinearities induced at the high-frequency signal, such as sidebands at the spectral components as long as modulations at the measured sensory voltage are evaluated as damage indicators. Experimental results quantify the potential of the method in detecting small delamination cracks through spectral sideband components. The influence of high-frequency on the effectiveness of the method is shown. Additionally, the effect of the magnitude of applied voltage on the low frequency actuator on the formation of spectral components is investigated. Finally, the obtained results of the present method are compared with a guided wave based pitch and catch SHM method using the same actuator-sensor pair to excite and monitor the propagation of the first symmetric and asymmetric Lamb waves.
Ion-beam-assisted deposition of metal nanocluster thin films with nonlinear optical properties
Cotell, C.M.; Carosella, C.A.; Flom, S.R.; Schiestel, S.; Haralampus, N.; Barnett, T.W.; Bartoli, F.J.
1996-12-31
Metal nanocluster thin films ({approximately} 200 nm thickness) consisting of noble metal (Au) clusters (5--30 nm) in an active metal oxide (Nb{sub 2}O{sub 5}) matrix were deposited by evaporation or ion beam assisted deposition (IBAD). In some cases the films were given a post-deposition anneal. The microstructure of the films was examined by plan view and cross sectional transmission electron microscopy (TEM). The size of the metal nanoclusters was found to depend upon the temperature of the post-deposition anneal as well as the conditions of ion bombardment. Ion bombardment was found to stabilize smaller size particles. The linear optical properties of the films, as measured by VIS/UV spectroscopy, show particle size-dependent surface plasmon resonance effects. The nonlinear optical (NLO) properties of the nanoclusters in oxidized niobium were probed experimentally using degenerate four wave mixing (DFWM) and nonlinear transmission (NLT). The DFWM measurements yielded signals that showed strong evidence of saturation and give large values of {vert_bar}{chi}{sup (3)}{sub xxxx}{vert_bar}. NLT measurements demonstrated that the nonlinear absorption coefficient and, hence, I{sub m}{chi}{sup (3)}{sub xxxx} was negative. Time resolved DFWM measurements exhibited dynamics that decayed on a several picosecond time scale. The magnitude and the picosecond dynamics of the NLO response were compared to those observed in gold nanoclusters formed by ion implantation in other media. The advantages of the IBAD method for fabricating third order NLO films include the ability to deposit films of arbitrary active region thickness and, more importantly, high cluster densities.
High power microwave beam steering based on gyromagnetic nonlinear transmission lines
Romanchenko, I. V. Rostov, V. V.; Gunin, A. V.; Konev, V. Yu.
2015-06-07
We demonstrate electronically controlled beam steering by high power RF pulses produced by two gyromagnetic nonlinear transmission lines (NLTLs) connected to a one high voltage driver. Each NLTL is capable of producing several ns RF pulses with peak power from 50 to 700â€‰MW (6% standard deviation) at frequencies from 0.5 to 1.7â€‰GHz (1% standard deviation) with 100â€‰Hz repetition rate. Using a helix antenna allows irradiating of RF pulses with almost circular polarization and 350â€‰MW maximum peak power, which corresponds to 350â€‰kV effective potential of radiation. At the installation of two identical channels, we demonstrate the possibility of beam steering within Â±15Â° in the horizontal plane by coherent RF pulses with circular polarization at 1.0â€‰GHz center frequency. Fourfold increase in the power flux density for in-phase irradiation of RF pulses is confirmed by comparison with one-channel operation.
Cornacchia, M.; Evans, L.
1985-06-01
A nonlinear lens may be used to study the effect of high-order multipolar field imperfections on a stored proton beam. Such a nonlinear lens is particulary suitable to simulate field imperfections of the types encountered in coil dominated superconducting magnets. We have studied experimentally at the SPS the effect of high order (5th and 8th) single isolated resonances driven by the nonlinear lens. The width of these resonances is of the order one expects to be caused by field errors in superconducting magnets of the SSC type. The experiment shows that, in absence of tune modulation, these resonances are harmless. Slow crossings of the resonance, on the other hand, have destructive effects on the beam, much more so than fast crossings caused by synchrotron oscillations. In the design of future storage rings, sources of low-frequency tune modulation should be avoided as a way to reduce the harmful effects of high order multipolar field imperfection.
Karaton, Muhammet
2014-01-01
A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-? method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667
Karaton, Muhammet
2014-01-01
A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-? method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667
NASA Astrophysics Data System (ADS)
Lapsanska, Hana; Chmelickova, Hana; Hrabovsky, Miroslav
2010-10-01
Weld geometric characteristics in laser overlapping spot welding of 0.6-mm AISI 304 stainless steel sheets were investigated. A pulsed Nd:YAG laser with maximal average power of 150 W was used for welding experiments with different laser beam energies in the range of 3.5 J to 6.2 J, keeping all other processing parameters constant. The main objective of these experiments was to study the effect of energy changes and to identify the welding mode in dependency on the beam effective peak power density. Each weld surface and its cross section were analyzed using a laser scanning confocal microscope. The spot diameter on the specimen, weld width, and penetration depth were measured. Three-dimensional surface reconstruction was realized to describe the effect of energy changes on weld surface properties.
Pili, Giorgio; Grimaldi, Luca; Fidanza, Christian; Florio, Elena T.; Petruzzelli, Maria F.; D'Errico, Maria P.; De Tommaso, Cristina; Tramacere, Francesco; Musaio, Francesca; Castagna, Roberta; Francavilla, Maria C.; Gianicolo, Emilio A.L.; Portaluri, Maurizio
2011-11-01
Purpose: To evaluate the probability of late cardiac mortality resulting from left breast irradiation planned with tangential fields and to compare this probability between the wedged beam and field-in-field (FIF) techniques and to investigate whether some geometric/dosimetric indicators can be determined to estimate the cardiac mortality probability before treatment begins. Methods and Materials: For 30 patients, differential dose-volume histograms were calculated for the wedged beam and FIF plans, and the corresponding cardiac mortality probabilities were determined using the relative seriality model. As a comparative index of the dose distribution uniformity, the planning target volume (PTV) percentages involved in 97-103% of prescribed dose were determined for the two techniques. Three geometric parameters were measured for each patient: the maximal length, indicates how much the heart contours were displaced toward the PTV, the angle subtended at the center of the computed tomography slice by the PTV contour, and the thorax width/thickness ratio. Results: Evaluating the differential dose-volume histograms showed that the gain in uniformity between the two techniques was about 1.5. With the FIF technique, the mean dose sparing for the heart, the left anterior descending coronary artery, and the lung was 15% (2.5 Gy vs. 2.2 Gy), 21% (11.3 Gy vs. 9.0 Gy), and 42% (8.0 Gy vs. 4.6 Gy) respectively, compared with the wedged beam technique. Also, the cardiac mortality probability decreased by 40% (from 0.9% to 0.5%). Three geometric parameters, the maximal length, angle subtended at the center of the computed tomography slice by the PTV contour, and thorax width/thickness ratio, were the determining factors (p = .06 for FIF, and p = .10 for wedged beam) for evaluating the cardiac mortality probability. Conclusion: The FIF technique seemed to yield a lower cardiac mortality probability than the conventional wedged beam technique. However, although our study demonstrated that FIF technique improved the dose coverage of the PTV, the restricted number of patients enrolled and the short follow-up did not allow us to evaluate and compare the breast cancer survival rates of the patients.
Mourenas, D.; Beghin, C. )
1991-04-01
This paper investigates the generation mechanism responsible for the packets of electron cyclotron waves induced by an electron beam injected from the Space Shuttle and measured by Spacelab I instruments. The observed electron cyclotron emissions as well as their amplitude modulation are explained using a linear and a nonlinear treatments. Using a linear theory, it is shown that the emissions consist of the electronic Bernstein modes which are generated by an interaction between the neutralization return current and the ambient ionospheric plasma, and not directly by the primary beam. The observation of successive harmonic packets around the fundamental wave is interpreted using a two-dimensional single-wave model of the nonlinear interaction between a finite size ring beam and an infinite homogeneous magnetized plasma. 43 refs.
Bobylev, Yu. B.; Kuzelev, M. V.
2012-06-15
A nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in an isotropic dielectric medium is presented. A quantum model based on the Klein-Gordon equation is used. The growth rates of beam instabilities caused by the effect of stimulated Cherenkov radiation have been determined in the linear approximation. Mechanisms of the nonlinear saturation of relativistic quantum Cherenkov beam instabilities have been analyzed and the corresponding analytical solutions have been obtained.
NASA Astrophysics Data System (ADS)
Kala, Zden?k; Kala, Ji?í
2012-09-01
The paper deals with the influence of correlation length, of Gauss random field, and of yield strength of a hotrolled I-beam under bending on the ultimate load carrying capacity limit state. Load carrying capacity is an output random quantity depending on input random imperfections. Latin Hypercube Sampling Method is used for sampling simulation. Load carrying capacity is computed by the programme ANSYS using shell finite elements and nonlinear computation methods. The nonlinear FEM computation model takes into consideration the effect of lateral-torsional buckling on the ultimate limit state.
NASA Technical Reports Server (NTRS)
Intrator, T.; Hershkowitz, N.; Chan, C.
1984-01-01
Counterstreaming large-diameter electron beams in a steady-state laboratory experiment are observed to generate transverse radiation at twice the upper-hybrid frequency (2omega-UH) with a quadrupole radiation pattern. The electromagnetic wave power density is nonlinearly enhanced over the power density obtained from a single beam-plasma system. Electromagnetic power density scales exponentially with beam energy and increases with ion mass. Weak turbulence theory can predict similar (but weaker) beam energy scaling but not the high power density, or the predominance of the 2omega-UH radiation peak over the omega-UH peak. Significant noise near the upper-hybrid and ion plasma frequencies is also measured, with normalized electrostatic wave energy density W(ES)/n(e)T(e) approximately 0.01.
NASA Technical Reports Server (NTRS)
Moyer, E. T., Jr.
1984-01-01
The nonlinear vibration response of a double cantilevered beam subjected to pulse loading over a central sector is studied. The initial response is generated in detail to ascertain the energetics of the response. The total energy is used as a gauge of the stability and accuracy of the solution. It is shown that to obtain accurate and stable initial solutions an extremely high spatial and time resolution is required. This requirement was only evident through an examination of the energy of the system. It is proposed, therefore, to use the total energy of the system as a necessary stability and accuracy criterion for the nonlinear response of conservative systems. The results also demonstrate that even for moderate nonlinearities, the effects of membrane forces have a significant influence on the system. It is also shown that while the fundamental response is contained in a first mode envelope, the fluctuations caused by the higher order modes must be resolved.
Gao, Q. D.; Budny, R. V.
2015-03-15
By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (T{sub i,e}) and toroidal velocity (V{sub ?}) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.
Fenili, AndrÃ©; Lopes Rebello da Fonseca Brasil, Reyolando Manoel
2014-12-10
We derive nonlinear governing equations without assuming that the beam is inextensible. The derivation couples the equations that govern a weak electric motor, which is used to rotate the base of the beam, to those that govern the motion of the beam. The system is considered non-ideal in the sense that the response of the motor to an applied voltage and the motion of the beam must be obtained interactively. The moment that the motor exerts on the base of the beam cannot be determined without solving for the motion of the beam.
NASA Technical Reports Server (NTRS)
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
Edward A. Startsev; Ronald C. Davidson
2004-04-09
To achieve high focal spot intensities in heavy ion fusion, the ion beam must be compressed longitudinally by factors of ten to one hundred before it is focused onto the target. The longitudinal compression is achieved by imposing an initial velocity profile tilt on the drifting beam. In this paper, the problem of longitudinal drift compression of intense charged particle beams is solved analytically for the two important cases corresponding to a cold beam, and a pressure-dominated beam, using a one-dimensional warm-fluid model describing the longitudinal beam dynamics.
NASA Astrophysics Data System (ADS)
Zeng, Juan; Garg, Anurag; Kovacs, Andrew; Bajaj, Anil K.; Peroulis, Dimitrios
2015-05-01
Anchor supports in MEMS beams are often far from the ideally assumed built-in or step-up conditions. Practical fabrication processes often result in non-vertical anchoring supports (referred to as inclined supports in the following text) which significantly influence the post-release performance of the beam. This paper brings attention to the presence of the inclined supports in surface micromachined fixed-fixed beams and models the mechanical and electromechanical effects of inclined supports for the first time. Specifically, we calculate and validate the effects of residual stress and loading on the post-release beam behavior including their nonlinear large-displacement characteristics. In addition the model accounts for non-flat beam profiles caused by residual stress and/or a non-flat sacrificial layer profile. Inclined supports are modeled as cantilever beams connected to a horizontal beam. The Euler-Bernoulli equations for all beams are simultaneously solved to calculate the axial stress of the horizontal beam and the axial, translational, and rotational compliance of the supports. Nonlinear effects due to stretching and residual stress are also included. The calculated beam displacements agree with FEM models to within 1.1% in both the linear and nonlinear regimes. Furthermore, experimentally-obtained displacements of six fabricated beams with inclined supports agree to within 5.2% with the presented model.
NASA Astrophysics Data System (ADS)
Bernal, M. A.; deAlmeida, C. E.; David, M.; Pires, E.
2011-12-01
The PENELOPE code is used to determine direct strand break yields corresponding to photons from a 60Co source and 28 and 30 kV x-ray beams impacting on a B-DNA geometrical model, which accounts for five organizational levels of the human genetic material. Direct single, double and total strand break probabilities are determined in a liquid water homogeneous medium with 1.06 g cm-3 density. The spectra produced by the x-ray beams at various depths in the phantom have been used to study the dependence of the damage yield on the depth. The relative biological effectiveness (RBE) is also estimated using the 60Co radiation qualities as the reference. According to this work, the damage probabilities and thus the RBE are, within the uncertainties, similar for both x-ray energies and are independent of the depth into the phantom. Furthermore, the total strand break yield is invariant with respect to the energy of the incident photons. The RBE for low-energy x-ray beams determined here (1.3 Â± 0.1) is lower than that reported by Kellerer, taking into account that he used a 200 kV radiation as the reference quality. However, our RBE values are consistent with those determined by KÃ¼hne et al (2005 Radiat. Res. 164 669-76), which used the same biological endpoint and reference quality as our study. Also, our RBE values are similar to those determined by Verhaegen and Reniers (2004 Radiat. Res. 162 592-9).
Kanagawa, Tetsuya
2015-05-01
This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set. PMID:25994696
Energy harvesting in a nonlinear piezomagnetoelastic beam subjected to random excitation
NASA Astrophysics Data System (ADS)
De Paula, Aline S.; Inman, Daniel J.; Savi, Marcelo A.
2015-03-01
This work addresses the influence of nonlinearities in energy harvesting from a piezomagnetoelastic structure subjected to random vibrations. Nonlinear equations of motion that describe the electromechanical system are given along with theoretical simulations. The numerical analysis presents a comparison between the voltage provided from a linear, nonlinear bistable and nonlinear monostable systems due to random vibration. Experimental performance of the generator exhibits qualitative agreement with the theory, showing an enhancement of piezoelectric power generation in a bistable system when it vibrates around both stable equilibrium points. A relationship between variations in the excitation and a bistable system response is established from numerical simulations, defining a region of enhanced power generation when compared to the linear and nonlinear monostable cases.
C. L. Bohn , P. Piot and B. Erdelyi
2008-05-31
According to its original Statement of Work (SOW), the overarching objective of this project is: 'To enhance substantially the understanding of the fundamental dynamics of nonequilibrium high-brightness beams with space charge.' Our work and results over the past three and half years have been both intense and fruitful. Inasmuch as this project is inextricably linked to a larger, growing research program - that of the Beam Physics and Astrophysics Group (BPAG) - the progress that it has made possible cannot easily be separated from the global picture. Thus, this summary report includes major sections on 'global' developments and on those that can be regarded as specific to this project.
NASA Astrophysics Data System (ADS)
Dantu, Subbarao; Uma, R.
2000-10-01
The nonlinear Schrodinger equation in cylindrical geometry with saturating nonlinearity like the ponderomotive or relativistic nonlinearity in a plasma is analysed with the help of Symmetry Group Analysis. The symmetry group of the equation is deduced and a fiber-preserving subgroup of linear transformations are identified that leave such a nonlinear Schrodinger equation invariant. The MACSYMA-based Lie algebra of the symmetry group is realized to the extent possible. The theory results in an ordinary differential equation apart from a dictated beam profile. The resulting ordinary differential equation for self-focusing is compared with similar equations obtained from other existing theories of self-focusing in cylindrical geometry like the modified paraxial theory based on harmonic-oscillator basis, the moments theory and the variational theory . New types of solutions are identified and the limitations of the different methods are indicated.Acknowledgements: Financial assistance of CSIR(India)(Research Project,03(0815)/97/ EMR-II) for this work is acknowledged.
NASA Astrophysics Data System (ADS)
Munish, Aggarwal; Shivani, Vij; Niti, Kant
2015-11-01
The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated. An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field, with linear absorption and due to saturation effects for arbitrary large intensity. The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters. Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode. Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence. The beam is more focussed at lower intensity in both cases viz. extraordinary and ordinary mode.
NASA Astrophysics Data System (ADS)
Rapoport, Yu G.; Boardman, A. D.; Grimalsky, V. V.; Ivchenko, V. M.; Kalinich, N.
2014-05-01
The idea of nonlinear ‘transformation optics-inspired’ [1-6] electromagnetic cylindrical field concentrators has been taken up in a preliminary manner in a number of conference reports [7-9]. Such a concentrator includes both external linear region with a dielectric constant increased towards the centre and internal region with nonlinearity characterized by constant coefficients. Then, in the process of farther investigations we realized the following factors considered neither in [7-9] nor in the recent paper [10]: saturation of nonlinearity, nonlinear losses, linear gain, numerical convergence, when nonlinear effect becomes very strong and formation of ‘hotspots’ starts. It is clearly demonstrated here that such a strongly nonlinear process starts when the nonlinear amplitude of any incident beam(s) exceeds some ‘threshold’ value. Moreover, it is shown that the formation of hotspots may start as the result of any of the following processes: an increase of the input amplitude, increasing the linear amplification in the central nonlinear region, decreasing the nonlinear losses, a decrease in the saturation of the nonlinearity. Therefore, a tendency to a formation of ‘hotspots’ is a rather universal feature of the strongly nonlinear behaviour of the ‘nonlinear resonator’ system, while at the same time the system is not sensitive to the ‘prehistory’ of approaching nonlinear threshold intensity (amplitude). The new proposed method includes a full-wave nonlinear solution analysis (in the nonlinear region), a new form of complex geometric optics (in the linear inhomogeneous external cylinder), and new boundary conditions, matching both solutions. The observed nonlinear phenomena will have a positive impact upon socially and environmentally important devices of the future. Although a graded-index concentrator is used here, it is a direct outcome of transformation optics. Numerical evaluations show that for known materials these nonlinear effects could be readily achieved.
Optimization of nonlinear structural resonance using the incremental harmonic balance method
NASA Astrophysics Data System (ADS)
Dou, Suguang; Jensen, Jakob Søndergaard
2015-01-01
We present an optimization procedure for tailoring the nonlinear structural resonant response with time-harmonic loads. A nonlinear finite element method is used for modeling beam structures with a geometric nonlinearity and the incremental harmonic balance method is applied for accurate nonlinear vibration analysis. An optimization procedure based on a gradient-based algorithm is developed and we use the adjoint method for efficient computation of design sensitivities. We consider several examples in which we find optimized beam width distributions that minimize or maximize fundamental or super-harmonic resonant responses.
Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams
NASA Astrophysics Data System (ADS)
Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.
2015-04-01
In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized by the cantilever-surface mechanism. The optimization results show that the 2DOF nonlinear system presents the best average performance when the excitation signals have three possible forms. Moreover, we observe that while for the linear systems the optimal performance is obtained for small values of the electromagnetic damping, for the 2DOF nonlinear system optimal performance is achieved for large values of damping. This feature is of particular importance for the system's robustness to parasitic damping.
NASA Astrophysics Data System (ADS)
Zhu, Ronghua; Xie, Huimin; Dai, Xianglu; Zhu, Jianguo; Jin, Aizi
2014-09-01
Stress generated during thin film deposition is a critical issue for many applications. In general, the possible origins of the residual stress include intrinsic and extrinsic stresses. Since high residual stresses can cause detrimental effects on the film, such as delamination and wrinkle, it is of great importance to quantify the residual stress for the optimal design and the evaluation of its mechanical behavior. In this study, a method combining focused ion beam (FIB) milling and geometric phase analysis (GPA) is developed to assess the residual stress of thin films. The procedures of the residual stress measurement using this method include grating fabrication and slot milling by FIB, high-resolution scanning electron microscope (SEM) imaging of the grating before and after stress relaxation, and deformation analysis by GPA. The residual stress can be inferred from the released deformation using the reference displacements of the finite element model. As an application, this method was utilized to measure the residual stress in a TiAlSiN film, and the measured result is in good agreement with that obtained by the curvature method. In order to analyze the measurement error, the influence factors of Ga+ bombardment and the deposited platinum layer on the stress calculation are also discussed in detail.
NASA Astrophysics Data System (ADS)
Wang, Qian; Li, Bincheng
2015-12-01
In this paper, photocarrier radiometry (PCR) technique with multiple pump beam sizes is employed to determine simultaneously the electronic transport parameters (the carrier lifetime, the carrier diffusion coefficient, and the front surface recombination velocity) of silicon wafers. By employing the multiple pump beam sizes, the influence of instrumental frequency response on the multi-parameter estimation is totally eliminated. A nonlinear PCR model is developed to interpret the PCR signal. Theoretical simulations are performed to investigate the uncertainties of the estimated parameter values by investigating the dependence of a mean square variance on the corresponding transport parameters and compared to that obtained by the conventional frequency-scan method, in which only the frequency dependences of the PCR amplitude and phase are recorded at single pump beam size. Simulation results show that the proposed multiple-pump-beam-size method can improve significantly the accuracy of the determination of the electronic transport parameters. Comparative experiments with a p-type silicon wafer with resistivity 0.1-0.2 Î©.cm are performed, and the electronic transport properties are determined simultaneously. The estimated uncertainties of the carrier lifetime, diffusion coefficient, and front surface recombination velocity are approximately Â±10.7%, Â±8.6%, and Â±35.4% by the proposed multiple-pump-beam-size method, which is much improved than Â±15.9%, Â±29.1%, and >Â±50% by the conventional frequency-scan method. The transport parameters determined by the proposed multiple-pump-beam-size PCR method are in good agreement with that obtained by a steady-state PCR imaging technique.
Moolla, S.; Bharuthram, R.; Singh, S. V.; Lakhina, G. S.; Reddy, R. V.
2010-02-15
Observations from the Fast Auroral SnapshoT (FAST) satellite indicate that the parallel and perpendicular (to the Earth's magnetic field) electric field structures exhibit a spiky appearance. In this study, a magnetized plasma system consisting of protons, electrons, and a cold oxygen ion beam is considered. Both background electrons and protons are treated as hot species with Boltzmann density distributions. The dynamics of the oxygen ion beam is governed by the fluid equations. Effect of charge separation is studied on nonlinear fluctuations arising from a coupling of ion cyclotron and ion-acoustic waves. A scan of parameter space reveals a range of solutions for the parallel electric field from sinusoidal to sawtooth to highly spiky waveforms. The inclusion of charge separation effects tends to in most cases increase the frequency of oscillation of the nonlinear structures. In the case of a weakly magnetized plasma, the amplitude of the oscillations are found to be constant while they are modulated for a strongly magnetized plasma. The findings are compared with satellite observations.
Bindoni, Luca . E-mail: lucabindoni@inwind.it
2005-06-15
A technique for geometric and dosimetric pretreatment verification of step-and-shoot intensity modulated radiotherapy treatments (IMRT) using a beam imaging system (BIS) made up of a charge-coupled device (CCD) digital camera optically coupled with a metal-plate/phosphor screen is described. Some physical properties of BIS were investigated in order to demonstrate its capability to perform measurements with a high spatial resolution and a high sampling rate. High-speed imaging, with a minimum charge integration time on the CCD of 120 ms, can be performed. The study of the signal-to-noise ratio as a function of sampling time is presented. In-plane and cross-line pixel size was measured to be 0.368{+-}0.004 mm/pixel, which agrees within 0.5% of the manufacturer value of 0.366 mm. Spatial linearity results are very good and there are no detectable image distortions on whole 30x30 cm{sup 2} detector area. A software routine was written to automatically extract positions of the collimator leaves from the images of the field shaped by the multileaf collimator (MLC) and also to compare them with the coordinates from the treatment planning system (TPS), thus directly testing both the MLC positioning and the treatment parameters transfer from TPS to the linear accelerator in a fast and precise way. The dosimetric capabilities (characteristics) of the imaging device for photon beams with energies of 6 and 15 MV were studied. Additional plexiglass buildup layers, depending on x-ray energy, were needed to reach maximum efficiency. The energy dependence of the BIS response versus dose and dose rate was found to be linear over a wide range. Relative output factors of BIS as a function of field size, compared with values measured with an ionization chamber, were in good accord for smaller field sizes {<=}10x10 cm{sup 2} but showed differences up to 4% for all the energies at the respective buildup depth for bigger fields. Square field profiles at water-equivalent buildup depths, extracted from BIS maps, are compared with the corresponding scans performed with a diode detector. Disagreement is always shown in the regions outside the field penumbra (tails) and near the field edges only for field sizes {>=}15x15 cm{sup 2} due to the metal/phosphor screen higher sensitivity to low energy scattering x-rays. A straightforward correction method for the 'tails effect' was developed and then generalized to MLC-shaped fields. In order to demonstrate the validity of this procedure, the comparison between the two-dimensional (2D) dose distributions of a triangle MLC-shaped field and of two simple IMRT fields created by the superimposition of five segments resulting from BIS images and the dose distribution of the same fields achieved by film, was measured and reported. The gamma index method, introduced by Low et al. (1998), was used for 2D dose distributions analysis. Agreements are good for both 6 and 15 MV energies. The described technique provides a lower time-expensive mean to verify geometric and dosimetric accuracy of the treatment delivered in IMRT with the use of a high resolution beam imaging system and homemade software tools.
Nonlinear Plasma Waves Excitation by Intense Ion Beams in Background Plasma
Igor D. Kaganovich; Edward A. Startsev; Ronald C. Davidson
2004-04-15
Plasma neutralization of an intense ion pulse is of interest for many applications, including plasma lenses, heavy ion fusion, cosmic ray propagation, etc. An analytical electron fluid model has been developed to describe the plasma response to a propagating ion beam. The model predicts very good charge neutralization during quasi-steady-state propagation, provided the beam pulse duration {tau}{sub b} is much longer than the electron plasma period 2{pi}/{omega}{sub p}, where {omega}{sub p} = (4{pi}e{sup 2}n{sub p}/m){sup 1/2} is the electron plasma frequency and n{sub p} is the background plasma density. In the opposite limit, the beam pulse excites large-amplitude plasma waves. If the beam density is larger than the background plasma density, the plasma waves break. Theoretical predictions are compared with the results of calculations utilizing a particle-in-cell (PIC) code. The cold electron fluid results agree well with the PIC simulations for ion beam propagation through a background plasma. The reduced fluid description derived in this paper can provide an important benchmark for numerical codes and yield scaling relations for different beam and plasma parameters. The visualization of numerical simulation data shows complex collective phenomena during beam entry and exit from the plasma.
NASA Astrophysics Data System (ADS)
Diamessis, P. J.; Wunsch, S.; Delwiche, I.; Richter, M. P.
2014-06-01
The interaction of an internal wave beam (IWB) with an idealized oceanic pycnocline is examined using two-dimensional fully nonlinear direct numerical simulations based on a spectral multidomain penalty method in the vertical direction. The phenomenon of focus is the nonlinear generation of harmonics. A total of 24 simulations have been performed, varying the normalized pycnocline thickness and the ratio of peak pycnocline Brunt-VÃ¤isÃ¤lÃ¤ frequency to that of the stratified lower layer. Harmonics at the point of IWB entry into the pycnocline increase in amplitude and number with a measure of the maximum gradient of the Brunt-VÃ¤isÃ¤lÃ¤ frequency, suggesting refraction as an important factor in harmonic generation. Among the simulations performed, two distinct limits of pycnocline thickness are identified. For thin pynoclines, whose thickness is 10% of the incident IWB's horizontal wavelength, harmonics trapped within the pycnocline have maximum amplitude when their frequency and wavenumber match those of the natural pycnocline interfacial wave mode. Results in this case are compared with weakly nonlinear theory for harmonic generation by plane wave refraction. For thicker pycnoclines, whose thickness is equal the incident IWB's horizontal wavelength, IWB refraction results in harmonic generation at multiple locations in addition to pycnocline entry, giving rise to complex flow structure inside the pycnocline.
Focal-Plane Imaging of Crossed Beams in Nonlinear Optics Experiments
NASA Technical Reports Server (NTRS)
Bivolaru, Daniel; Herring, G. C.
2007-01-01
An application of focal-plane imaging that can be used as a real time diagnostic of beam crossing in various optical techniques is reported. We discuss two specific versions and demonstrate the capability of maximizing system performance with an example in a combined dual-pump coherent anti-Stokes Raman scattering interferometric Rayleigh scattering experiment (CARS-IRS). We find that this imaging diagnostic significantly reduces beam alignment time and loss of CARS-IRS signals due to inadvertent misalignments.
NASA Technical Reports Server (NTRS)
Kvaternik, R. G.; Kaza, K. R. V.
1976-01-01
The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.
Fourier continuation methods for high-fidelity simulation of nonlinear acoustic beams.
Albin, Nathan; Bruno, Oscar P; Cheung, Theresa Y; Cleveland, Robin O
2012-10-01
On the basis of recently developed Fourier continuation (FC) methods and associated efficient parallelization techniques, this text introduces numerical algorithms that, due to very low dispersive errors, can accurately and efficiently solve the types of nonlinear partial differential equation (PDE) models of nonlinear acoustics in hundred-wavelength domains as arise in the simulation of focused medical ultrasound. As demonstrated in the examples presented in this text, the FC approach can be used to produce solutions to nonlinear acoustics PDEs models with significantly reduced discretization requirements over those associated with finite-difference, finite-element and finite-volume methods, especially in cases involving waves that travel distances that are orders of magnitude longer than their respective wavelengths. In these examples, the FC methodology is shown to lead to improvements in computing times by factors of hundreds and even thousands over those required by the standard approaches. A variety of one-and two-dimensional examples presented in this text demonstrate the power and capabilities of the proposed methodology, including an example containing a number of scattering centers and nonlinear multiple-scattering events. PMID:23039433
Niethammer, Marc; Hart, Gabriel L.; Pace, Danielle F.; Vespa, Paul M.; Irimia, Andrei; Van Horn, John D.; Aylward, Stephen R.
2013-01-01
Standard image registration methods do not account for changes in image appearance. Hence, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image appearance to construct a spatio-temporal trajectory smoothly transforming a source to a target image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a geometric metamorphosis formulation, which explains changes in image appearance by a global deformation, a deformation of a geometric model, and an image composition model. This work is motivated by the clinical challenge of predicting the long-term effects of traumatic brain injuries based on time-series images. This work is also applicable to the quantification of tumor progression (e.g., estimating its infiltrating and displacing components) and predicting chronic blood perfusion changes after stroke. We demonstrate the utility of the method using simulated data as well as scans from a clinical traumatic brain injury patient. PMID:21995083
Niethammer, Marc; Hart, Gabriel L; Pace, Danielle F; Vespa, Paul M; Irimia, Andrei; Van Horn, John D; Aylward, Stephen R
2011-01-01
Standard image registration methods do not account for changes in image appearance. Hence, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image appearance to construct a spatio-temporal trajectory smoothly transforming a source to a target image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a geometric metamorphosis formulation, which explains changes in image appearance by a global deformation, a deformation of a geometric model, and an image composition model. This work is motivated by the clinical challenge of predicting the long-term effects of traumatic brain injuries based on time-series images. This work is also applicable to the quantification of tumor progression (e.g., estimating its infiltrating and displacing components) and predicting chronic blood perfusion changes after stroke. We demonstrate the utility of the method using simulated data as well as scans from a clinical traumatic brain injury patient. PMID:21995083
NASA Astrophysics Data System (ADS)
Shibata, A.; Ohishi, S.; Yabuno, H.
2015-08-01
In the present paper, we propose a simple method for controlling the nonlinear characteristics of the frequency response curve in a parametrically excited hinged-hinged beam with a movable end (changing from softening to hardening and decreasing the overhang in the frequency response curve). The proposed method is achieved simply by the attachment of a linear spring in the axial direction to the movable end and does not require any power. By applying the extended Hamilton's principle, the equation of motion of the beam in the lateral direction is derived, and the change in the nonlinear characteristics of the parametric resonance is theoretically analyzed while tuning the linear stiffness of the attached linear spring. The linear spring affects only the nonlinearity in the lateral vibration, but not the linear natural frequency of the beam. That is, the linear unstable region in the parametric resonance is not shifted, but only the frequency response curve can be changed. This is advantageous in applications to resonators, such as mass sensors and mechanical filters. It is shown experimentally that the nonlinear characteristics of the frequency response curve can be changed by tuning the stiffness of a linear spring. Furthermore, the experimental results reveal that quadratic damping plays a dominant role in determining the nonlinear characteristics of the steady-state amplitude for the case in which the nonlinearity in the system is modified to be relatively small.
Makarov, V A; Petnikova, V M; Shuvalov, V V
2013-10-31
We have analysed self-similar solutions to the propagation problem of a slit beam with a plane wavefront in a linear medium and in a photorefractive crystal with diffusion nonlinearity. It is shown that in the latter case, despite the presence of the nonlinear term in the wave equation, the linear superposition principle holds true for the solutions of this class due to saturation. At the same time, the mirror symmetry violation of the wave equation for the transverse coordinate in the nonlinear case and the requirement to the spatial localisation modify one of the localised partial solutions (Airy beam) to the corresponding linear problem and prohibit the existence of other solutions of this class. (laser beams)
Progress on Optimization of the Nonlinear Beam Dynamics in the MEIC Collider Rings
Morozov, Vasiliy S.; Derbenev, Yaroslav S.; Lin, Fanglei; Pilat, Fulvia; Zhang, Yuhong; Cai, Y.; Nosochkov, Y. M.; Sullivan, Michael; Wang, M.-H.; Wienands, Uli
2015-09-01
One of the key design features of the Medium-energy Electron-Ion Collider (MEIC) proposed by Jefferson Lab is a small beta function at the interaction point (IP) allowing one to achieve a high luminosity of up to 1034 cm-2s-1. The required strong beam focusing unavoidably causes large chromatic effects such as chromatic tune spread and beam smear at the IP, which need to be compensated. This paper reports recent progress in our development of a chromaticity correction scheme for the ion ring including optimization of dynamic aperture and momentum acceptance.
Progress on optimization of the nonlinear beam dynamics in the MEIC collider rings
None, None
2015-07-13
One of the key design features of the Medium-energy Electron-Ion Collider (MEIC) proposed by Jefferson Lab is a small beta function at the interaction point (IP) allowing one to achieve a high luminosity of up to 10^{34} cm^{-2}s^{-1}. The required strong beam focusing unavoidably causes large chromatic effects such as chromatic tune spread and beam smear at the IP, which need to be compensated. This paper reports recent progress in our development of a chromaticity correction scheme for the ion ring including optimization of dynamic aperture and momentum acceptance.
Ali Shan, S.; National Centre For Physics , Shahdra Valley Road, 44000 Islamabad; Pakistan Institute of Engineering and Applied Sciences , Islamabad ; El-Tantawy, S. A.; Moslem, W. M.
2013-08-15
Arbitrary amplitude ion-acoustic waves in an unmagnetized plasma consisting of cold positive ions, superthermal electrons, and positrons beam are reported. The basic set of fluid equations is reduced to an energy-balance like equation. The latter is numerically analyzed to examine the existence regions for solitary and shock waves. It is found that only solitary waves can propagate, however, the model cannot support shocks. The effects of superthermality and beam parameters (via, positrons concentration and streaming velocity) on the existence region, as well as solitary wave profile have been discussed.
Piezomagnetoelastic broadband energy harvester: Nonlinear modeling and characterization
NASA Astrophysics Data System (ADS)
Aravind Kumar, K.; Ali, S. F.; Arockiarajan, A.
2015-11-01
Piezomagnetoelastic energy harvesters are one among the widely explored configurations to improve the broadband characteristics of vibration energy harvesters. Such nonlinear harvesters follow a Moon beam model with two magnets at the base and one at the tip of the beam. The present article develops a geometric nonlinear mathematical model for the broadband piezomagnetoelastic energy harvester. The electromechanical coupling and the nonlinear magnetic potential equations are developed from the dimensional system parameters to describe the nonlinear dynamics exhibited by the system. The developed model is capable of characterizing the monostable, bistable and tristable operating regimes of the piezomagnetoelastic energy harvester, which are not explicit in the Duffing representation of the system. Bifurcations and attractor motions are analyzed as nonlinear functions of the distance between base magnets and the field strength of the tip magnet. The model is further used to characterize the potential wells and stable states, with due focus on the performance of the system in broadband energy harvesting.
Nonlinear Steady-State Vibration Analysis of a Beam with Breathing Cracks
NASA Astrophysics Data System (ADS)
Kamiya, Keisuke; Yoshinaga, Terumitsu
This paper presents a method for analysis of steady-state vibration of a beam with breathing cracks, which open and close during vibration. There are several papers treating problems of vibration analysis of a beam with breathing cracks. However, due to their treatments of the condition which determines the switch between the open and closed states of the crack, it is difficult for one to obtain steady-state vibration efficiently by methods such as the incremental harmonic balance method. Since opening and closing of a breathing crack depends on the sign of the bending moment, or the curvature, of the beam, the key point to this problem is explicit treatment of the bending moment. The mixed variational principle allows one to use deflection as well as bending moment as primary variables in the governing equation. In this paper a governing equation of a beam with breathing cracks is derived by a finite element procedure based on the mixed variational principle. Then, the derived governing equations are solved by combining the iteration method and the harmonic balance method. Finally, examples of analysis by the presented method are given.
Kheifets, S.
1983-01-01
A perturbation method which allows one to find the distribution function and the beam size for a broad class of storage ring nonlinear problems is described in Part I of this work. In present note I apply this method to a particular problem. Namely, I want to evaluate an enhancement of the vertical beam size of a bunch due to the presence of the ring of nonlinear magnetic fields. The main part of the work deals with sextupole magnets. Formula for the beam size in the presence of octupole fields are also developed to the first order in the octupole strength, although octupole magnets are not widely used in present storage ring designs. This calculation is done mainly because the octupole field has the same symmetry as the beam-beam force for the head-on collision. This will give us the opportunity to compare the conduct of the bunch due to this two types of nonlinear kicks. The general terms of the applicability of the Green's function method is discussed in the first part of this work.
NASA Technical Reports Server (NTRS)
Hodges, D. H.; Ormiston, R. A.
1973-01-01
The nonlinear partial differential equations for the flapping and lead-lag degrees of freedom of a torisonally rigid, rotating cantilevered beam are derived. These equations are linearized about an equilibrium condition to study the flap-lag stability characteristics of hingeless helicopter rotor blades with zero twist and uniform mass and stiffness in the hovering flight condition. The results indicate that these configurations are stable because the effect of elastic coupling more than compensates for the destabilizing flap-lag Coriolis and aerodynamic coupling. The effect of higher bending modes on the lead-lag damping was found to be small and the common, centrally hinged, spring restrained, rigid blade approximation for elastic rotor blades was shown to be resonably satisfactory for determining flap-lag stability. The effect of pre-cone was generally stabilizing and the effects of rotary inertia were negligible.
Optimization of absorption placement using geometrical acoustic models and least squares.
Saksela, Kai; Botts, Jonathan; Savioja, Lauri
2015-04-01
Given a geometrical model of a space, the problem of optimally placing absorption in a space to match a desired impulse response is in general nonlinear. This has led some to use costly optimization procedures. This letter reformulates absorption assignment as a constrained linear least-squares problem. Regularized solutions result in direct distribution of absorption in the room and can accommodate multiple frequency bands, multiple sources and receivers, and constraints on geometrical placement of absorption. The method is demonstrated using a beam tracing model, resulting in the optimal absorption placement on the walls and ceiling of a classroom. PMID:25920877
NASA Astrophysics Data System (ADS)
Wei, Jingsong; Yan, Hui
2014-08-01
Self-focusing is a well-researched phenomenon. Nanoscale spots can be achieved through self-focusing, which is an alternative method for achieving high-density data storage, high-resolution light imaging, and maskless nanolithography. Several research groups have observed that self-focusing spots can be reduced to nanoscale levels via incident laser power manipulation. Self-focusing spots can be analyzed by solving the nonlinear Schrödinger equation and the finite difference time domain method. However, both procedures are complex and time-consuming. In the present work, a multi-layer thin-lens self-focusing model that considers diffraction effects and changes of refractive index along the radial and film thickness directions is proposed to analyze the self-focusing behavior and traveling process of light beams intuitively. The self-focusing behaviors of As2S3 are simulated, and results show that a nanoscale self-focusing spot with a radius of about 0.12 ?m can be formed at the bottom of nonlinear sample when the incident laser power exceeds 4.25 mW. Our findings are basically consistent with experimental reports and provide a good method for analyzing and understanding the self-focusing process. An appropriate application schematic design is also provided.
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines
NASA Astrophysics Data System (ADS)
Franchetti, G.; Schmidt, F.
2015-06-01
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom).
Wei, Jingsong; Yan, Hui
2014-08-14
Self-focusing is a well-researched phenomenon. Nanoscale spots can be achieved through self-focusing, which is an alternative method for achieving high-density data storage, high-resolution light imaging, and maskless nanolithography. Several research groups have observed that self-focusing spots can be reduced to nanoscale levels via incident laser power manipulation. Self-focusing spots can be analyzed by solving the nonlinear Schrödinger equation and the finite difference time domain method. However, both procedures are complex and time-consuming. In the present work, a multi-layer thin-lens self-focusing model that considers diffraction effects and changes of refractive index along the radial and film thickness directions is proposed to analyze the self-focusing behavior and traveling process of light beams intuitively. The self-focusing behaviors of As{sub 2}S{sub 3} are simulated, and results show that a nanoscale self-focusing spot with a radius of about 0.12??m can be formed at the bottom of nonlinear sample when the incident laser power exceeds 4.25?mW. Our findings are basically consistent with experimental reports and provide a good method for analyzing and understanding the self-focusing process. An appropriate application schematic design is also provided.
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines.
Franchetti, G; Schmidt, F
2015-06-12
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of PoincarÃ© at the end of the nineteenth century: Les MÃ©thodes Nouvelles de la MÃ©canique CÃ©leste, Vols.Â 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "PoincarÃ© surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom). PMID:26196806
Nonlinear optical properties of bulk cuprous oxide using single beam Z-scan at 790â€‰nm
Serna, J.; Rueda, E.; GarcÃa, H.
2014-11-10
The two-photon absorption (TPA) coefficient Î² and the nonlinear index of refraction n{sub 2} for bulk cuprous oxide (Cu{sub 2}O) direct gap semiconductor single crystal have been measured by using a balance-detection Z-scan single beam technique, with an excellent signal to noise ratio. Both coefficients were measured at 790â€‰nm using a 65 fs laser pulse at a repetition rate of 90.9â€‰MHz, generated by a Ti:Sapphire laser oscillator. The experimental values for Î² were explained by using a model that includes allowed-allowed, forbidden-allowed, and forbidden-forbidden transitions. It was found that the forbidden-forbidden transition is the dominant mechanism, which is consistent with the band structure of Cu{sub 2}O. The low value for Î² found in bulk, as compared with respect to thin film, is explained in terms of the structural change in thin films that result in opposite parities of the conduction and valence band. The n{sub 2} is also theoretically calculated by using the TPA dispersion curve and the Kramers-Kronig relations for nonlinear optics.
Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system
NASA Technical Reports Server (NTRS)
Whelan, D. A.; Stenzel, R. L.
1985-01-01
It is shown that the unstable electron-plasma waves of a beam-plasma system can generate electromagnetic radiation in a uniform plasma. The generation mechanism is a scattering of the unstable electron plasma waves off ion-acoustic waves, producing electromagnetic waves whose frequency is near the local plasma frequency. The wave vector and frequency matching conditions of the three-wave mode coupling are experimentally verified. The electromagnetic radiation is observed to be polarized with the electric field parallel to the beam direction, and its source region is shown to be localized to the unstable plasma wave region. The frequency spectrum shows negligible intensity near the second harmonic of the plasma frequency. These results suggest that the observed electromagnetic radiation of type III solar bursts may be generated near the local plasma frequency and observed downstream where the wave frequency is near the harmonic of the plasma frequency.
Technique for Reducing Laser Beam Divergence of Intra-Cavity Nonlinear Conversion
NASA Astrophysics Data System (ADS)
Hays, Alan D.
During the past few years the Monoblock laser has become the laser-of-choice for laser range-finders. It's eye-safe 1570 nm emission, high pulse energy, simple construction, and high efficiency, when pumped by a laser-diode stack, provide advantages that are not available with other laser types. Although the relative divergence of the Monoblock output beam is large, it can be reduced to the required <1 mR using a telescope with a large magnification. This solution, however, is not acceptable for applications where the laser and telescope size must be kept to a minimum. A simple and compact technique for achieving significant reduction in the Monoblock beam divergence using a partial reflector that is placed a short distance from the optical parametric oscillator (OPO) has been developed. Using an ultra-compact 38 mm Monoblock with a 10 mm long KTP OPO, we achieved a beam divergence of <4 mR, corresponding to a >2.5 X reduction from the unmodified laser. Modeling and experimental results are presented detailing the theory and performance for this novel technique.
Esfandyari-Kalejahi, A.; Kourakis, I.; Shukla, P. K.
2008-02-15
The nonlinear propagation of finite amplitude ion acoustic solitary waves in a plasma consisting of adiabatic warm ions, nonisothermal electrons, and a weakly relativistic electron beam is studied via a two-fluid model. A multiple scales technique is employed to investigate the nonlinear regime. The existence of the electron beam gives rise to four linear ion acoustic modes, which propagate at different phase speeds. The numerical analysis shows that the propagation speed of two of these modes may become complex-valued (i.e., waves cannot occur) under conditions which depend on values of the beam-to-background-electron density ratio {alpha}, the ion-to-free-electron temperature ratio {sigma}, and the electron beam velocity v{sub 0}; the remaining two modes remain real in all cases. The basic set of fluid equations are reduced to a Schamel-type equation and a linear inhomogeneous equation for the first and second-order potential perturbations, respectively. Stationary solutions of the coupled equations are derived using a renormalization method. Higher-order nonlinearity is thus shown to modify the solitary wave amplitude and may also deform its shape, even possibly transforming a simple pulse into a W-type curve for one of the modes. The dependence of the excitation amplitude and of the higher-order nonlinearity potential correction on the parameters {alpha}, {sigma}, and v{sub 0} is numerically investigated.
Selvaraj, J
2014-06-15
Purpose: To determine required PTV margins for ?1% loss in mean population TCP using systematic (?) and random (?) errors calculated from daily cone-beam CT (CBCT) images of head and neck patients. Methods: Daily CBCT images were acquired for 50 head and neck patients. The CBCT image sets acquired at each fraction were registered with planning CT to obtain positional errors for each patient for each fraction. Systematic and random errors were calculated from data collected for 50 patients as described in IPEM On Target report. CTV delineation uncertainty of 2mm is added quadratically to systematic error. Assuming a spherical target volume, the dose in each voxel of target volume is summed for each fraction in the treatment by shifting the dose grid to calculate mean population TCP inclusive of geometric uncertainties using a Monte Carlo method. These simulations were repeated for the set of ? and ? in each axis for different PTV margins and drop in TCP for each margin are obtained. In order to study the effect of dose-response curve on PTV margins, two different ?? of 0.048 Gy-1 and 0.218 Gy-1 representing steep and shallow dose-response curves are studied. ? were 2.5, 2.5, 2.1 mm and ? were 0.3, 0.3 0.2 mm respectively in x, y and z axis respectively. Results: PTV margins based on tumor radiobiological characteristics are 4.8, 4.8 and 4 mm in x, y and z axis assuming 25 treatment fractions for ?? 0.048 Gy-1 (steep) and 4.2,4.2 and 2.2 for ?? of 0.218 Gy-1 (shallow). While the TCP-based margins did not differ much in x and y axis, it is considerably smaller in z axis for shallow DRC. Conclusion: TCP based margins are substantially smaller than physical dose-based margin recipes. This study also demonstrates the importance of considering tumor radiobiological characteristics while deriving margins.
NASA Astrophysics Data System (ADS)
Tsysar, S. A.; Nikolaeva, A. V.; Svet, V. D.; Khokhlova, V. A.; Yuldashev, P. V.; Sapozhnikov, O. A.
2015-10-01
In the paper the use of receiving and radiating system, which allows to determine the parameters of bone by nonlinear pulse-echo technique and to image of brain structures through the skull bones, was proposed. Accuracy of the skull bone characterization is due to higher measured harmonic and is significantly better than in linear case. In the experimental part focused piezoelectric transducer with diameter 100 mm, focal distance 100 mm, the frequency of 1.092 MHz was used. It was shown that skull bone profiling can be performed with the use of 3rd harmonic since 1st harmonic can be used for visualization of the underlying objects. The use of wideband systems for both skull profiling and brain visualization is restricted by skull attenuation and resulting low effective sensitivity.
Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals
Assanto, Gaetano; Minzoni, Antonmaria A.; Smyth, Noel F.; Worthy, Annette L.
2010-11-15
The propagation of solitary waves in nematic liquid crystals in the presence of localized nonuniformities is studied. These nonuniformities can be caused by external electric fields, other light beams, or any other mechanism which results in a modified director orientation in a localized region of the liquid-crystal cell. The net effect is that the solitary wave undergoes refraction and trajectory bending. A general modulation theory for this refraction is developed, and particular cases of circular, elliptical, and rectangular perturbations are considered. The results are found to be in excellent agreement with numerical solutions.
NASA Astrophysics Data System (ADS)
Abrikosov, A. A.; Gozzi, E.; Mauro, D.
2005-05-01
Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional "supertime," we can dequantize the system in the sense of turning the Feynman path integral version of QM into the functional counterpart of the Koopman-von Neumann operatorial approach to CM. Somehow this procedure is the inverse of geometric quantization and we present it in three different polarizations: the Schrödinger, the momentum and the coherent states ones.
Abrikosov, A.A. . E-mail: persik@itep.ru; Gozzi, E. . E-mail: gozzi@ts.infn.it; Mauro, D. . E-mail: mauro@ts.infn.it
2005-05-01
Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional 'supertime,' we can dequantize the system in the sense of turning the Feynman path integral version of QM into the functional counterpart of the Koopman-von Neumann operatorial approach to CM. Somehow this procedure is the inverse of geometric quantization and we present it in three different polarizations: the Schroedinger, the momentum and the coherent states ones.
Nonlinear thermally induced distortions of a laser beam in a cryogenic disk amplifier
Vyatkin, A G; Khazanov, Efim A
2009-09-30
Taking into account the temperature dependences of the heat conductivity, the refractive index, and the thermal expansion coefficient, we calculated the temperature, elastic stresses, a thermally induced lens and depolarisation of a beam in a cryogenic disk amplifier (an Yb:YAG disk placed between a copper cylinder and a sapphire disk cooled by liquid nitrogen). When the active element (the thickness is 0.6 mm, the orientation is [001], the atomic concentration of Yb is 10%) is pumped by radiation from a diode laser (the beam diameter is 6 mm), the temperature does not exceed 140 K for the heat release power of 100 W. In this case, elastic stresses in the active element are six times lower than the maximum permissible value. The focal distance of the thermally induced lens is 5.5 m and the depolarisation rate is 0.038% per two passes through the active element. Although the heat conductivity of the active element rapidly decreases with temperature, the thermal load can be increased by 1.5-2 times when the dimensions of the active element remain constant. (active media)
Neurocontroller alternatives for "fuzzy" ball-and-beam systems with nonuniform nonlinear friction.
Eaton, P H; Prokhorov, D V; Wunsch, D I
2000-01-01
The ball-and-beam problem is a benchmark for testing control algorithms. In the World Congress on Neural Networks, 1994, Prof. L. Zadeh proposed a twist to the problem, which, he suggested, would require a fuzzy logic controller. This experiment uses a beam, partially covered with a sticky substance, increasing the difficulty of predicting the ball's motion. We complicated this problem even more by not using any information concerning the ball's velocity. Although it is common to use the first differences of the ball's consecutive positions as a measure of velocity and explicit input to the controller, we preferred to exploit recurrent neural networks, inputting only consecutive positions instead. We have used truncated backpropagation through time with the node-decoupled extended Kalman filter (NDEKF) algorithm to update the weights in the networks. Our best neurocontroller uses a form of approximate dynamic programming called an adaptive critic design. A hierarchy of such designs exists. Our system uses dual heuristic programming (DHP), an upper-level design. To our best knowledge, our results are the first use of DHP to control a physical system. It is also the first system we know of to respond to Zadeh's challenge. We do not claim this neural network control algorithm is the best approach to this problem, nor do we claim it is better than a fuzzy controller. It is instead a contribution to the scientific dialogue about the boundary between the two overlapping disciplines. PMID:18249772
Davidson, R.C.; Chen, C.
1997-08-01
A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B{sup sol}({rvec x}) is developed. The analysis is carried out for a thin beam with characteristic beam radius r{sub b} {much_lt} S, and directed axial momentum {gamma}{sub b}m{beta}{sub b}c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f{sub b}({rvec x},{rvec p},t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B{sub z}(z) = B{sub 0} = const. and for the case of a periodic solenoidal focusing field B{sub z}(z + S) = B{sub z}(z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field {rvec B}{sup sol}({rvec x}) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.
Direct generation of Bessel beams.
Muys, Peter; Vandamme, Eefje
2002-10-20
Two implementations are identified to create a Bessel beam directly, i.e. without the spatial filtering of an initially Gaussian beam. The first implementation is based on a resonator configuration whose lowest-loss transverse mode is a Bessel beam. Numerical simulation to corroborate the geometrical optical arguments is presented. The second implementation is based on the theorem that the angular-plane wave spectrum of a Bessel beam is composed of a cone of wave vectors. This cone is also generated through a phase-matching condition in a four-wave mixing process. This leads to the conclusion that anti-Stokes radiation generated in a nonlinear material will leave the substrate under the form of a Bessel beam. PMID:12396188
NASA Astrophysics Data System (ADS)
Belashov, Vasily
We study the formation, structure, stability and dynamics of the multidimensional soliton-like beam structures forming on the low-frequency branch of oscillation in the ionospheric and magnetospheric plasma for cases when beta=4pinT/B(2) <<1 and beta>1. In first case with the conditions omega
Davidson, R.C.; Lee, W.W.; Stoltz, P.
1997-08-01
This paper presents a detailed formulation and analysis of the rate equations for statistically-averaged quantities for an intense nonneutral beam propagating through a periodic solenoidal focusing field B{sup sol}(x). The analysis is based on the nonlinear Vlasov-Maxwell equations in the electrostatic approximation, assuming a thin beam with characteristic beam radius r{sub b} {much_lt} S. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum {l_angle}P{sub {theta}}{r_angle}, center-of-mass motion for {l_angle}X{r_angle} and {l_angle}Y{r_angle}, mean kinetic energy (1/2) {l_angle}X{sup {prime}2} + Y{sup {prime}2}{r_angle}, mean-square beam radius {l_angle}X{sup 2} + Y{sup 2}{r_angle}, and coupled rate equations for the unnormalized transverse emittance {epsilon}(s) and root-mean-square beam radius R{sub b}(s) = {l_angle}X{sup 2} + Y{sup 2}{r_angle}{sup 1/2}. Global energy balance is discussed, and the coupled rate equations for {epsilon}(s) and R{sub b}(s) are examined for the class of axisymmetric beam distributions F{sub b}.
NASA Technical Reports Server (NTRS)
Manning, Robert M.
2012-01-01
The method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for high-energy propagation through the Earth s atmosphere. These expressions are augmented with the integral invariants of the corresponding nonlinear parabolic equation that describes the electric field of high-energy laser beam to propagation to yield universal equations for the aforementioned quantities; the beam deflection is a linear function of the propagation distance whereas the beam broadening is a quadratic function of distance. The coefficients of these expressions are then derived from a thin screen approximation solution of the nonlinear parabolic equation to give corresponding analytical expressions for a target located outside the Earth s atmospheric layer. These equations, which are graphically presented for a host of propagation scenarios, as well as the thin screen model, are easily amenable to the phase expansions of the wave front for the specification and design of adaptive optics algorithms to correct for the inherent phase aberrations. This work finds application in, for example, the analysis of beamed energy propulsion for space-based vehicles.
NASA Astrophysics Data System (ADS)
Liu, Yongqi; Qi, Xinyuan; Lu, Yang; Cao, Zheng; Li, Shasha; Bai, Jintao
2016-01-01
We numerically and experimentally investigated the deflection of a laser beam in a photo-induced one dimensional (1D) photonic lattice (PL) in a pure LiNbO3 crystal accompanied with self-focusing and self-defocusing nonlinearities, respectively. The results show that the probe beam will be self-focused or self-defocused when the sample temperature is increased or decreased. Moreover, the light beam deflects to the direction of heat flux if there exists an additional temperature difference between the two lateral sides of the sample. The probe beam forms a deflected discrete circle soliton in the PL when the sample temperature is increased from 25 °C to 45°C and the additional temperature difference is ±5 °C. Our simulation results are in agreement with the experimental observation.
NASA Astrophysics Data System (ADS)
Zheng, Ziyi; Sun, Mingshan; Pavkovich, John; Star-Lack, Josh
2011-03-01
A challenge in using on-board cone beam computed tomography (CBCT) to image lung tumor motion prior to radiation therapy treatment is acquiring and reconstructing high quality 4D images in a sufficiently short time for practical use. For the 1 minute rotation times typical of Linacs, severe view aliasing artifacts, including streaks, are created if a conventional phase-correlated FDK reconstruction is performed. The McKinnon-Bates (MKB) algorithm provides an efficient means of reducing streaks from static tissue but can suffer from low SNR and other artifacts due to data truncation and noise. We have added truncation correction and bilateral nonlinear filtering to the MKB algorithm to reduce streaking and improve image quality. The modified MKB algorithm was implemented on a graphical processing unit (GPU) to maximize efficiency. Results show that a nearly 4x improvement in SNR is obtained compared to the conventional FDK phase-correlated reconstruction and that high quality 4D images with 0.4 second temporal resolution and 1 mm3 isotropic spatial resolution can be reconstructed in less than 20 seconds after data acquisition completes.
Structural optimization for nonlinear dynamic response.
Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S
2015-09-28
Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour. PMID:26303922
Microstructure-dependent couple stress theories of functionally graded beams
NASA Astrophysics Data System (ADS)
Reddy, J. N.
2011-11-01
A microstructure-dependent nonlinear Euler-Bernoulli and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material are developed using the principle of virtual displacements. The formulation is based on a modified couple stress theory, power-law variation of the material, and the von Kármán geometric nonlinearity. The model contains a material length scale parameter that can capture the size effect in a functionally graded material, unlike the classical Euler-Bernoulli and Timoshenko beam theories. The influence of the parameter on static bending, vibration and buckling is investigated. The theoretical developments presented herein also serve to develop finite element models and determine the effect of the geometric nonlinearity and microstructure-dependent constitutive relations on post-buckling response.
ValeÅ¡, Jan
2015-03-10
The paper deals with statistical analysis of the resistance of simply supported I-beams subjected to bending. The resistance was solved by applying the geometrically nonlinear solution. The influence of lateral-beam buckling on resistance is studied. Initial geometrical imperfections originating from the first eigenmode of lateral-beam buckling and from the cross section rotation at the stability lost were ascribed to the beams. These imperfections consist of initial axial lateral buckling and rotation of cross sections along the beam axis length. The correlation between the amplitudes of these imperfections is considered to be the parameter of solutions within the interval from -1 to 1. The influence of this correlation on the change of mean values and standard deviations of random resistance of beams with nondimensional slenderness close to 1 is studied. The imperfections mentioned were considered, together with geometrical and material characteristics of cross section and material characteristics of steel, to be random quantities.
NASA Astrophysics Data System (ADS)
Ettehadi Abari, Mehdi; Sedaghat, Mahsa; Shokri, Babak
2015-10-01
The propagation characteristics of a Gaussian laser beam in collisional magnetized plasma are investigated by considering the ponderomotive and ohmic heating nonlinearities. Here, by taking into account the effect of the external magnetic field, the second order differential equation of the dimensionless beam width parameter is solved numerically. Furthermore, the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the Gaussian laser pulse is obtained, and its variation in terms of the dimensionless plasma length is analyzed at different initial normalized plasma and cyclotron frequencies. The results show that the dimensionless beam width parameter is strongly affected by the initial plasma frequency, magnetic strength, and laser pulse intensity. Furthermore, it is found that there exists a certain intensity value below which the laser pulse tends to self focus, while the beam diverges above of this value. In addition, the results confirm that, by increasing the plasma and cyclotron frequencies (plasma density and magnetic strength), the self-focusing effect can occur intensively.
Three-Dimensional Postbuckling Analysis of Curved Beams
NASA Technical Reports Server (NTRS)
Pai, P. Frank; Lee, Seung-Yoon
2002-01-01
Presented here is a method of solving highly flexible curved beam undergoing huge static or quasi-static deformations. A geometrically exact beam theory based on the use of Jaumann stresses and strains and exact coordinate transformation is presented in terms of 17 first-order ordinary differential equations, and a multiple shooting method is used to solve the corresponding nonlinear two-point boundary value problems. The geometrically exact beam theory accounts far large rotations, large displacements, initial curvatures, extensionality, and transverse shear strains. Four examples are used to demonstrate this method, including a rotating clamped-free beam under the influence of gravity and centrifugal forces, an L-frame subjected to an in-plane tip load, a circular arch subjected to a concentrated load, and a clamped-hinged helical spring subjected to an axial displacement. Results show that the combination of the multiple shooting method and the geometrically exact beam theory works very well. Moreover, the obtained numerically exact solutions can be used to verify the accuracy of nonlinear finite element codes for nonlinear analysis of complex structures.
Single-beam Z-scan measurement of the third-order optical nonlinearities of azo dyes.
Gayathri, C; Ramalingam, A
2007-11-01
Organic dyes are very attractive optical materials for photonics and biophotonic applications. To quantitatively characterize their third-order nonlinear coefficients we have performed the experiments on two different azo dyes using a diode-pumped Nd:YAG laser at 532 nm. The |chi(3)| is of the order of 10(-6) esu. The relative contributions from nonlinear absorption (NLA) and nonlinear refraction (NLR) are dependent on the chemical structure and linear absorption of the dyes. PMID:17324613
NASA Astrophysics Data System (ADS)
Al-Gorafi, M. A.; Ali, A. A. A.; Othman, I.; Jaafar, M. S.; Anwar, M. P.
2011-02-01
Externally Prestressed segmental beams are widely used in the construction of bridge structures today. These beams have many attractive advantages for rehabilitation and strengthening of existing structures as well. However, segmental beams experience significant effect under combined stresses at the joint interfaces between segments. This paper presents a finite element study on the effect of torsion on the structural behavior of both external prestressed monolithic and segmental concrete beams. Geometric and material nonlinearities were included in the study. The results show significant difference in the behavior of monolithic and segmental beams under torsion.
A case study of analysis methods for large deflections of a cantilever beam
NASA Technical Reports Server (NTRS)
Craig, L. D.
1994-01-01
A load case study of geometric nonlinear large deflections of a cantilever beam is presented. The bending strain must remain elastic. Closed form solution and finite element methods of analysis are illustrated and compared for three common load cases. A nondimensional nomogram for each case is presented in the summary.
Geometric Phase for Adiabatic Evolutions of General Quantum States
Wu, Biao; Liu, Jie; Niu, Qian; Singh, David J
2005-01-01
The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.
Influence of axial loads on the nonplanar vibrations of cantilever beams
NASA Astrophysics Data System (ADS)
Carvalho, Eulher C.; Gonçalves, Paulo B.; Del Prado, Zenón; Rega, Giuseppe
2012-11-01
The three-dimensional motions of cantilever beams have been extensively studied in the past. This structural element can be found in several applications, including MEMS and NEMS. In many applications the beam is subjected to axial loads which can play an important role in the dynamics of very slender beams. In this paper a cantilever inextensible beam subject to a concentrated axial load and a lateral harmonic excitation is investigated. Special attention is given to the effect of axial load on the frequency-amplitude relation, bifurcations and instabilities of the beam, a problem not tackled in the previous literature on this subject. To this aim, the nonlinear integro-differential equations describing the flexural-flexural-torsional couplings of the beam are used, together with the Galerkin method, to obtain a set of discretized equations of motion, which are in turn solved by numerical integration using the Runge-Kutta method. Both inertial and geometric nonlinearities are considered in the present analysis. Due to symmetries of the beam cross section, the beam exhibits a 1:1 internal resonance which has an important role on the nonlinear oscillations and bifurcation scenario. The results show that the axial load influences the stiffness of the beam changing its nonlinear behavior from hardening to softening. A detailed parametric analysis using several tools of nonlinear dynamics, unveils the complex dynamics of the beam in the parametric or external resonance regions. Bifurcations leading to multiple coexisting solutions are observed.
NASA Astrophysics Data System (ADS)
Djomo Mbong, T. L. M.; Siewe Siewe, M.; Tchawoua, C.
2015-05-01
This research work is based on the study of the dynamic of one-degree-of freedom nonlinear oscillator representing a built-in clamped-clamped prestressed beam model with a nonlinear damping. First of all, we model this moving structure where we regard the perturbations as a combination of both low-frequency force and high-frequency force. Then, we analyze the occurrence of vibrational resonance, where the response consists of a slow motion and a fast motion respectively with low and high frequencies. Through this, we obtain an approximate analytical expression of the response amplitude and we determine the values of the low frequency and the amplitude of the high-frequency force at which vibrational resonance occurs. The theoretical predictions are found to be in good agreement with numerical results. Moreover, for fixed parameters values of the system, as the nonlinear damping vary, we found appearance and the disappearance of resonance with or without cross-well motion. Secondly, we study the chaotic dynamic of the beam. In this case, critical values of perturbation parameters for the onset of the chaotic motion are specified using Melnikov's method. Hence, the global dynamical changes of the system have been examined by plotting phase portrait, bifurcation diagram and their corresponding Lyapunov exponent.
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.
NASA Astrophysics Data System (ADS)
Milanchian, K.; Tajalli, H.; Gilani, A. Ghanadzadeh; Zakerhamidi, M. S.
2009-11-01
The nonlinear optical properties of the two oxazine dyes, i.e. oxazine 720 (OX720) and oxazine 750 (OX750), in aqueous solution and in polyacrylamide hydrogel (PAA) matrix were studied by Z-scan technique using CW He-Ne laser at 632.8 nm. All the polymeric and aqueous samples showed a negative nonlinearity and large nonlinear refractive index of the order of 10 -8 cm 2/W. The concentration-dependent nonlinear refractive index was also investigated. In the case of PAA-dye systems, two types of transit (fast) and steady state (slow) nonlinear effects were observed. It is believed that these effects are due to the thermo-optical induced refractive index gradient and a concentration gradient induced by a temperature gradient present in a medium.
Geometrically nonlinear analysis of laminated elastic structures
NASA Technical Reports Server (NTRS)
Reddy, J. N.
1984-01-01
Laminated composite plates and shells that can be used to model automobile bodies, aircraft wings and fuselages, and pressure vessels among many other were analyzed. The finite element method, a numerical technique for engineering analysis of structures, is used to model the geometry and approximate the solution. Various alternative formulations for analyzing laminated plates and shells are developed and their finite element models are tested for accuracy and economy in computation. These include the shear deformation laminate theory and degenerated 3-D elasticity theory for laminates.
Geometrical expression of excess entropy production.
Sagawa, Takahiro; Hayakawa, Hisao
2011-11-01
We derive a geometrical expression of the excess entropy production for quasistatic transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct the thermodynamics of nonequilibrium steady states. PMID:22181372
Jafari Bahman, F.; Maraghechi, B.
2013-02-15
Efficiency enhancement in free-electron laser is studied by three-dimensional and nonlinear simulation using tapered helical wiggler magnetic field or tapered ion-channel density. In order to reduce the saturation length, prebunched electron beam is used. A set of nonlinear and coupled differential equations are derived that provides the self-consistent description of the evolution of both an ensemble of electrons and the electromagnetic radiation. These equations are solved numerically to show that the combined effect of tapering and prebunching results in significant enhancement of power and considerable reduction of the saturation length. To have a deeper insight into the problem, an analytical treatment is also presented that uses the small signal theory to derive a modified pendulum equation.
NASA Astrophysics Data System (ADS)
Grigoriev, K. S.; Makarov, V. A.; Perezhogin, I. A.
2016-01-01
For the first time we have obtained the analytical expressions describing the spatial distribution of the polarization of a second harmonic beam’s light field reflected from the surface of an isotropic gyrotropic medium in the case when a normally incident fundamental beam contains a polarization singularity of an arbitrary type. The contribution of bulk and surface responses of the nonlinear medium in the formation of the lines of circular polarization in the second harmonic beam were analyzed. The relation between topological characteristics and polarization states of the singularities in the incident and reflected beams was established.
Visualizing the Geometric Series.
ERIC Educational Resources Information Center
Bennett, Albert B., Jr.
1989-01-01
Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)
Nonlinear ordinary difference equations
NASA Technical Reports Server (NTRS)
Caughey, T. K.
1979-01-01
Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.
NASA Astrophysics Data System (ADS)
Maraghechi, B.; Jokar, M.; Bahman, F. Jafari; Naeimabadi, A.; Naeimabadi
2013-10-01
A nonlinear simulation of the E × B drifting electron laser (DEL) and the free-electron laser (FEL), in three dimensions, is presented for a prebunched electron beam to study efficiency enhancement. For the planar wiggler with flat pole faces, prebunching considerably shortens the saturation length, which favors the DEL compared to the FEL. Operation of the DEL with the planar wiggler with parabolic pole faces was not found to be possible due to the modulation of the E × B drift by the wiggler. However, simulation results of the FEL with this type of wiggler are reported.
Reliability-based design optimization for nonlinear energy harvesters
NASA Astrophysics Data System (ADS)
Seong, Sumin; Lee, Soobum; Hu, Chao
2015-03-01
The power output of a vibration energy harvesting device is highly sensitive to uncertainties in materials, manufacturing, and operating conditions. Although the use of a nonlinear spring (e.g., snap-through mechanism) in energy harvesting device has been reported to reduce the sensitivity of power output with respect to the excitation frequency, the nonlinear spring characteristic remains significantly sensitive and it causes unreliable power generation. In this paper, we present a reliability-based design optimization (RBDO) study of vibration energy harvesters. For a nonlinear harvester, a purely mechanical nonlinear spring design implemented in the middle of cantilever beam harvester is considered in the study. This design has the curved section in the center of beam that causes bi-stable configuration. When vibrating, the inertia of the tip mass activates the curved shell to cause snap-through buckling and make the nature of vibration nonlinear. In this paper, deterministic optimization (DO) is performed to obtain deterministic optimum of linear and nonlinear energy harvester configuration. As a result of the deterministic optimization, an optimum bi-stable vibration configuration of nonlinear harvester can be obtained for reliable power generation despite uncertainty on input vibration condition. For the linear harvester, RBDO is additionally performed to find the optimum design that satisfies a target reliability on power generation, while accounting for uncertainty in material properties and geometric parameters.
NASA Astrophysics Data System (ADS)
Almehmadi, F. S.; Chatterjee, M. R.
2014-04-01
In standard weak interaction theory, acousto-optic Bragg analysis typically assumes that the incident light and sound beams are uniform plane waves. Acousto-optic Bragg diffraction with nonuniform profiled input beams is numerically examined under open loop via a transfer function formalism. Unexpected deviations in the first-order diffracted beam from the standard theory are observed for high Q values. These deviations are significant because the corresponding closed-loop system is sensitive to input amplitudes and initial conditions, and the overall impact on the dynamical behavior has not been studied previously in standard analyses. To explore the effect of such nonuniform output profiles on the feedback system, the numerically generated scattered output is fed back to the acoustic driver, and the resulting nonlinear dynamics are manipulated to create novel monostable, bistable, multistable, and chaotic regimes. The effects of the nonuniform input on these regimes are examined using the techniques of Lyapunov exponents and bifurcation maps. The orbital behavior is characterized with quadratic maps, which are an intuitive method of predicting the parametric behavior of the system. The latter trajectory-based approach offers yet a third arm in the process of developing a fuller understanding of the profiled output beam under feedback. The results of this work indicate that the nonlinear dynamical thresholds of the hybrid cell are significantly different for the profiled propagation problem than for the uniform case. The mono and bistable regimes do not coincide with the well-known uniform plane wave results, and the chaotic thresholds, which are critical to understanding encryption applications, are altered noticeably.
NASA Astrophysics Data System (ADS)
Hramov, A. E.; Kurkin, S. A.; Koronovskii, A. A.; Filatova, A. E.
2012-11-01
The report is devoted to the results of the numerical study of the virtual cathode (VC) formation conditions in the relativistic electron beam (REB) under the influence of the self-magnetic and external axial magnetic fields. The azimuthal instability of the relativistic electron beam leading to the formation of the vortex electron structure in the system was found out. This instability is determined by the influence of the self-magnetic fields of the relativistic electron beam, and it leads to the decrease of the critical value of the electron beam current (current when the non-stationary virtual cathode is formed in the drift space). The typical dependencies of the critical current on the external uniform magnetic field value were discovered. The effect of the beam thickness on the virtual cathode formation conditions was also analyzed.
Hramov, A. E.; Koronovskii, A. A.; Kurkin, S. A.; Filatova, A. E.
2012-11-15
The report is devoted to the results of the numerical study of the virtual cathode (VC) formation conditions in the relativistic electron beam (REB) under the influence of the self-magnetic and external axial magnetic fields. The azimuthal instability of the relativistic electron beam leading to the formation of the vortex electron structure in the system was found out. This instability is determined by the influence of the self-magnetic fields of the relativistic electron beam, and it leads to the decrease of the critical value of the electron beam current (current when the non-stationary virtual cathode is formed in the drift space). The typical dependencies of the critical current on the external uniform magnetic field value were discovered. The effect of the beam thickness on the virtual cathode formation conditions was also analyzed.
NASA Astrophysics Data System (ADS)
LarrÃ©, Pierre-Ã‰lie; Carusotto, Iacopo
2016-03-01
We study the coherence properties of a laser beam after propagation along a one-dimensional lossless nonlinear optical waveguide. Within the paraxial, slowly-varying-envelope, and single-transverse-mode approximations, the quantum propagation of the light field in the nonlinear medium is mapped onto a quantum Gross-Pitaevskii-type evolution of a closed one-dimensional system of many interacting photons. Upon crossing the entrance and the back faces of the waveguide, the photon-photon interaction parameter undergoes two sudden jumps, resulting in a pair of quantum quenches of the system's Hamiltonian. In the weak-interaction regime, we use the modulus-phase Bogoliubov theory of dilute Bose gases to describe the quantum fluctuations of the fluid of light and predict that correlations typical of a prethermalized state emerge locally in their final form and propagate in a light-cone way at the Bogoliubov speed of sound in the photon fluid. This peculiar relaxation dynamics, visible in the light exiting the waveguide, results in a loss of long-lived coherence in the beam of light.
Experimental verification of a bridge-shaped, nonlinear vibration energy harvester
Gafforelli, Giacomo Corigliano, Alberto; Xu, Ruize; Kim, Sang-Gook
2014-11-17
This paper reports a comprehensive modeling and experimental characterization of a bridge shaped nonlinear energy harvester. A doubly clamped beam at large deflection requires stretching strain in addition to the bending strain to be geometrically compatible, which stiffens the beam as the beam deflects and transforms the dynamics to a nonlinear regime. The Duffing mode non-linear resonance widens the frequency bandwidth significantly at higher frequencies than the linear resonant frequency. The modeling includes a nonlinear measure of strain coupled with piezoelectric constitutive equations which end up in nonlinear coupling terms in the equations of motion. The main result supports that the power generation is bounded by the mechanical damping for both linear and nonlinear harvesters. Modeling also shows the power generation is over a wider bandwidth in the nonlinear case. A prototype is manufactured and tested to measure the power generation at different load resistances and acceleration amplitudes. The prototype shows a nonlinear behavior with well-matched experimental data to the modeling.
NASA Astrophysics Data System (ADS)
Wilcox, Jamianne C.; Lopez, Benjamin J.; Campas, Otger; Valentine, Megan T.
2015-08-01
Optical traps allow for the precise application and measurement of pico-Newton forces in a wide variety of situations, and are particularly well suited for biophysical measurements of motor proteins and cells. Nearly all experiments exploit the linear regime of the optical trap, where force and displacement are related by a simple spring constant that does not depend on the trapped object's position. This typically limits the useful force range to < 100 pN for high-NA objective lenses and reasonable laser powers. Several biological studies require larger forces, which are not accessible in the linear regime of the trap. The best means to extend the maximum force is to make use of the entire nonlinear range; however, current techniques for calibrating the full nonlinear regime are limited. Here we report a new method for calibrating the nonlinear trap region that uses the fluctuations in the position of a trapped object when it is displaced from the center of a single gradient optical trap by controlled flow. From the position fluctuations, we measure the local trap stiffness, in both the linear and non-linear regimes. This approach requires only knowledge of the system temperature, and is especially useful for measurements involving trapped objects of unknown size, or objects in a fluid of unknown viscosity.
Saberian, E.; Esfandyari-Kalejahi, A.; Rastkar-Ebrahimzadeh, A.; Afsari-Ghazi, M.
2013-03-15
The propagation of ion-acoustic (IA) solitons is studied in a plasma system, comprised of warm ions and superthermal (Kappa distributed) electrons in the presence of an electron-beam by using a hydrodynamic model. In the linear analysis, it is seen that increasing the superthermality lowers the phase speed of the IA waves. On the other hand, in a fully nonlinear investigation, the Mach number range and characteristics of IA solitons are analyzed, parametrically and numerically. It is found that the accessible region for the existence of IA solitons reduces with increasing the superthermality. However, IA solitons with both negative and positive polarities can coexist in the system. Additionally, solitary waves with both subsonic and supersonic speeds are predicted in the plasma, depending on the value of ion-temperature and the superthermality of electrons in the system. It is examined that there are upper critical values for beam parameters (i.e., density and velocity) after which, IA solitary waves could not propagate in the plasma. Furthermore, a typical interaction between IA waves and the electron-beam in the plasma is confirmed.
A geometric algebra reformulation of geometric optics
NASA Astrophysics Data System (ADS)
Sugon, Quirino M.; McNamara, Daniel J.
2004-01-01
We present a tutorial on the Clifford (geometric) algebra Cl3,0 and use it to reformulate the laws of geometric optics. This algebra is essentially a Pauli algebra, with the Pauli sigma matrices interpreted as unit rays or vectors. In this algebra, the exponentials of imaginary vectors act as vector rotation operators. This property lets us rewrite the laws of reflection and refraction of light in geometric optics in exponential form. The reformulated laws allow easy translation of symbols to words and to diagrams. They also are shown to be equivalent to standard vector formulations. These coordinate-free laws can be shown to simplify the analysis of geometric optics problems such as the tracing of meridional and skew rays in lenses and optical fibers.
Deforming geometric transitions
NASA Astrophysics Data System (ADS)
Rossi, Michele
2015-04-01
After a quick review of the wild structure of the complex moduli space of Calabi-Yau 3-folds and the role of geometric transitions in this context (the Calabi-Yau web) the concept of deformation equivalence for geometric transitions is introduced to understand the arrows of the Gross-Reid Calabi-Yau web as deformation-equivalence classes of geometric transitions. Then the focus will be on some results and suitable examples to understand under which conditions it is possible to get simple geometric transitions, which are almost the only well-understood geometric transitions both in mathematics and in physics.
Sarkisov, S.S.; Williams, E.K.; Curley, M.; Smith, C.C.; Ila, D.; Venkateswarlu, P.; Poker, D.B.; Hensley, D.K.
1997-11-01
Ion implantation has been shown to produce a high density of metal colloids in glasses and crystalline materials. The high-precipitate volume fraction and small size of metal nanoclusters formed leads to values for the third-order susceptibility much greater than those for metal doped solids. This has stimulated interest in use of ion implantation to make nonlinear optical materials. On the other side, LiNbO{sub 3} has proved to be a good material for optical waveguides produced by MeV ion implantation. Light confinement in these waveguides is produced by refractive index step difference between the implanted region and the bulk material. Implantation of LiNbO{sub 3} with MeV metal ions can therefore result into nonlinear optical waveguide structures with great potential in a variety of device applications. The authors describe linear and nonlinear optical properties of a waveguide structure in LiNbO{sub 3}-based composite material produced by silver ion implantation in connection with mechanisms of its formation.
Comparison of Nonlinear Random Response Using Equivalent Linearization and Numerical Simulation
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Muravyov, Alexander A.
2000-01-01
A recently developed finite-element-based equivalent linearization approach for the analysis of random vibrations of geometrically nonlinear multiple degree-of-freedom structures is validated. The validation is based on comparisons with results from a finite element based numerical simulation analysis using a numerical integration technique in physical coordinates. In particular, results for the case of a clamped-clamped beam are considered for an extensive load range to establish the limits of validity of the equivalent linearization approach.
Akimoto, Tetsuo . E-mail: takimoto@showa.gunma-u.ac.jp; Katoh, Hiroyuki; Kitamoto, Yoshizumi; Shirai, Katsuyuki; Shioya, Mariko; Nakano, Takashi
2006-04-01
Purpose: To evaluate the advantages of anatomy-based inverse optimization (IO) in planning high-dose-rate (HDR) brachytherapy. Methods and Materials: A total of 114 patients who received HDR brachytherapy (9 Gy in two fractions) combined with hypofractionated external beam radiotherapy (EBRT) were analyzed. The dose distributions of HDR brachytherapy were optimized using geometric optimization (GO) in 70 patients and by anatomy-based IO in the remaining 44 patients. The correlation between the dose-volume histogram parameters, including the urethral dose and the incidence of acute genitourinary (GU) toxicity, was evaluated. Results: The averaged values of the percentage of volume receiving 80-150% of the prescribed minimal peripheral dose (V{sub 8}-V{sub 15}) of the urethra generated by anatomy-based IO were significantly lower than the corresponding values generated by GO. Similarly, the averaged values of the minimal dose received by 5-50% of the target volume (D{sub 5}-D{sub 5}) obtained using anatomy-based IO were significantly lower than those obtained using GO. Regarding acute toxicity, Grade 2 or worse acute GU toxicity developed in 23% of all patients, but was significantly lower in patients for whom anatomy-based IO (16%) was used than in those for whom GO was used (37%), consistent with the reduced urethral dose (p <0.01). Conclusion: The results of this study suggest that anatomy-based IO is superior to GO for dose optimization in HDR brachytherapy for prostate cancer.
On geometric factors for neutral particle analyzers
Stagner, L.; Heidbrink, W. W.
2014-11-15
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, â€œAnalytical derivation of the geometric factor of a particle detector having circular or rectangular geometry,â€ J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, â€œGeometric factor and directional response of single and multi-element particle telescopes,â€ Nucl. Instrum. Methods 95(1), 5â€“11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
On geometric factors for neutral particle analyzers
NASA Astrophysics Data System (ADS)
Stagner, L.; Heidbrink, W. W.
2014-11-01
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
On geometric factors for neutral particle analyzers.
Stagner, L; Heidbrink, W W
2014-11-01
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories. PMID:25430216
Parallel processors and nonlinear structural dynamics algorithms and software
NASA Technical Reports Server (NTRS)
Belytschko, Ted
1989-01-01
A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.
NASA Technical Reports Server (NTRS)
1976-01-01
A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity.
Non-isothermal elastoviscoplastic analysis of planar curved beams
NASA Technical Reports Server (NTRS)
Simitses, G. J.; Carlson, R. L.; Riff, R.
1988-01-01
The development of a general mathematical model and solution methodologies, to examine the behavior of thin structural elements such as beams, rings, and arches, subjected to large nonisothermal elastoviscoplastic deformations is presented. Thus, geometric as well as material type nonlinearities of higher order are present in the analysis. For this purpose a complete true abinito rate theory of kinematics and kinetics for thin bodies, without any restriction on the magnitude of the transformation is presented. A previously formulated elasto-thermo-viscoplastic material constitutive law is employed in the analysis. The methodology is demonstrated through three different straight and curved beams problems.
Geometric Gyrokinetic Theory for Edge Plasma
Qin, H; Cohen, R H; Nevins, W M; Xu, X Q
2007-01-18
It turns out that gyrokinetic theory can be geometrically formulated as special cases of a geometrically generalized Vlasov-Maxwell system. It is proposed that the phase space of the spacetime is a 7-dimensional fiber bundle P over the 4-dimensional spacetime M, and that a Poincare-Cartan-Einstein 1-form {gamma} on the 7-dimensional phase space determines particles worldlines in the phase space. Through Liouville 6-form {Omega} and fiber integral, the 1-form {gamma} also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system. In its most general form, gyrokinetic theory is about a symmetry, called gyro-symmetry, for magnetized plasmas, and the 1-form {gamma} again uniquely defines the gyro-symmetry. The objective is to decouple the gyro-phase dynamics from the rest of particle dynamics by finding the gyro-symmetry in {gamma}. Compared with other methods of deriving the gyrokinetic equations, the advantage of the geometric approach is that it allows any approximation based on mathematical simplification or physical intuition to be made at the 1-form level, and yet the field theories still have the desirable exact conservation properties such as phase space volume conservation and energy-momentum conservation if the 1-form does not depend on the spacetime coordinate explicitly. A set of generalized gyrokinetic equations valid for the edge plasmas is then derived using this geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. The fact that we adopted the geometric method in the present study does not necessarily imply that the major results reported here can not be achieved using classical methods. What the geometric method offers is a systematic treatment and simplified calculations.
Geometric gyrokinetic theory for edge plasmas
Qin, H.; Cohen, R. H.; Nevins, W. M.; Xu, X. Q.
2007-05-15
It turns out that gyrokinetic theory can be geometrically formulated as a special case of a geometrically generalized Vlasov-Maxwell system. It is proposed that the phase space of the space-time is a seven-dimensional fiber bundle P over the four-dimensional space-time M, and that a Poincare-Cartan-Einstein 1-form {gamma} on the seven-dimensional phase space determines a particle's worldline in the phase space. Through Liouville 6-form {omega} and fiber integral, the 1-form {gamma} also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system. In its most general form, gyrokinetic theory is about a symmetry, called gyrosymmetry, for magnetized plasmas, and the 1-form {gamma} again uniquely defines the gyrosymmetry. The objective is to decouple the gyrophase dynamics from the rest of the particle dynamics by finding the gyrosymmetry in {gamma}. Compared to other methods of deriving the gyrokinetic equations, the advantage of the geometric approach is that it allows any approximation based on mathematical simplification or physical intuition to be made at the 1-form level, and yet the field theories still have the desirable exact conservation properties, such as phase space volume conservation and energy-momentum conservation if the 1-form does not depend on the space-time coordinate explicitly. A set of generalized gyrokinetic equations valid for the edge plasmas is then derived using this geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. The fact that we adopted the geometric method in the present study does not necessarily imply that the major results reported here cannot be achieved using classical methods. What the geometric method offers is a systematic treatment and simplified calculations.
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Kuchik, Igor E.
2015-05-01
We develop an explicit solution of the problem describing collinear four-waves mixing in medium with cubic nonlinear response. This solution is carried out for a set of Schrödinger equations using plane wave approximation under phase matching of interacting waves. This solution allows to provide full analysis of four-wave interaction modes in dependence of the problem parameters. We have shown, in particular, an existence of bistable mode for energy conversion from pump waves to signal wave under certain conditions. In general case, there are greater than 10 various modes of four-wave interaction. Knowledge about these modes is very important for spectroscopic experiment results understanding using four-waves mixing because its result depends on them in a strong way. Analytical solution and developed modes can explain complicated regime of four-wave interaction which may appear at high intensity of interacting waves.
Geometric effects in tomographic reconstruction
Barnes, F.L.; Azevedo, S.G.; Martz, H.E. Jr.; Roberson, G.P.; Schneberk, D.J.; Skeate, M.F.
1990-01-08
In x-ray and ion-beam computerized tomography, there are a number of reconstruction effects, manifested as artifacts, that can be attributed to the geometry of the experimental setup and of the object being scanned. In this work, we will examine four geometric effects that are common to first-and third-generation (parallel beam, 180 degree) computerized tomography (CT) scanners and suggest solutions for each problem. The geometric effects focused on in this paper are: X-pattern'' artifacts (believed to be caused by several errors), edge-generated ringing artifacts (due to improper choice of the reconstruction filter and cutoff frequency), circular-ring artifacts (caused by employing uncalibrated detectors), and tuning-fork artifacts (generated by an incorrectly specified center-of-rotation). Examples of four effects are presented. The X-pattern and edge-generated ringing artifacts are presented with actual experimental data introducing the artifact. given the source of the artifact, we present simulated data designed to replicate the artifact. Finally, we suggest ways to reduce or completely remove these artifacts. The circular-ring and tuning-fork artifacts are introduced with actual experimental data as well, while digital signal processing solutions are employed to remove the artifacts from the data. 15 refs., 12 figs.
Exploring New Geometric Worlds
ERIC Educational Resources Information Center
Nirode, Wayne
2015-01-01
When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes aâ€¦
Multidimensional nonlinear systems
Savel'ev, M.V.
1987-06-01
The problem of the construction and of the integrability of systems of nonlinear partial differential equations in a multidimensional space is discussed. A proposed algebraic-geometric construction is illustrated for the example of completely integrable equations of the Bourlet type and their generalizations, for which, in particular, Baecklund transformations are obtained.
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam
2005-01-01
An investigation of the effect of basis selection on geometric nonlinear response prediction using a reduced-order nonlinear modal simulation is presented. The accuracy is dictated by the selection of the basis used to determine the nonlinear modal stiffness. This study considers a suite of available bases including bending modes only, bending and membrane modes, coupled bending and companion modes, and uncoupled bending and companion modes. The nonlinear modal simulation presented is broadly applicable and is demonstrated for nonlinear quasi-static and random acoustic response of flat beam and plate structures with isotropic material properties. Reduced-order analysis predictions are compared with those made using a numerical simulation in physical degrees-of-freedom to quantify the error associated with the selected modal bases. Bending and membrane responses are separately presented to help differentiate the bases.
NASA Astrophysics Data System (ADS)
Leadenham, Stephen; Erturk, Alper
2014-04-01
Inherent nonlinearities of piezoelectric materials are inevitably pronounced in various engineering applications such as sensing, actuation, their combined applications for vibration control, and most recently, energy harvesting from dynamical systems. The existing literature focusing on the dynamics of electroelastic structures made of piezoelectric materials have explored such nonlinearities in a disconnected way for the separate problems of mechanical and electrical excitation such that nonlinear resonance trends have been assumed to be due to different additional terms in constitutive equations by different researchers. Similar manifestations of softening nonlinearities have been attributed to purely elastic nonlinear terms, coupling nonlinearities, hysteresis, or a combination of these effects, by various authors. However, a reliable nonlinear constitutive equation for a given piezoelectric material is expected to be rather unique and valid regardless of the application, e.g. energy harvesting, sensing, or actuation. A systematic approach focusing on the two-way coupling can result in a sound mathematical framework. To this end, the present work investigates the nonlinear dynamic behavior of a bimorph piezoelectric cantilever under low-to-high mechanical and electrical excitation levels in energy harvesting, sensing, and actuation. A physical model is proposed including both ferroelastic hysteresis, stiffness, and electromechanical coupling nonlinearities. A lumped parameter electroelastic model is developed by accounting for these nonlinearities to analyze the primary resonance of a cantilever using the method of harmonic balance. Strong agreement between the model and experimental investigation is found, providing solid evidence that the the dominant source of observed softening nonlinear effects in geometrically linear piezolectric cantilever beams is well represented by a quadratic term resulting from ferroelastic hysteresis. Electromechanical coupling and cubic softening nonlinearities are observed to become effective only near the physical limits of the brittle and stiff bimorph cantilever used in the experiments, revealing that the quadratic nonlinearity associated with hysteresis has the primary role in nonlinear nonconservative dynamic behavior.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Astrometry without Geometric Distortion
NASA Astrophysics Data System (ADS)
Peng, Qingyu; Wang, Na; Peng, Huanwen; Zhang, Qingfeng; Li, Zhan
2015-08-01
Geometric distortion often exists in an astronomical CCD image even though a long focal length telescope is used. Two algorithms are developed to solve the pattern of geometric distortion and are tested based on many dithering CCD images observed at Yunnan Observatory using the 1 m telescope and 2.4 m telescope. Our results have shown that the astrometry for some moving targets such as an asteroid (Apophis) or a planetary natural satellite (Phoebe) is improved significantly after removing the geometric distortion in each CCD image. The algorithms can be also extended to applying to other telescopes for the purpose of precise astrometry or the check of positional propriety of a telescope.
Geometrizing Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Falciano, F. T.; Novello, M.; Salim, J. M.
2010-12-01
We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of them in the non-relativistic limit.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
A Babylonian Geometrical Algebra.
ERIC Educational Resources Information Center
Bidwell, James K.
1986-01-01
A possible method of derivation of prescriptions for solving problems, found in Babylonian cuneiform texts, is presented. It is a kind of "geometric algebra" based mainly on one figure and the manipulation of or within various areas and segments. (MNS)
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2003-07-01
As leading experts in geometric algebra, Chris Doran and Anthony Lasenby have led many new developments in the field over the last ten years. This book provides an introduction to the subject, covering applications such as black hole physics and quantum computing. Suitable as a textbook for graduate courses on the physical applications of geometric algebra, the volume is also a valuable reference for researchers working in the fields of relativity and quantum theory.
Spatial and Time Dynamics of Non-Linear Vortices in Plasma Lens for High-Current Ion Beam Focusing
NASA Astrophysics Data System (ADS)
Goncharov, Alexei A.; Maslov, Vasyl I.; Onishchenko, Ivan N.; Tretyakov, Vitalij N.
2002-11-01
It is known from numerical simulation (see, for example, [1]) and from experiments (see, for example, [2]), that an electron density bunches as discrete vortices are long - living structures in vacuum. However, in laboratory experiments [2] it has been shown that the vortices are changed faster, when they are submersed in electrons, distributed around them. The charged plasma lens intended for a focussing of high-current ion beams, has the same crossed configuration of a radial electrical and longitudinal magnetic field [3], as only electron plasma. In this lens the vortical turbulence is excited [3]. The vortex - bunch and vortex - hole are rotated in the inverse directions in system of their rest. The instability development in initially homogeneous plasma causes that the vortices are excited by pairs. Namely, if the vortex - bunch of electrons is generated, near the vortex - hole of electrons is also generated. It is shown, that in nonuniform plasma the vortices behave is various in time. Namely, the vortex - bunch goes to area of larger electron density, and the vortex - hole goes to area of smaller electron density. The speed of the vortex - hole is less than speed of the vortex - bunch. It is shown, that the electron vortices, generated in the plasma lens, can result in to formation of spiral distribution of electron density. The physical mechanism of coalescence of electron vortices - bunches is proposed. 1.Driscoll C.F. et al. Plasma Phys. Contr. Fus. Res. 3 (1989) 507. 2.Kiwamoto Y. et al. Non-neutral plasma physics. Princeton. 1999. P. 99-105. 3.Goncharov A. et al. Plasma Phys. Rep. 20 (1994) 499.
Information Intrinsic Geometric Flows
NASA Astrophysics Data System (ADS)
Barbaresco, Frédéric
2006-11-01
Geometric Flow Theory is cross fertilized by diverse elements coming from Pure Mathematic and Mathematical Physic, but its foundation is mainly based on Riemannian Geometry, as explained by M. Berger in a recent panoramic view of this discipline, its extension to complex manifolds, the Erich Kähler's Geometry, vaunted for its unabated vitality by J.P. Bourguignon, and Minimal Surface Theory. This paper would like to initiate seminal studies for applying intrinsic geometric flows in the framework of information geometry theory. More specifically, after having introduced Information metric deduced for Complex Auto-Regressive (CAR) models from Fisher Matrix (Siegel Metric and Hyper-Abelian Metric from Entropic Kähler Potential), we study asymptotic behavior of reflection coefficients of CAR models driven by intrinsic Information geometric Kähler-Ricci and Calabi flows. These Information geometric flows can be used in different contexts to define distance between CAR models interpreted as geodesics of Entropy Manifold. We conclude with potential application of Intrinsic Geometric Flow on Gauss Map to transform Manifold of any dimension by mean of Generalized Weierstrass Formula introduced by Kenmotsu that can represent arbitrary surfaces with non-vanishing mean curvature in terms of the mean curvature function and the Gauss map. One of the advantages of the generalized formulae is that they allow to construct a new class of deformations of surfaces by use of Intrinsic Geometric Flow on Gauss Map. We conclude with the Heat equation interpretation in the framework of Information Geometry.
Transition from linear- to nonlinear-focusing regime in filamentation
Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin
2014-01-01
Laser filamentation in gases is often carried out in the laboratory with focusing optics to better stabilize the filament, whereas real-world applications of filaments frequently involve collimated or near-collimated beams. It is well documented that geometrical focusing can alter the properties of laser filaments and, consequently, a transition between a collimated and a strongly focused filament is expected. Nevertheless, this transition point has not been identified. Here, we propose an analytical method to determine the transition, and show that it corresponds to an actual shift in the balance of physical mechanisms governing filamentation. In high-NA conditions, filamentation is primarily governed by geometrical focusing and plasma effects, while the Kerr nonlinearity plays a more significant role as NA decreases. We find the transition between the two regimes to be relatively insensitive to the intrinsic laser parameters, and our analysis agrees well with a wide range of parameters found in published literature. PMID:25434678
Geometrical deployment for braided stent.
Bouillot, Pierre; Brina, Olivier; Ouared, Rafik; Yilmaz, Hasan; Farhat, Mohamed; Erceg, Gorislav; Lovblad, Karl-Olof; Vargas, Maria Isabel; Kulcsar, Zsolt; Pereira, Vitor Mendes
2016-05-01
The prediction of flow diverter stent (FDS) implantation for the treatment of intracranial aneurysms (IAs) is being increasingly required for hemodynamic simulations and procedural planning. In this paper, a deployment model was developed based on geometrical properties of braided stents. The proposed mathematical description is first applied on idealized toroidal vessels demonstrating the stent shortening in curved vessels. It is subsequently generalized to patient specific vasculature predicting the position of the filaments along with the length and local porosity of the stent. In parallel, in-vitro and in-vivo FDS deployments were measured by contrast-enhanced cone beam CT (CBCT) in idealized and patient-specific geometries. These measurements showed a very good qualitative and quantitative agreement with the virtual deployments and provided experimental validations of the underlying geometrical assumptions. In particular, they highlighted the importance of the stent radius assessment in the accuracy of the deployment prediction. Thanks to its low computational cost, the proposed model is potentially implementable in clinical practice providing critical information for patient safety and treatment outcome assessment. PMID:26891065
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics. PMID:25401574
BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint
Wang, Q.; Sprague, M.; Jonkman, J.; Johnson, N.
2015-01-01
BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented as validation.
Inflation from geometrical tachyons
Thomas, Steven; Ward, John
2005-10-15
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is {radical}(2/k) times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.
Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes.
Kirkendall, Christopher R; Kwon, Jae W
2016-01-01
Nonlinear modal interactions have recently become the focus of intense research in micro- and nanoscale resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. However, our understanding of modal coupling is largely restricted to clamped-clamped beams, and lacking in systems with both geometric and material nonlinearities. Here we report multistable energy transfer between internally resonant modes of an electroelastic crystal plate and use a mixed analytical-numerical approach to provide new insight into these complex interactions. Our results reveal a rich bifurcation structure marked by nested regions of multistability. Even the simple case of two coupled modes generates a host of topologically distinct dynamics over the parameter space, ranging from the usual Duffing bistability to complex multistable behaviour and quasiperiodic motion. PMID:26961749
Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes
Kirkendall, Christopher R.; Kwon, Jae W.
2016-01-01
Nonlinear modal interactions have recently become the focus of intense research in micro- and nanoscale resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. However, our understanding of modal coupling is largely restricted to clamped-clamped beams, and lacking in systems with both geometric and material nonlinearities. Here we report multistable energy transfer between internally resonant modes of an electroelastic crystal plate and use a mixed analytical-numerical approach to provide new insight into these complex interactions. Our results reveal a rich bifurcation structure marked by nested regions of multistability. Even the simple case of two coupled modes generates a host of topologically distinct dynamics over the parameter space, ranging from the usual Duffing bistability to complex multistable behaviour and quasiperiodic motion. PMID:26961749
Perturbation approach to dispersion curves calculation for nonlinear Lamb waves
NASA Astrophysics Data System (ADS)
Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2015-05-01
Analysis of elastic wave propagation in nonlinear media has gained recent research attention due to the recognition of their amplitude-dependent behavior. This creates opportunities for increased accuracy of damage detection and localization, development of new structural monitoring strategies, and design of new structures with desirable acoustic behavior (e.g., amplitude-dependent frequency bandgaps, wave beaming, and filtering). This differs from more traditional nonlinear analysis approaches which target the prediction of higher harmonic growth. Of particular interest in this work is the analysis of amplitude-dependent shifts in Lamb wave dispersion curves. Typically, dispersion curves are calculated for nominally linear material parameters and geometrical features of a waveguide, even when the constitutive law is nonlinear. Instead, this work employs a Lindstedt - Poincare perturbation approach to calculate amplitude-dependent dispersion curves, and shifts thereof, for nonlinearly-elastic plates. As a result, a set of first order corrections to frequency (or equivalently wavenumber) are calculated. These corrections yield significant amplitude dependence in the spectral characteristics of the calculated waves, especially for high frequency waves, which differs fundamentally from linear analyses. Numerical simulations confirm the analytical shifts predicted. Recognition of this amplitude-dependence in Lamb wave dispersion may suggest, among other things, that the analysis of guided wave propagation phenomena within a fully nonlinear framework needs to revisit mode-mode energy flux and higher harmonics generation conditions.
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
NASA Astrophysics Data System (ADS)
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: ?SR measurements on single crystals Oren Ofer, Amit Keren, Jess H Brewer, Tianheng H Han and Young S Lee Classical topological order in kagome ice Andrew J Macdonald, Peter C W Holdsworth and Roger G Melko Magnetic phase diagrams of classical triangular and kagome antiferromagnets M V Gvozdikova, P-E Melchy and M E Zhitomirsky The ordering of XY spin glasses Hikaru Kawamura Dynamic and thermodynamic properties of the generalized diamond chain model for azurite Andreas Honecker, Shijie Hu, Robert Peters and Johannes Richter Classical height models with topological order Christopher L Henley A search for disorder in the spin glass double perovskites Sr2CaReO6 and Sr2MgReO6 using neutron diffraction and neutron pair distribution function analysis J E Greedan, Shahab Derakhshan, F Ramezanipour, J Siewenie and Th Proffen Order and disorder in the local and long-range structure of the spin-glass pyrochlore, Tb2Mo2O7 Yu Jiang, Ashfia Huq, Corwin H Booth, Georg Ehlers, John E Greedan and Jason S Gardner The magnetic phase diagram of Gd2Sn2O7 R S Freitas and J S Gardner Calculation of the expected zero-field muon relaxation rate in the geometrically frustrated rare earth pyrochlore Gd2Sn2O7 antiferromagnet P A McClarty, J N Cosman, A G Del Maestro and M J P Gingras Magnetic frustration in the disordered pyrochlore Yb2GaSbO7 J A Hodges, P Dalmas de Réotier, A Yaouanc, P C M Gubbens, P J C King and C Baines Titanium pyrochlore magnets: how much can be learned from magnetization measurements? O A Petrenko, M R Lees and G Balakrishnan Local susceptibility of the Yb2Ti2O7 rare earth pyrochlore computed from a Hamiltonian with anisotropic exchange J D Thompson, P A McClarty and M J P Gingras Slow and static spin correlations in Dy2 + xTi2 - xO7 - ? J S Gardner, G Ehlers, P Fouquet, B Farago and J R Stewart The spin ice Ho2Ti2O7 versus the spin liquid Tb2Ti2O7: field-induced magnetic structures A P Sazonov, A Gukasov and I Mirebeau Magnetic monopole dynamics in spin ice L D C Jaubert and P C W Holdsworth
Analysis of nonlinear self-focusing phenomenon in high-power laser system based on ray-tracing
NASA Astrophysics Data System (ADS)
Wang, Weiwei; Li, Xiaotong; Cen, Zhaofeng; Zhang, Luwei
2014-11-01
In high power laser systems, nonlinear effect, one of the key factors of beam wavefront aberration and even irreversible damage to system, has always been one of the top considerations of researchers for decades. A hybrid ray-tracing method for both linear media and nonlinear media based on geometric optics is presented in this paper and realized by programming. In a simple optic system with KDP crystal, an obvious decline of beam quality is observed in high laser power density conditions and a method taking component intervals as compensation of beam quality is proved feasible. Considering the complexity of traditional modeling method based on surfaces, a modeling method based on components is established. Hopefully, the conclusions and flaws of this paper can shed light on relevant work and further research.
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
Time and Geometric Quantization
NASA Astrophysics Data System (ADS)
Abrikosov, A. A.; Gozzi, E.; Mauro, D.
In this paper we briefly review the functional version of the Koopman-von Neumann operatorial approach to classical mechanics. We then show that its quantization can be achieved by freezing to zero two Grassmannian partners of time. This method of quantization presents many similarities with the one known as Geometric Quantization.
ERIC Educational Resources Information Center
Smart, Julie; Marshall, Jeff
2007-01-01
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…
ERIC Educational Resources Information Center
Smart, Julie; Marshall, Jeff
2007-01-01
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact thatâ€¦
Geometric Series via Probability
ERIC Educational Resources Information Center
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
ERIC Educational Resources Information Center
Burgess, Claudia R.
2014-01-01
Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…
1500 System Geometric Dictionary.
ERIC Educational Resources Information Center
Peloquin, Paul V.
A general description is provided of the "geometric dictionary," a graphic display aid, used by the Computer-Assisted Instruction Laboratory at the Pennsylvania State University. The purpose of the description is to enable the reader to duplicate and use the dictionary on any cathode ray tube terminal of the IBM 1500 system. The major advantages…
Pragmatic geometric model evaluation
NASA Astrophysics Data System (ADS)
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to calculate basically two model variations that can be seen as geometric extremes of all available input data. This does not lead to a probability distribution for the spatial position of geometric elements but it defines zones of major (or minor resp.) geometric variations due to data uncertainty. Both model evaluations are then analyzed together to give ranges of possible model outcomes in metric units.
Nonlinear analysis and redesign of the mixed-mode bending delamination test
NASA Technical Reports Server (NTRS)
Reeder, J. R.; Crews, J. H., Jr.
1991-01-01
The Mixed Mode Bending (MMB) test uses a lever to simultaneously apply mode I and mode II loading to a split beam specimen. An iterative analysis that accounts for the geometric nonlinearity of the MMB test was developed. The analysis accurately predicted the measured load displacement response and the strain energy release rate, G, of an MMB test specimen made of APC2 (AS4/PEEK). The errors in G when calculated using linear theory were found to be as large as thirty percent in some cases. Because it would be inconvenient to use a nonlinear analysis to analyze MMB data, the MMB apparatus was redesigned to minimize the nonlinearity. The nonlinear analysis was used as a guide in redesigning the MMB apparatus. With the redesigned apparatus, loads were applied through a roller attached to the level and loaded just above the midplane of the test specimen. The redesigned apparatuus has geometric nonlinearity errors of less than three percent, even for materials substantially tougher than APC2. This apparatus was demonstrated by measuring the mixed mode delamination fracture toughness of APC2.
Tuning piezoresistive transduction in nanomechanical resonators by geometrical asymmetries
NASA Astrophysics Data System (ADS)
Llobet, J.; Sansa, M.; Lorenzoni, M.; Borrisé, X.; San Paulo, A.; Pérez-Murano, F.
2015-08-01
The effect of geometrical asymmetries on the piezoresistive transduction in suspended double clamped beam nanomechanical resonators is investigated. Tapered silicon nano-beams, fabricated using a fast and flexible prototyping method, are employed to determine how the asymmetry affects the transduced piezoresistive signal for different mechanical resonant modes. This effect is attributed to the modulation of the strain in pre-strained double clamped beams, and it is confirmed by means of finite element simulations.
Columnar deformation of human red blood cell by highly localized fiber optic Bessel beam stretcher.
Lee, Sungrae; Joo, Boram; Jeon, Pyo Jin; Im, Seongil; Oh, Kyunghwan
2015-11-01
A single human red blood cell was optically stretched along two counter-propagating fiber-optic Bessel-like beams in an integrated lab-on-a-chip structure. The beam enabled highly localized stretching of RBC, and it induced a nonlinear mechanical deformation to finally reach an irreversible columnar shape that has not been reported. We characterized and systematically quantified this optically induced mechanical deformation by the geometrical aspect ratio of stretched RBC and the irreversible stretching time. The proposed RBC mechanism can realize a versatile and compact opto-mechanical platform for optical diagnosis of biological substances in the single cell level. PMID:26601005
Columnar deformation of human red blood cell by highly localized fiber optic Bessel beam stretcher
Lee, Sungrae; Joo, Boram; Jeon, Pyo Jin; Im, Seongil; Oh, Kyunghwan
2015-01-01
A single human red blood cell was optically stretched along two counter-propagating fiber-optic Bessel-like beams in an integrated lab-on-a-chip structure. The beam enabled highly localized stretching of RBC, and it induced a nonlinear mechanical deformation to finally reach an irreversible columnar shape that has not been reported. We characterized and systematically quantified this optically induced mechanical deformation by the geometrical aspect ratio of stretched RBC and the irreversible stretching time. The proposed RBC mechanism can realize a versatile and compact opto-mechanical platform for optical diagnosis of biological substances in the single cell level. PMID:26601005
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam
2004-01-01
The goal of this investigation is to further develop nonlinear modal numerical simulation methods for prediction of geometrically nonlinear response due to combined thermal-acoustic loadings. As with any such method, the accuracy of the solution is dictated by the selection of the modal basis, through which the nonlinear modal stiffness is determined. In this study, a suite of available bases are considered including (i) bending modes only; (ii) coupled bending and companion modes; (iii) uncoupled bending and companion modes; and (iv) bending and membrane modes. Comparison of these solutions with numerical simulation in physical degrees-of-freedom indicates that inclusion of any membrane mode variants (ii - iv) in the basis affects the bending displacement and stress response predictions. The most significant effect is on the membrane displacement, where it is shown that only the type (iv) basis accurately predicts its behavior. Results are presented for beam and plate structures in the thermally pre-buckled regime.
Analysis of transverse shear strains in pre-twisted thick beams using variational asymptotic method
Ameen, Maqsood M.; Harursampath, Dineshkumar E-mail: dinesh@aero.iisc.ernet.in
2015-03-10
The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam ref-erence curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.
Geometrical aspects of quantum spaces
Ho, P.M.
1996-05-11
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S{sub 1}{sup 2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S{sub q}{sup 2} and CP{sub q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP{sub q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.
Geometrical deuteron stripping revisited
Neoh, Y. S.; Yap, S. L.
2014-03-05
We investigate the reality of the idea of geometrical deuteron stripping originally envisioned by Serber. By taking into account of realistic deuteron wavefunction, nuclear density, and nucleon stopping mean free path, we are able to estimate inclusive deuteron stripping cross section for deuteron energy up to before pion production. Our semiclassical model contains only one global parameter constant for all nuclei which can be approximated by Woods-Saxon or any other spherically symmetric density distribution.
Geometric measures of entanglement
Uyanik, K.; Turgut, S.
2010-03-15
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Aerospace plane guidance using geometric control theory
NASA Technical Reports Server (NTRS)
Van Buren, Mark A.; Mease, Kenneth D.
1990-01-01
A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.
Geometric diffusion of quantum trajectories
Yang, Fan; Liu, Ren-Bao
2015-01-01
A quantum object can acquire a geometric phase (such as Berry phases and Aharonovâ€“Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745
Foundations of Geometric Algebra computing
NASA Astrophysics Data System (ADS)
Hildenbrand, Dietmar
2012-09-01
Geometric Algebra has the power to lead easily from the geometric intuition of solving an engineering application to its efficient implementation on current and future computing platforms. It is easy to develop new algorithms in areas such as computer graphics, robotics, computer animation and computer simulation. Owing to its geometric intuitiveness, compactness and simplicity, algorithms based on Geometric Algebra can lead to enhanced quality, a reduction in development time and solutions that are more easily understandable and maintainable. Often, a clear structure and greater elegance result in lower runtime performance. However, based on our computing technology, Geometric Algebra implementations can even be faster and more robust than conventional ones. We present an example on how easy it is to describe algorithms in Geometric Algebra and introduce our technology for the integration of Geometric Algebra into standard programming languages. We really do hope that this technology can support the widespread use of Geometric Algebra Computing technology in many engineering fields.
Geometric Representation of the Entropy Group in Nonextensive Statistical Mechanics
NASA Astrophysics Data System (ADS)
Zaripov, R. G.
2014-05-01
A geometric representation of the entropy group has been derived for the general law of composition of parametric entropies with quadratic nonlinearity in nonextensive statistical mechanics. Hyperbolic functions of two-parameter entropy and the Havrda-Charvat-Daróczy entropy and also hyperbolic number functions have been determined in different geometries.
Super finite elements for nonlinear static and dynamic analysis of stiffened plate structures
NASA Astrophysics Data System (ADS)
Koko, Tamunoiyala Stanley
1990-10-01
New plate and stiffener beam finite elements are developed for the nonlinear static and dynamic analysis of stiffened plate structures. The elements are specially designed to contain all the basic modes of deformation response which occur in stiffened plates. Only one plate element per bay or one beam element per span is needed to achieve engineering design level accuracy at minimum cost. The Von Karman large deflection theory is used to model the nonlinear geometric behavior. Material nonlinearities are modeled by Von Mises yield criterion and associated flow rule using a bilinear stress strain law. The finite element equations are derived using the virtual work principle and the matrix quantities are evaluated by Gauss quadrature. Temporal integration is carried out using the Newmark-beta method with Newton-Raphson iteration. A computer code was written to implement the theory. This was applied to the static, vibration, and transient analysis of unstiffened plates, beams, and plates stiffened in one or two orthogonal directions. Good approximations were obtained for both linear and nonlinear problems. The displacement and stress responses obtained compare well with experimental, analytical, or other numerical results.
NASA Astrophysics Data System (ADS)
Lopez, Salvatore
2013-08-01
A minimal set vectorial parameterization involving vector space operations is proposed for finite 3D rotations in structural analysis. In this approach, based on the updated Lagrangian description, complex manipulations required to obtain conservative descriptions and well-posed transformation matrices are avoided. In particular, slopes are used instead of rotation parameters to compute the nonlinear representations of the strain measures in the inertial frame of reference. This approach is applied to a geometrically nonlinear formulation for 3D beam elements in the hypotheses of large rotations and small strains. Numerical tests have been carried out to validate the developed technique in the frame structures context.
Nonlinear competition in nematicon propagation.
Laudyn, Urszula A; Kwasny, Micha?; Piccardi, Armando; Karpierz, Miros?aw A; Dabrowski, Roman; Chojnowska, Olga; Alberucci, Alessandro; Assanto, Gaetano
2015-11-15
We investigate the role of competing nonlinear responses in the formation and propagation of bright spatial solitons. We use nematic liquid crystals (NLCs) exhibiting both thermo-optic and reorientational nonlinearities with continuous-wave beams. In a suitably prepared dye-doped sample and dual beam collinear geometry, thermal heating in the visible affects reorientational self-focusing in the near infrared, altering light propagation and self-trapping. PMID:26565843
NASA Astrophysics Data System (ADS)
Lu, Haw-Minn
1998-11-01
This dissertation takes the first steps in the use of differential geometry in the study of images in pixel space. Unlike previous applications of geometry which focused on the surfaces of objects, this dissertation examines image manifolds. Previous work on image manifolds did not examine their intrinsic geometry. This work unifies many observations found in past work. Beyond that, many new results are obtained. In the first parts of this dissertation, the dimensions of some selected image manifolds are experimentally determined, yielding a ratio of pixel space dimension to image manifold dimension on the order of 100:1. This leads immediately to some new bounds on image source entropy. A novel approach to defining images as signals yields an analogous sampling theorem. The main repercussion of this approach is the discovery that sampling within reason is a geometric invariant. This work resurrects a classic signal interpolation method which has not been previously applied to images. With the geometric invariance of sampling in hand, more advanced aspects of image manifold geometry are explored. The first of these aspects is curvature, which is shown to be extremely high. The discovery of high curvature explains the well established but poorly understood fact that linear subspace coding methods applied to images are far from optimal. Some geometric theory concerning the use of geodesics to represent images is presented. More advanced aspects of image manifold structures are explored experimentally. Preliminary results in this area indicate that there may be a structural relation between images of crudely similar objects in similar poses. Supplementary to the theory, a novel approach to image warping is devised called multimorphing. Unlike traditional morphing, multimorphing allows one to combine several images.
Geometric phase in inhomogeneous optical nutation
NASA Astrophysics Data System (ADS)
Yu, Yanxia; Pan, Hui; Xue, Liyuan; Guo, Liping; Wang, Zisheng
2015-11-01
Optical nutation and its geometric phase are investigated in terms of an inhomogeneous Bloch equation with a constant term. The analytic solution of optical nutation is obtained by mapping it onto a Bloch sphere structure. We find that a constant, from the equilibrium value of the population inversion in the absence of the laser beam, trends to keep the quantum coherence and is helpful to preserve quantum message. We show that the Berry phase of optical nutation is related to the inner evolution in processing of the optical nutation under a quasicyclic evolution. Furthermore, we find that the Berry phases of two-state mixture change very slowly with its environment variable so as to be robust against the decoherent effect. Our results provide a guidance to implement fault-tolerant geometric quantum computation in the echo approach with an inhomogeneous Bloch equation.
Nonlinear Optics and Applications
NASA Technical Reports Server (NTRS)
Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)
2007-01-01
Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.
TRANSVERSE BEAM TRANSFER FUNCTIONS OF COLLIDING BEAMS IN RHIC
FISCHER,W.; BLASKIEWICZ, M.; CALAGA, R.; CAMERON, P.; HERR, W.; PIELONI, T.
2007-06-25
We use transverse beam transfer functions to measure tune distributions of colliding beams in RHIC. The tune has a distribution due to the beam-beam interaction, nonlinear magnetic fields -- particularly in the interaction region magnets, and non-zero chromaticity in conjunction with momentum spread. The measured tune distributions are compared with calculations.
Geometric phase in Bohmian mechanics
Chou, Chia-Chun; Wyatt, Robert E.
2010-10-15
Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2{pi}. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov-Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant.
Development of solution techniques for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Vos, R. G.; Andrews, J. S.
1974-01-01
Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.
Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments
NASA Astrophysics Data System (ADS)
Karagiozis, K. N.; Païdoussis, M. P.; Amabili, M.; Misra, A. K.
2008-01-01
This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid-structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.
NASA Technical Reports Server (NTRS)
Gray, Carl E., Jr.
1988-01-01
Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.
Geometrical Wake of a Smooth Flat Collimator
Stupakov, G.V.; /SLAC
2011-09-09
A transverse geometrical wake generated by a beam passing through a smooth flat collimator with a gradually varying gap between the upper and lower walls is considered. Based on generalization of the approach recently developed for a smooth circular taper we reduce the electromagnetic problem of the impedance calculation to the solution of two much simpler static problems - a magnetostatic and an electrostatic ones. The solution shows that in the limit of not very large frequencies, the impedance increases with the ratio h/d where h is the width and d is the distance between the collimating jaws. Numerical results are presented for the NLC Post Linac collimator.
Geometrical aspects of entanglement
Leinaas, Jon Magne; Myrheim, Jan; Ovrum, Eirik
2006-07-15
We study geometrical aspects of entanglement, with the Hilbert-Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a 'relativistic' formulation leads to a complete analysis of the question of separability. Our approach is based on Schmidt decomposition of density matrices for a composite system and nonunitary transformations to a standard form. The positivity of the density matrices is crucial for the method to work. A similar approach works to some extent in higher dimensions, but is a less powerful tool. We further present a numerical method for examining separability and illustrate the method by a numerical study of bound entanglement in a composite system of two three-level systems.
Goldberg, P.W.
1993-04-01
In this paper we consider the problem of learning the positions of spheres in metric spaces, given as data randomly drawn points classified according to whether they are internal or external to an unknown sphere. The particular metrics under consideration are geometrical shape metrics, and the results are intended to be applicable to the problem of learning to identify a shape from related shapes classified according to whether they resemble it visually. While it is typically NP-hard to locate a central point for a hypothesis sphere, we find that it is however often possible to obtain a non-spherical hypothesis which can accurately predict whether further random points lie within the unknown sphere. We exhibit algorithms which achieve this, and in the process indicate useful general techniques for computational learning. Finally we exhibit a natural shape metric and show that it defines a class of spheres not predictable in this sense, subject to standard cryptographic assumptions.
NASA Astrophysics Data System (ADS)
Gunda, Jagadish Babu; Venkateswara Rao, Gundabathula
2015-11-01
Post-buckling and large amplitude free vibration analysis of composite beams with axially immovable ends is investigated in the present study using a simple intuitive formulation. Geometric nonlinearity of Von-Karman type is considered in the analysis which accounts for mid-plane stretching action of the beam. Intuitive formulation uses only two parameters: the critical bifurcation point and the axial stretching force developed due to membrane stretching action of the beam. Hinged-hinged, clamped-clamped and clamped-hinged boundary conditions are considered. Numerical accuracy of the proposed analytical closed-form solutions obtained from the intuitive formulation are compared to available finite element solutions for symmetric and asymmetric layup schemes of laminated composite beam which indicates the confidence gained on the present formulation.
Vibration energy harvesting by a Timoshenko beam model and piezoelectric transducer
NASA Astrophysics Data System (ADS)
Stoykov, S.; Litak, G.; Manoach, E.
2015-11-01
An electro-mechanical system of vibrational energy harvesting is studied. The beam is excited by external and kinematic periodic forces and damped by an electrical resistor through the coupled piezoelectric transducer. Nonlinearities are introduced by stoppers limiting the transverse displacements of the beam. The interaction between the beam and the stoppers is modeled as Winkler elastic foundation. The mechanical properties of the piezoelectric layer are taken into account and the beam is modeled as a composite structure. For the examined composite beam, the geometrically nonlinear version of the Timoshenko's beam theory is assumed. The equations of motion are derived by the principle of virtual work considering large deflections. An isogeometric approach is applied for space discretization and B-Splines are used as shape functions. Finally, the power output and the efficiency of the system due to harmonic excitations are discussed. The influence of the position of the stoppers and their length on the dynamics of the beam and consequently on the power output are analyzed and presented.
Characteristics of steady vibration in a rotating hub-beam system
NASA Astrophysics Data System (ADS)
Zhao, Zhen; Liu, Caishan; Ma, Wei
2016-02-01
A rotating beam features a puzzling character in which its frequencies and modal shapes may vary with the hub's inertia and its rotating speed. To highlight the essential nature behind the vibration phenomena, we analyze the steady vibration of a rotating Euler-Bernoulli beam with a quasi-steady-state stretch. Newton's law is used to derive the equations governing the beam's elastic motion and the hub's rotation. A combination of these equations results in a nonlinear partial differential equation (PDE) that fully reflects the mutual interaction between the two kinds of motion. Via the Fourier series expansion within a finite interval of time, we reduce the PDE into an infinite system of a nonlinear ordinary differential equation (ODE) in spatial domain. We further nondimensionalize the ODE and discretize it via a difference method. The frequencies and modal shapes of a general rotating beam are then determined numerically. For a low-speed beam where the ignorance of geometric stiffening is feasible, the beam's vibration characteristics are solved analytically. We validate our numerical method and the analytical solutions by comparing with either the past experiments or the past numerical findings reported in existing literature. Finally, systematic simulations are performed to demonstrate how the beam's eigenfrequencies vary with the hub's inertia and rotating speed.
NASA Astrophysics Data System (ADS)
Amaro de Faria Júnior, A. C.
2015-09-01
In this work we present a method of investigation of nonlinear optical beams generated from non-Hermitian optical systems1 . This method can be applied in the development of optical filters and optical sensors to process, analyze and choose the passband of the propagation modes of an optical pulse from an non-Hermitian optical system. Non-Hermitian optical systems can be used to develop optical fiber sensors that suppress certain propagation modes of optical pulses that eventually behave as quantum noise. Such systems are described by the Nonlinear Schrödinger-like Equation with Parity-Time (PT) Symmetric Optical Potentials. There are optical fiber sensors that due to high laser intensity and frequency can produce quantum noise, such as Raman and Brillouin scattering. However, the optical fiber, for example, can be designed so that its geometry suppress certain propagation modes of the beam. We apply some results of non- Hermitian optical systems with PT symmetry to simulate optical lattice by a appropriate potential function, which among other applications, can naturally suppress certain propagation modes of an optical beam propagating through a waveguide. In other words, the optical system is modeled by a potential function in the Nonlinear Schrödinger-like Equation that one relates with the geometric aspects of the wave guides and with the optical beam interacting with the waveguide material. The paper is organized as follows: sections 1 and 2 present a brief description about nonlinear optical systems and non-Hermitian optical systems with PT symmetry. Section 3 presents a description of the dynamics of nonlinear optical pulses propagating through optical networks described by a optical potential non-Hermitian. Sections 4 and 5 present a general description of this non-Hermitian optical systems and how to get them from a more general model. Section 6 presents some conclusions and comment and the final section presents the references. Begin the abstract two lines below author names and addresses.
NASA Astrophysics Data System (ADS)
Li, Ning; Li, Zhongxian; Xie, Lili
2013-09-01
A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial, flexural, and shear deformations. This model is achieved using a shear-bending interdependent formulation (SBIF). The shape function of the element is derived from the exact solution of the homogeneous form of the equilibrium equation for the Timoshenko deformation hypothesis.The proposed element is free from shear-locking. The sectional fiber model is constituted with a multi-axial plasticity material model, which is used to simulate the coupled shear-axial nonlinear behavior of each fiber. By imposing deformation compatibility conditions among the fibers, the sectional and elemental resisting forces are calculated. Since the SBIF shape functions are interactive with the shear-corrector factor for different shapes of sections, an iterative procedure is introduced in the nonlinear state determination of the proposed Timoshenko element. In addition, the proposed model tackles the geometric nonlinear problem by adopting a corotational coordinate transformation approach. The derivation procedure of the corotational algorithm of the SBIF Timoshenko element for nonlinear geometrical analysis is presented. Numerical examples confirm that the SBIF Timoshenko element with a fiber-section model has the same accuracy and robustness as the flexibility-based formulation. Finally, the SBIF Timoshenko element is extended and demonstratedin a three-dimensional numerical example.
Compact surface plasma H- ion source with geometrical focusing
NASA Astrophysics Data System (ADS)
Dudnikov, V.; Dudnikova, G.
2016-02-01
Factors limiting operating lifetime of a Compact Surface Plasma Sources (CSPS) are analyzed and possible treatments for lifetime enhancement are considered. Increased cooling permeate increased discharge power and increased beam intensity and duty factor. A design of an advanced CSPS with geometrical focusing of H- flux is presented.
Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer
NASA Technical Reports Server (NTRS)
Pai, P. F.; Lee, S.-Y.
2003-01-01
This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \\ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.
Geometrical Detector Considerations in Laser Sensing Applications
NASA Technical Reports Server (NTRS)
Killinger, Dennis
2000-01-01
We have studied the influence of the geometrical interaction of different detectors with the impinging optical/laser received beam for a wide range of laser sensing applications. Although different techniques apply, it is found that similar aspects of geometrical physics plays a role in direct detection of a range-resolved large M(sup 2) OPO atmospheric Lidar, heterodyne multi-detector reception of atmospheric turbulence distorted coherent lidar type laser sensing, and the distribution and summation of laser induced fluorescence signals after being spectrally resolved with a spectrometer and detected by a column summing CCD detector. In each of these systems, the focused received light is spatially and spectrally distributed due to several factors including Field-of-View considerations, laser beam quality/divergence, multi-detector aspects, and hardware and software summation (coherent and non-coherent) of multi-element or spatially integrated signals. This invited talk will present some of our recent results in these areas and show the similarities in the detector spatial and temporal summation techniques of these different laser sensing systems.
Nonlinear vibrations of viscoelastic rectangular plates
NASA Astrophysics Data System (ADS)
Amabili, Marco
2016-02-01
Nonlinear vibrations of viscoelastic thin rectangular plates subjected to normal harmonic excitation in the spectral neighborhood of the lowest resonances are investigated. The von Kármán nonlinear strain-displacement relationships are used and geometric imperfections are taken into account. The material is modeled as a Kelvin-Voigt viscoelastic solid by retaining all the nonlinear terms. The discretized nonlinear equations of motion are studied by using the arclength continuation and collocation method. Numerical results are obtained for the fundamental mode of a simply supported square plate with immovable edges by using models with 16 and 22 degrees of freedom and investigating solution convergence. Comparison to viscous damping and the effect of neglecting nonlinear viscoelastic damping terms are shown. The change of the frequency-response with the retardation time parameter is also investigated as well as the effect of geometric imperfections.
Nonlinear vibrational microscopy
Holtom, Gary R.; Xie, Xiaoliang Sunney; Zumbusch, Andreas
2000-01-01
The present invention is a method and apparatus for microscopic vibrational imaging using coherent Anti-Stokes Raman Scattering or Sum Frequency Generation. Microscopic imaging with a vibrational spectroscopic contrast is achieved by generating signals in a nonlinear optical process and spatially resolved detection of the signals. The spatial resolution is attained by minimizing the spot size of the optical interrogation beams on the sample. Minimizing the spot size relies upon a. directing at least two substantially co-axial laser beams (interrogation beams) through a microscope objective providing a focal spot on the sample; b. collecting a signal beam together with a residual beam from the at least two co-axial laser beams after passing through the sample; c. removing the residual beam; and d. detecting the signal beam thereby creating said pixel. The method has significantly higher spatial resolution then IR microscopy and higher sensitivity than spontaneous Raman microscopy with much lower average excitation powers. CARS and SFG microscopy does not rely on the presence of fluorophores, but retains the resolution and three-dimensional sectioning capability of confocal and two-photon fluorescence microscopy. Complementary to these techniques, CARS and SFG microscopy provides a contrast mechanism based on vibrational spectroscopy. This vibrational contrast mechanism, combined with an unprecedented high sensitivity at a tolerable laser power level, provides a new approach for microscopic investigations of chemical and biological samples.
Gradient Nonlinear Pancharatnam-Berry Metasurfaces
NASA Astrophysics Data System (ADS)
Tymchenko, Mykhailo; Gomez-Diaz, J. Sebastian; Lee, Jongwon; Nookala, Nishant; Belkin, Mikhail A.; AlÃ¹, Andrea
2015-11-01
We apply the Pancharatnam-Berry phase approach to plasmonic metasurfaces loaded by highly nonlinear multiquantum-well substrates, establishing a platform to control the nonlinear wave front at will based on giant localized nonlinear effects. We apply this approach to design flat nonlinear metasurfaces for efficient second-harmonic radiation, including beam steering, focusing, and polarization manipulation. Our findings open a new direction for nonlinear optics, in which phase matching issues are relaxed, and an unprecedented level of local wave front control is achieved over thin devices with giant nonlinear responses.
Nonlinear free vibration of piezoelectric nanobeams incorporating surface effects
NASA Astrophysics Data System (ADS)
Hosseini-Hashemi, Shahrokh; Nahas, Iman; Fakher, Mahmood; Nazemnezhad, Reza
2014-03-01
In this study, the nonlinear free vibration of piezoelectric nanobeams incorporating surface effects (surface elasticity, surface tension, and surface density) is studied. The governing equation of the piezoelectric nanobeam is derived within the framework of Euler-Bernoulli beam theory with the von Kármán geometric nonlinearity. In order to satisfy the balance conditions between the nanobeam bulk and its surfaces, the component of the bulk stress, ?zz, is assumed to vary linearly through the nanobeam thickness. An exact solution is obtained for the natural frequencies of a simply supported piezoelectric nanobeam in terms of the Jacobi elliptic functions using the free vibration mode shape of the corresponding linear problem. Then, the influences of the surface effects and the piezoelectric field on the nonlinear free vibration of nanobeams made of aluminum and silicon with positive and negative surface elasticity, respectively, have been studied for various properties of the piezoelectric field, various nanobeam sizes and amplitude ratios. It is observed that if the Young’s modulus of a nanobeam is lower, the effect of the piezoelectric field on the frequency ratios (FRs) of the nanobeam will be greater. In addition, it is seen that by increasing the nanobeam length so that the nanobeam cross section is set to be constant, the surface effects and the piezoelectric field with negative voltage values increases the FRs, whereas it is the other way around when the nanobeam cross section is assumed to be dependent on the length of the nanobeam.
NASA Astrophysics Data System (ADS)
Sharma, Amalendu; Singh, P.; Abdurrahim; Ghodke, A. D.; Singh, Gurnam
2013-01-01
In charged particle accelerators, higher order optics studies become important from various points of view, such as dynamic aperture, emittance dilution, beam loss, etc. For some new applications, nonlinear study has become important in single pass optics also. For studying the higher order optics, each magnetic element is represented by a higher order transfer function (map, i.e., a function that relates output coordinates of a trajectory with initial coordinates and momentum deviation). Here in this paper we have provided an alternate method to obtain the analytical formulation of the transfer function for a dipole magnet. This formulation is obtained on the basis of basic geometrical analysis and is exact up to all orders under hard edge approximation. Being an analytical expression, the estimation of higher order effects of dipole magnet can be studied quickly. For checking the correctness of this formulation, we separated terms up to third order, which can be used to obtain the standard transfer matrices up to same order. An example of emittance growth and bunch length modification for a C-chicane-type electron beam bunch compressor is provided using the analytical expression.
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.
Geometric and topological approaches to significance testing in wavelet analysis
NASA Astrophysics Data System (ADS)
Schulte, J. A.; Duffy, C.; Najjar, R. G.
2015-03-01
Geometric and topological methods are applied to significance testing in the wavelet domain. A geometric test was developed for assigning significance to pointwise significance patches in local wavelet spectra, i.e., contiguous regions of significant wavelet power coefficients with respect to some noise model. This geometric significance test was found to produce results similar to an existing areawise significance test while being more computationally flexible and efficient. The geometric significance test can be readily applied to pointwise significance patches at various pointwise significance levels in wavelet power and coherence spectra. The geometric test determined that features in wavelet power of the North Atlantic Oscillation (NAO) are indistinguishable from a red-noise background, suggesting that the NAO is a stochastic, unpredictable process, which could render difficult the future projections of the NAO under a changing global system. The geometric test did, however, identify features in the wavelet power spectrum of an El Niño index (Niño 3.4) as distinguishable from a red-noise background. A topological analysis of pointwise significance patches determined that holes, deficits in pointwise significance embedded in significance patches, are capable of identifying important structures, some of which are undetected by the geometric and areawise tests. The application of the topological methods to ideal time series and to the time series of the Niño 3.4 and NAO indices showed that the areawise and geometric tests perform similarly in ideal and geophysical settings, while the topological methods showed that the Niño 3.4 time series contains numerous phase-coherent oscillations that could be interacting nonlinearly.
Coiling of elastic rods from a geometric perspective
NASA Astrophysics Data System (ADS)
Jawed, Mohammad; Brun, Pierre-Thomas; Reis, Pedro
2015-03-01
We present results from a systematic numerical investigation of the pattern formation of coiling obtained when a slender elastic rod is deployed onto a moving substrate; a system known as the elastic sewing machine (ESM). The Discrete Elastic Rods method is employed to explore the parameter space, construct phase diagrams, identify their phase boundaries and characterize the morphology of the patterns. The nontrivial geometric nonlinearities are described in terms of the gravito-bending length and the deployment height. Our results are interpreted using a reduced geometric model for the evolution of the position of the contact point with the belt and the curvature of the rod in its neighborhood. This geometric model reproduces all of the coiling patterns of the ESM, which allows us to establish a universal link between our elastic problem and the analogous patterns obtained when depositing a viscous thread onto a moving surface; a well-known system referred to as the fluid mechanical sewing machine.
Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings
NASA Astrophysics Data System (ADS)
Dakel, Mzaki; Baguet, SÃ©bastien; Dufour, RÃ©gis
2014-05-01
The major purpose of this study is to predict the dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings in the presence of rigid support movements, the target application being turbochargers of vehicles or rotating machines subject to seismic excitation. The proposed on-board rotor model is based on Timoshenko beam finite elements. The dynamic modeling takes into account the geometric asymmetry of shaft and/or rigid disk as well as the six deterministic translations and rotations of the rotor rigid support. Depending on the type of analysis used for the bearing, the fluid film forces computed with the Reynolds equation are linear/nonlinear. Thus the application of Lagrange's equations yields the linear/nonlinear equations of motion of the rotating rotor in bending with respect to the moving rigid support which represents a non-inertial frame of reference. These equations are solved using the implicit Newmark time-step integration scheme. Due to the geometric asymmetry of the rotor and to the rotational motions of the support, the equations of motion include time-varying parametric terms which can lead to lateral dynamic instability. The influence of sinusoidal rotational or translational motions of the support, the accuracy of the linear 8-coefficient bearing model and the interest of the nonlinear model for a hydrodynamic journal bearing are examined and discussed by means of stability charts, orbits of the rotor, time history responses, fast Fourier transforms, bifurcation diagrams as well as PoincarÃ© maps.
Optical traps with geometric aberrations
Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G
2006-05-20
We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems.
Geometric phases in chiral superconductors
NASA Astrophysics Data System (ADS)
Abanov, Alexander; Wiegmann, Paul; Zhou, Fei
2001-03-01
We revisit the derivation of topological terms (geometric phases) in effective theories of chiral superconductors. We are particularly interested in a chiral p-wave superconductor in two-dimensions with potential applications to Sr2 Ru O4 and ^3He-A films. This problem has been intensively discussed in the past. We found that the important nonperturbative geometric phases, related to the global chiral anomaly were overlooked. Without them the theory is not self-consistent. We discuss physical consequences of these geometric phases.
Optimization of biotechnological systems through geometric programming
Marin-Sanguino, Alberto; Voit, Eberhard O; Gonzalez-Alcon, Carlos; Torres, Nestor V
2007-01-01
Background In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM) was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary. Results A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA) system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency. Conclusion GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into the GMA form. Thus, efficient methods for optimizing GMA systems have multifold appeal. PMID:17897440
Acoustic nonlinearity in fluorinert FC-43
Pantea, Cristian; Sinha, Dipen N; Osterhoudt, Curtis F; Mombourquette, Paul C
2009-01-01
Fluorinert FC-43 nonlinearity was investigated using two approaches: (i) a finite amplitude method with harmonic production; and (ii) a nonlinear frequency mixing in the fluid with consequent beam profile measurement of the difference frequency. The finite amplitude method provides information on the coefficient of nonlinearity, {beta}, through the amplitudes of the fundamental and the second harmonic, at a certain transmitter-receiver distance. A calibrated hydrophone was used as a receiver, in order to obtain direct pressure measurements of the acoustic waves in the fluid. The role of transmitter-receiver distance in {beta} determination is investigated. In the second approach, a single transducer is used to provide two high-frequency beams. The collinear high-frequency beams mix nonlinearly in the fluid resulting in a difference frequency beam and higher order harmonics of the primaries. The difference frequency beam profite is investigated at lengths beyond the mixing distance. The experimental data are compured with the KZK theory.
Clique topology reveals intrinsic geometric structure in neural correlations
Giusti, Chad; Pastalkova, Eva; Curto, Carina; Itskov, Vladimir
2015-01-01
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown. PMID:26487684
Program for analysis of nonlinear equilibrium and stability (PANES)
NASA Technical Reports Server (NTRS)
Vos, R. G.
1975-01-01
PANES utilizes improved techniques for analysis of structures with material and geometric nonlinearities, including limit point and bifurcations behavior which occurs in buckling and collapse problems. Incremental loading, Newton-Raphson iteration, and higher order methods are used in program.
Guitars, Violins, and Geometric Sequences
ERIC Educational Resources Information Center
Barger, Rita; Haehl, Martha
2007-01-01
This article describes middle school mathematics activities that relate measurement, ratios, and geometric sequences to finger positions or the placement of frets on stringed musical instruments. (Contains 2 figures and 2 tables.)
One step geometrical calibration method for optical coherence tomography
NASA Astrophysics Data System (ADS)
DÃaz DÃaz, JesÃºs; Stritzel, Jenny; Rahlves, Maik; Majdani, Omid; Reithmeier, Eduard; Ortmaier, Tobias; Roth, Bernhard
2016-01-01
We present a novel one-step calibration methodology for geometrical distortion correction for optical coherence tomography (OCT). A calibration standard especially designed for OCT is introduced, which consists of an array of inverse pyramidal structures. The use of multiple landmarks situated on four different height levels on the pyramids allow performing a 3D geometrical calibration. The calibration procedure itself is based on a parametric model of the OCT beam propagation. It is validated by experimental results and enables the reduction of systematic errors by more than one order of magnitude. In future, our results can improve OCT image reconstruction and interpretation for medical applications such as real time monitoring of surgery.
NASA Astrophysics Data System (ADS)
Zhu, Y.; Zhang, Y. X.
2010-08-01
A simple and shear-flexible rectangular composite layered plate element and nonlinear finite element analysis procedures are developed in this paper for nonlinear analysis of fiber reinforced plastic (FRP)-reinforced concrete slabs. The composite layered plate element is constructed based on Mindlin-Reissner plate theory and Timoshenko’s composite beam functions, and transverse shear effects and membrane-bending coupling effects are accounted for. Both geometric nonlinearity and material nonlinearity of the materials, which incorporates tension, compression, tension stiffening and cracking of the concrete, are included in the new model. The developed element and the nonlinear finite element analysis procedures are validated by comparing the computed numerical results of numerical examples with those obtained from experimental investigations and from the commercial finite element analysis package ABAQUS. The element is then employed to investigate the nonlinear structural behavior and the cracking progress of a clamped two-way FRP-reinforced concrete slab. The influences of reinforcement with different materials, ratio and layout in tension or compressive regions on structural behavior of the clamped slabs are investigated by parametric studies.
Algorithms of NCG geometrical module
Gurevich, M. I.; Pryanichnikov, A. V.
2012-12-15
The methods and algorithms of the versatile NCG geometrical module used in the MCU code system are described. The NCG geometrical module is based on the Monte Carlo method and intended for solving equations of particle transport. The versatile combinatorial body method, the grid method, and methods of equalized cross sections and grain structures are used for description of the system geometry and calculation of trajectories.
Discontinuous Buckling of Wide Beams and Metabeams
NASA Astrophysics Data System (ADS)
Coulais, Corentin; Overvelde, Johannes T. B.; Lubbers, Luuk A.; Bertoldi, Katia; van Hecke, Martin
2015-07-01
We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams—beams made from a mechanical metamaterial—exhibit discontinuous buckling, an unstable form of buckling where the postbuckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit an increasingly negative postbuckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as 1% numerically and 5% experimentally.
Antenna with Dielectric Having Geometric Patterns
NASA Technical Reports Server (NTRS)
Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)
2013-01-01
An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.
Technology Transfer Automated Retrieval System (TEKTRAN)
This work examines the application of a geometric-optical canopy reflectance model to provide measures of woody shrub abundance in desert grasslands at the landscape scale. The approach is through inversion of the non-linear simple geometric model (SGM) against 631 nm multi-angle reflectance data fr...
Manifestation of the geometric phase in neutron spin-echo experiments
Kraan, W. H.; Rekveldt, M. T.; Grigoriev, S. V.
2010-07-15
We show how the geometric (Berry's) phase becomes manifest on adiabatic rotation of the polarization vector in the magnetic field configuration in the arms in a neutron spin echo (NSE) experiment. When the neutron beam used is monochromatic, a geometric phase collected in one spin-echo arm can be exactly compensated in the other arm either by an opposite geometrical rotation or by adding/subtracting a dynamic (Larmor) phase. This is not possible in a white beam, because, contrary to the dynamic phase, the geometric phase is independent of wavelength. Therefore, the NSE pattern can be disturbed. We demonstrate that adiabatic resonant spin flippers inherently produce a geometric phase which can influence the performance of NSE setups based on such flippers. This effect can be avoided by a proper mutual symmetry of the gradient fields in these flippers.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach
Arrieta, Jorge; Cartwright, Julyan H. E.; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number— in an inertialess environment—is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the “belly phase,” peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing. PMID:26154384
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing. PMID:26154384
Interplay of disorder and geometrical frustration in Gadolinium Gallium Garnet
NASA Astrophysics Data System (ADS)
Woo, Nayoon; Silevitch, D. M.; Rosenbaum, T. F.
2015-03-01
We study the effects of disorder on the geometrically frustrated Heisenberg antiferromagnet Gadolinium Gallium Garnet (GGG) using neodymium doping (0.1 to 1%) in combination with linear and nonlinear ac magnetic susceptibility. The Nd doping actually alleviates the effects of disorder due to excess Gd ions occupying Ga sites. The linear, frequency-dependent susceptibility reveals that 1% Nd doping suppresses the appearance of any long-range order from approximately 80mK to below 30mK. The dynamics of isolated, correlated spin clusters were studied as a function of doping level using nonlinear susceptometry. In this regime, both the aggregate moment of the clustered spins and the activation field required to excite a nonlinear response were inversely correlated with the dopant density.