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Автор: Grafiati

Опубліковано: 6 вересня 2023

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1

Achenbach, Jan D. "Reciprocity and Related Topics in Elastodynamics." Applied Mechanics Reviews 59, no. 1 (January 1, 2006): 13–32. http://dx.doi.org/10.1115/1.2110262.

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Reciprocity theorems in elasticity theory were discovered in the second half of the 19th century. For elastodynamics they provide interesting relations between two elastodynamic states, say states A and B. This paper will primarily review applications of reciprocity relations for time-harmonic elastodynamic states. The paper starts with a brief introduction to provide some historical and general background, and then proceeds in Sec. 2 to a brief discussion of static reciprocity for an elastic body. General comments on waves in solids are offered in Sec. 3, while Sec. 4 provides a brief summary of linearized elastodynamics. Reciprocity theorems are stated in Sec. 5. For some simple examples the concept of virtual waves is introduced in Sec. 6. A virtual wave is a wave motion that satisfies appropriate conditions on the boundaries and is a solution of the elastodynamic equations. It is shown that combining the desired solution as state A with a virtual wave as state B provides explicit results for state A. Basic elastodynamic states are discussed in Sec. 7. These states play an important role in the formulation of integral representations and integral equations, as shown in Sec. 8. Reciprocity in 1-D and full-space elastodynamics are discussed in Secs. 910, respectively. Applications to a half-space and a layer are reviewed in Secs. 1112. Section 13 is concerned with reciprocity of coupled acousto-elastic systems. The paper is completed with a brief discussion of reciprocity for piezoelectric systems. There are 61 references cited in this review article.

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2

Norris, A. N., and A. L. Shuvalov. "Elastodynamics of radially inhomogeneous spherically anisotropic elastic materials in the Stroh formalism." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2138 (October 12, 2011): 467–84. http://dx.doi.org/10.1098/rspa.2011.0463.

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A method for solving elastodynamic problems in radially inhomogeneous elastic materials with spherical anisotropy is presented, i.e. materials having c ijkl = c ijkl ( r ) in a spherical coordinate system { r , θ , ϕ }. The time-harmonic displacement field u ( r , θ , ϕ ) is expanded in a separation of variables form with dependence on θ , ϕ described by vector spherical harmonics with r -dependent amplitudes. It is proved that such separation of variables solution is generally possible only if the spherical anisotropy is restricted to transverse isotropy (TI) with the principal axis in the radial direction, in which case the amplitudes are determined by a first-order ordinary differential system. Restricted forms of the displacement field, such as u ( r , θ ), admit this type of separation of variables solution for certain lower material symmetries. These results extend the Stroh formalism of elastodynamics in rectangular and cylindrical systems to spherical coordinates.

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3

Bluman, G., A. F. Cheviakov, and J. F. Ganghoffer. "Nonlocally related PDE systems for one-dimensional nonlinear elastodynamics." Journal of Engineering Mathematics 62, no. 3 (March 22, 2008): 203–21. http://dx.doi.org/10.1007/s10665-008-9221-7.

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4

Trainiti, G., Y. Ra'di, M. Ruzzene, and A. Alù. "Coherent virtual absorption of elastodynamic waves." Science Advances 5, no. 8 (August 2019): eaaw3255. http://dx.doi.org/10.1126/sciadv.aaw3255.

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Анотація:

Absorbers suppress reflection and scattering of an incident wave by dissipating its energy into heat. As material absorption goes to zero, the energy impinging on an object is necessarily transmitted or scattered away. Specific forms of temporal modulation of the impinging signal can suppress wave scattering and transmission in the transient regime, mimicking the response of a perfect absorber without relying on material loss. This virtual absorption can store energy with large efficiency in a lossless material and then release it on demand. Here, we extend this concept to elastodynamics and experimentally show that longitudinal motion can be perfectly absorbed using a lossless elastic cavity. This energy is then released symmetrically or asymmetrically by controlling the relative phase of the impinging signals. Our work opens previously unexplored pathways for elastodynamic wave control and energy storage, which may be translated to other phononic and photonic systems of technological relevance.

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5

Schevenels, Mattias, Stijn François, and Geert Degrande. "EDT: An ElastoDynamics Toolbox for MATLAB." Computers & Geosciences 35, no. 8 (August 2009): 1752–54. http://dx.doi.org/10.1016/j.cageo.2008.10.012.

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6

Weaver, R. L. "Uniqueness in elastodynamics for systems with nonlocal impedance boundary conditions." Journal of the Acoustical Society of America 100, no. 5 (November 1996): 3447–49. http://dx.doi.org/10.1121/1.416987.

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7

Lei, Hin-Chi, and Ming-Jui Hung. "Linearity of waves in some systems of non-linear elastodynamics." International Journal of Non-Linear Mechanics 32, no. 2 (March 1997): 353–60. http://dx.doi.org/10.1016/s0020-7462(96)00064-9.

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8

Perthame, Benoit, and Athanasios E. Tzavaras. "Kinetic Formulation for Systems of Two¶Conservation Laws and Elastodynamics." Archive for Rational Mechanics and Analysis 155, no. 1 (October 1, 2000): 1–48. http://dx.doi.org/10.1007/s002050000109.

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9

Rossi, Riccarda, and Marita Thomas. "From adhesive to brittle delamination in visco-elastodynamics." Mathematical Models and Methods in Applied Sciences 27, no. 08 (April 28, 2017): 1489–546. http://dx.doi.org/10.1142/s0218202517500257.

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In this paper, we analyze a system for brittle delamination between two visco-elastic bodies, also subject to inertia, which can be interpreted as a model for dynamic fracture. The rate-independent flow rule for the delamination parameter is coupled with the momentum balance for the displacement, including inertia. This model features a nonsmooth constraint ensuring the continuity of the displacements outside the crack set, which is marked by the support of the delamination parameter. A weak solvabi- lity concept, generalizing the notion of energetic solution for rate-independent systems to the present mixed rate-dependent/rate-independent frame, is proposed. Via refined variational convergence techniques, existence of solutions is proved by passing to the limit in approximating systems which regularize the nonsmooth constraint by conditions for adhesive contact. The presence of the inertial term requires the design of suitable recovery spaces small enough to provide compactness but large enough to recover the information on the crack set in the limit.

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10

Sun, Qi, Jorge Angeles, and Genliang Chen. "The Cartesian elastodynamics linear model of mechanical systems with flexible links." Mechanism and Machine Theory 167 (January 2022): 104559. http://dx.doi.org/10.1016/j.mechmachtheory.2021.104559.

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11

Ambrósio, Jorge A. C., and Peter Ravn. "Elastodynamics of Multibody Systems Using Generalized Inertial Coordinates and Structural Damping*." Mechanics of Structures and Machines 25, no. 2 (January 1997): 201–19. http://dx.doi.org/10.1080/08905459708905287.

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12

Xue, Zhi-Peng, Ming Li, Yan-Hui Li, and Hong-Guang Jia. "A Simplified Flexible Multibody Dynamics for a Main Landing Gear with Flexible Leaf Spring." Shock and Vibration 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/595964.

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Анотація:

The dynamics of multibody systems with deformable components has been a subject of interest in many different fields such as machine design and aerospace. Traditional rigid-flexible systems often take a lot of computer resources to get accurate results. Accuracy and efficiency of computation have been the focus of this research in satisfying the coupling of rigid body and flex body. The method is based on modal analysis and linear theory of elastodynamics: reduced modal datum was used to describe the elastic deformation which was a linear approximate of the flexible part. Then rigid-flexible multibody system was built and the highly nonlinearity of the mass matrix caused by the limited rotation of the deformation part was approximated using the linear theory of elastodynamics. The above methods were used to establish the drop system of the leaf spring type landing gear of a small UAV. Comparisons of the drop test and simulation were applied. Results show that the errors caused by the linear approximation are acceptable, and the simulation process is fast and stable.

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13

Altmann, Robert. "Convergence of the Rothe Method Applied to Operator DAEs Arising in Elastodynamics." Computational Methods in Applied Mathematics 17, no. 4 (October 1, 2017): 533–52. http://dx.doi.org/10.1515/cmam-2017-0003.

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AbstractThe dynamics of elastic media, constrained by Dirichlet boundary conditions, can be modeled as an operator DAE of semi-explicit structure. These models include flexible multibody systems as well as applications with boundary control. In order to use adaptive methods in space, we analyze the properties of the Rothe method concerning stability and convergence for this kind of systems. We consider a regularization of the operator DAE and prove the weak convergence of the implicit Euler scheme. Furthermore, we consider perturbations in the semi-discrete systems which correspond to additional errors such as spatial discretization errors.

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14

Pan, Yuhua, Yuanfeng Wang, and Li Su. "ESTABLISHMENT OF DYNAMIC EQUATIONS FOR DAMPED SYSTEMS BASED ON QUASI-VARIATIONAL PRINCIPLES." Transactions of the Canadian Society for Mechanical Engineering 40, no. 5 (December 2016): 859–70. http://dx.doi.org/10.1139/tcsme-2016-0070.

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In this paper, quasi-variational principles for non-conservative damped systems are studied. A Hamiltontype quasi-variational principle for non-conservative systems in analytical mechanics and a quasi-variational principle of potential energy in non-conservative elastodynamics systems are proposed in simplified forms respectively, by using the direct variational integral method. On the basis of the standard linear solid model for viscoelastic materials, the dynamic equations of exponentially damped systems are established through the proposed quasi-variational principles. A distinction between the internal damping described by exponential damping and the external damping described by viscous one in a vibrating structure is according to different physical mechanisms, which gives some indication of the correct mechanism of damping.

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15

Ortner, N., and P. Wagner. "Fundamental matrices of homogeneous hyperbolic systems. Applications to crystal optics, elastodynamics, and piezoelectromagnetism." ZAMM 84, no. 5 (May 3, 2004): 314–46. http://dx.doi.org/10.1002/zamm.200310130.

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16

Ingrim, M. E., and G. Y. Masada. "Extended Bond Graph Representation of the Traction Problem in Linear Elastodynamics." Journal of Dynamic Systems, Measurement, and Control 113, no. 1 (March 1, 1991): 118–21. http://dx.doi.org/10.1115/1.2896335.

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To illustrate the use of the extended bond graph notation, a reticulation is developed for a conjugate variable approximation of the traction problem in linear elastodynamics. This reticulation is general in the sense that all vector and tensor quantities are expressed using direct notation; that is, no specific coordinate system is chosen a priori. In addition, the only limitation placed upon the elasticity tensor C(X) is that it be symmetric. This allows homogeneous and inhomogeneous isotropic, orthotropic, etc., linearly elastic bodies to be modeled using these results. The conjugate approximations used here are entirely compatible with Galerkin based finite element methods. Consequently, this extended bond graph reticulation allows well-developed approximation techniques in solid mechanics to be directly incorporated into bond graph based system models.

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17

Rodriguez Garcia, Jeronimo. "A Spurious-Free Space-Time Mesh Refinement for Elastodynamics." International Journal for Multiscale Computational Engineering 6, no. 3 (2008): 263–79. http://dx.doi.org/10.1615/intjmultcompeng.v6.i3.60.

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18

Dafermos, Constantine M. "Non-convex entropies for conservation laws with involutions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 2005 (December 28, 2013): 20120344. http://dx.doi.org/10.1098/rsta.2012.0344.

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The paper discusses systems of conservation laws endowed with involutions and contingent entropies. Under the assumption that the contingent entropy function is convex merely in the direction of a cone in state space, associated with the involution, it is shown that the Cauchy problem is locally well posed in the class of classical solutions, and that classical solutions are unique and stable even within the broader class of weak solutions that satisfy an entropy inequality. This is on a par with the classical theory of solutions to hyperbolic systems of conservation laws endowed with a convex entropy. The equations of elastodynamics provide the prototypical example for the above setting.

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19

Norris, A. N., A. L. Shuvalov, and A. A. Kutsenko. "Analytical formulation of three-dimensional dynamic homogenization for periodic elastic systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2142 (February 15, 2012): 1629–51. http://dx.doi.org/10.1098/rspa.2011.0698.

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Homogenization of the equations of motion for a three-dimensional periodic elastic system is considered. Expressions are obtained for the fully dynamic effective material parameters governing the spatially averaged fields by using the plane wave expansion method. The effective equations are of Willis form with coupling between momentum and stress and tensorial inertia. The formulation demonstrates that the Willis equations of elastodynamics are closed under homogenization. The effective material parameters are obtained for arbitrary frequency and wavenumber combinations, including but not restricted to Bloch wave branches for wave propagation in the periodic medium. Numerical examples for a one-dimensional system illustrate the frequency dependence of the parameters on Bloch wave branches and provide a comparison with an alternative dynamic effective medium theory, which also reduces to Willis form but with different effective moduli.

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20

Hu, Xianpeng, and Wenbin Zhao. "Global Existence of Compressible Dissipative Elastodynamics Systems with Zero Shear Viscosity in Two Dimensions." Archive for Rational Mechanics and Analysis 235, no. 2 (August 6, 2019): 1177–243. http://dx.doi.org/10.1007/s00205-019-01443-z.

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21

Gonzalez, O., J. H. Maddocks, and R. L. Pego. "Multi-Multiplier Ambient-Space Formulations of Constrained Dynamical Systems, with an Application to Elastodynamics." Archive for Rational Mechanics and Analysis 157, no. 4 (May 1, 2001): 285–323. http://dx.doi.org/10.1007/s002050100134.

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22

Vukobratovic, Miomir, Veljko Potkonjak, and Vladimir Matijevic. "Contribution to the study of dynamics and dynamic control of robots interacting with dynamic environment." Robotica 19, no. 2 (March 2001): 149–61. http://dx.doi.org/10.1017/s0263574700003064.

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Анотація:

The paper discusses some practical problems of contact dynamics. Modelling the dynamics of contact tasks is carried out in a completely general way. Two dynamic systems, active robot system and passive environment system are brought into contact and the relevant dynamics are analyzed. The effects are: rigid-body contact force, elastodynamics in contact zone, friction in contact points, etc. Simultaneous stabilization of contact force and position is obtained using New Dynamic Position/Force Control. The general model is then applied to some more concrete problems and the simulation results are presented.

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23

Beskos, Dimitri E. "Boundary Element Methods in Dynamic Analysis: Part II (1986-1996)." Applied Mechanics Reviews 50, no. 3 (March 1, 1997): 149–97. http://dx.doi.org/10.1115/1.3101695.

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Анотація:

A review of boundary element methods for the numerical solution of elastodynamic problems covering the period 1986-1996 is presented. It is a continuation of a review article on the same subject by the same author which appeared previously in Applied Mechanics Reviews (AMR 40(1) 1-23 (Jan 1987) Reprint No AMR015). Integral formulations and their advanced numerical treatment in both frequency and time domains from the direct boundary element method viewpoint are described. They cover two - and three - dimensional cases as well as the anti-plane case of linear elastodynamics under harmonic or transient disturbances. Indirect formulations, boundary methods, T-matrix methods, symmetric formulations, dual reciprocity boundary element methods and hybrid schemes combining boundary with finite elements are also described. All these boundary element methodologies are applied to: i) wave propagation analysis including wave propagation due to external loads, wave diffraction by surface or subsurface irregularities and cracks and crack propagation; ii) dynamic analysis of structures including beams, membranes, plates and shells as well as two - and three - dimensional structures; iii) soil-structure interaction including foundation analysis, piles and underground structures; iv) fluid-structure interaction including structures inside fluids or containing fluids and dam-reservoir systems; and v) the special subjects of viscoelasticity, inhomogeneity, anisotropy, poroelasticity-thermoelasticity, large deformations, contact analysis, inverse scattering and optimum design and control. Finally, areas where further research is needed are identified. There are 1333 references.

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24

Wang, Wei, Guozheng Yan, Zhiwu Wang, Pingping Jiang, Yicun Meng, Fanji Chen, and Rongrong Xue. "A Novel Expanding Mechanism of Gastrointestinal Microrobot: Design, Analysis and Optimization." Micromachines 10, no. 11 (October 26, 2019): 724. http://dx.doi.org/10.3390/mi10110724.

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Анотація:

In order to make the gastrointestinal microrobot (GMR) expand and anchor in the gastrointestinal tract reliably, a novel expanding mechanism of the GMR is proposed in this paper. The overlapping expanding arm is designed to be used to increase the variable diameter ratio (ratio of fully expanded diameter to fully folded diameter) to 3.3, which makes the robot more adaptable to the intestinal tract of different sections of the human body. The double-layer structure of the expanding arm increases the contact area with the intestine, reducing the risk of intestinal damage. The kinematics and mechanical model of the expanding arm are established, and the rigid velocity, rigid acceleration, and expanding force of the expanding arm are analyzed. The elastodynamics model of the expanding arm is established. Through the finite element analysis (FEA), the velocity, acceleration, and the value and distribution of the stress of the expanding arm under elastic deformation are obtained. Based on the elastodynamics analysis, the structure of the expanding arm is optimized. By the structure optimization, the thickness of the expanding mechanism is reduced by 0.4mm, the weight is reduced by 31%, and the stress distribution is more uniform. Through the mechanical test, the minimum expanding force of the expanding mechanism is 1.3 N and the maximum expanding force is 6.5 N. Finally, the robot is tested in the rigid pipeline and the isolated intestine to verify the reliability and safety of the expanding mechanism.

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25

Nguyen, Nhan, and Mark Ardema. "Optimality of Hyperbolic Partial Differential Equations With Dynamically Constrained Periodic Boundary Control—A Flow Control Application." Journal of Dynamic Systems, Measurement, and Control 128, no. 4 (April 26, 2006): 946–59. http://dx.doi.org/10.1115/1.2362814.

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Анотація:

This paper is concerned with optimal control of a class of distributed-parameter systems governed by first-order, quasilinear hyperbolic partial differential equations that arise in optimal control problems of many physical systems such as fluids dynamics and elastodynamics. The distributed system is controlled via a forced nonlinear periodic boundary condition that describes a boundary control action. Further, the periodic boundary control is subject to a dynamic constraint imposed by a lumped-parameter system governed by ordinary differential equations that model actuator dynamics. The partial differential equations are thus coupled with the ordinary differential equations via the periodic boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to solve a feedback control problem of the Mach number in a wind tunnel.

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26

Banerjee, Arun K. "Block-diagonal equations for multibody elastodynamics with geometric stiffness and constraints." Journal of Guidance, Control, and Dynamics 16, no. 6 (November 1993): 1092–100. http://dx.doi.org/10.2514/3.21132.

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27

Safjan, A., and J. T. Oden. "High-order Taylor-Galerkin and adaptive h-p methods for second-order hyperbolic systems: Application to elastodynamics." Computer Methods in Applied Mechanics and Engineering 103, no. 1-2 (March 1993): 187–230. http://dx.doi.org/10.1016/0045-7825(93)90046-z.

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28

A.Maugin, Gérard. "Applications of an energy-momentum tensor in nonlinear elastodynamics : Pseudomomentum and eshelby stress in solitonic elastic systems." Journal of the Mechanics and Physics of Solids 40, no. 7 (October 1992): 1543–58. http://dx.doi.org/10.1016/0022-5096(92)90035-z.

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29

Wang, Y., and R. K. N. D. Rajapakse. "An Exact Stiffness Method for Elastodynamics of a Layered Orthotropic Half-Plane." Journal of Applied Mechanics 61, no. 2 (June 1, 1994): 339–48. http://dx.doi.org/10.1115/1.2901450.

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Анотація:

A method is presented in this paper to compute displacements and stresses of a multilayered orthotropic elastic half-plane under time-harmonic excitations. The half-plane region under consideration consists of a number of layers with different thicknesses and material properties. Exact layer stiffness matrices describing the relationship between Fourier transforms of displacements and tractions at the upper and bottom surface of each layer are established explicitly by using the analytical general solutions for displacements and stresses of a homogeneous orthotropic elastic medium. The global stiff ness matrix which is also symmetric and banded is assembled by considering the traction continuity conditions at the interface between adjacent layers of the multilayered half-plane. The numerical solution of the global stiffness equation results in the solutions for Fourier transform of displacements at layer interfaces. Thereafter displacements and stresses of the multilayered plane can be obtained by the numerical integration of Fourier integrals. Only negative exponential terms of Fourier transform parameter are found to appear in the elements of layer stiffness matrices. This ensures the numerical stability in the solution of the global stiffness equation. In addition, the size of the final equation system is nearly onehalf of that corresponding to the conventional matrix approach for layered media based on the determination of layer arbitrary coefficients. The present method provides accurate solutions for both displacements and stresses over a wide range of frequencies and layer thicknesses. Selected numerical results are presented to portray the influence of layering, material orthotropy, and frequency of excitation on the response of five layered systems. Time-domain solutions are also presented to demonstrate the features of transient surface displacements due to a surface loading pulse applied to layered orthotropic half-planes.

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30

Räbinä, Jukka, Lauri Kettunen, Sanna Mönkölä, and Tuomo Rossi. "Generalized wave propagation problems and discrete exterior calculus." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 3 (May 2018): 1195–218. http://dx.doi.org/10.1051/m2an/2018017.

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Анотація:

We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulative pollution error can be practically eliminated in the case of harmonic wave problems. The restrictions following from the CFL condition can be bypassed with a local time-stepping scheme. The computational savings are at least one order of magnitude.

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31

Charlotte, Miguel, Ignacio Fernandez Núnez, Yves Gourinat, and Denis Matignon. "Port-Hamiltonian Formulations of Some Elastodynamics Theories of Isotropic and Linearly Elastic Shells: Naghdi–Reissner’s Moderately Thick Shells." Applied Sciences 13, no. 4 (February 17, 2023): 2608. http://dx.doi.org/10.3390/app13042608.

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Анотація:

The port-Hamiltonian system approach is intended to be an innovative and unifying way of modeling multiphysics systems, by expressing all of them as systems of conservation laws. Indeed, the increasing developments in recent years allow finding better control and coupling strategies. This work aimed to apply such an approach to Naghdi–Reissner’s five-kinematic-field shell model in linear elasticity, while including often-neglected higher-order intrinsic geometric coupling effects, therefore preparing the theoretical background required for the coupling (or interconnection) with an acoustic fluid model and the different types of interactions that can arise among them. The model derived thusly can be used for controller design in a wide variety of applications such as inflatable space structures, launcher tank vibration damping, payload vibration protection using smart materials, and many other related applications.

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32

Gaul, L., and M. Wagner. "BEAM RESPONSE DERIVED FROM 3-D HYBRID BOUNDARY INTEGRAL METHOD IN ELASTODYNAMICS." Mechanical Systems and Signal Processing 11, no. 2 (March 1997): 257–68. http://dx.doi.org/10.1006/mssp.1996.0075.

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33

Chen, Zhiguang, Chenguang Yang, Xin Liu, and Min Wang. "Learning control of flexible manipulator with unknown dynamics." Assembly Automation 37, no. 3 (August 7, 2017): 304–13. http://dx.doi.org/10.1108/aa-11-2016-148.

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Анотація:

Purpose The purpose of this paper is to study the controller design of flexible manipulator. Flexible manipulator system is a nonlinear, strong coupling, time-varying system, which is introduced elastodynamics in the study and complicated to control. However, due to the flexible manipulator, system has a significant advantage in response speed, control accuracy and load weight ratio to attract a lot of researchers. Design/methodology/approach Since the order of flexible manipulator system is high, designing controller process will be complex, and have a large amount of calculation, but this paper will use the dynamic surface control method to solve this problem. Findings Dynamic surface control method as a controller design method which can effectively solve the problem with the system contains nonlinear and reduced design complexity. Originality/value The authors assume that the dynamic parameters of flexible manipulator system are unknown, and use Radial Basis Function neural network to approach the unknown system, combined with the dynamic surface control method to design the controller.

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34

Ramakrishnan, Vinod, and Michael J. Frazier. "Architected material with independently tunable mass, damping, and stiffness via multi-stability and kinematic amplification." Journal of the Acoustical Society of America 153, no. 2 (February 2023): 1283–92. http://dx.doi.org/10.1121/10.0017346.

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We report on a class of architected material lattices that exploit multi-stability and kinematic amplification to independently adjust the local effective mass, damping, and stiffness properties, thereby realizing congruent alterations to the acoustic dispersion response post-fabrication. The fundamental structural tuning element permits a broad range in the effective property space; moreover, its particular design carries the benefit of tuning without altering the original size/shape of the emerging structure. The relation between the tuning element geometry and the achieved variability in effective properties is explored. Bloch's theorem facilitates the dynamic analysis of representative one- and two-dimensional (1D/2D) systems, revealing, e.g., bandgap formation, migration, and closure and positive/negative metadamping in accordance with the tuning element configuration. To demonstrate a utility, we improvise a waveguide by appropriately patterning the tuning element configuration within a 2D system. We believe that the proposed strategy offers a new way to expand the range of performance and functionality of architected materials for elastodynamics.

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35

McCoy, John J. "Comments on ‘‘Uniqueness in elastodynamics for systems with nonlocal impedance boundary conditions’’ [J. Acoust. Soc. Am. 100, 3447–3449 (1996)]." Journal of the Acoustical Society of America 100, no. 5 (November 1996): 3450. http://dx.doi.org/10.1121/1.416988.

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36

Hedrih-Stevanovic, Katica. "Advances in classical and analytical mechanics: A reviews of author’s results." Theoretical and Applied Mechanics 40, no. 2 (2013): 293–383. http://dx.doi.org/10.2298/tam1302293h.

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A review, in subjective choice, of author?s scientific results in area of: classical mechanics, analytical mechanics of discrete hereditary systems, analytical mechanics of discrete fractional order system vibrations, elastodynamics, nonlinear dynamics and hybrid system dynamics is presented. Main original author?s results were presented through the mathematical methods of mechanics with examples of applications for solving problems of mechanical real system dynamics abstracted to the theoretical models of mechanical discrete or continuum systems, as well as hybrid systems. Paper, also, presents serries of methods and scientific results authored by professors Mitropolyski, Andjelic and Raskovic, as well as author?s of this paper original scientific research results obtained by methods of her professors. Vector method based on mass inertia moment vectors and corresponding deviational vector components for pole and oriented axis, defined in 1991 by K. Hedrih, is presented. Results in construction of analytical dynamics of hereditary discrete system obtained in collaboration with O. A. Gorosho are presented. Also, some selections of results author?s postgraduate students and doctorantes in area of nonlinear dynamics are presented. A list of scientific projects headed by author of this paper is presented with a list of doctoral dissertation and magister of sciences thesis which contain scientific research results obtained under the supervision by author of this paper or their fist doctoral candidates.

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37

Moshtagh, Ehsan, Morteza Eskandari-Ghadi, and Ernian Pan. "Time-harmonic dislocations in a multilayered transversely isotropic magneto-electro-elastic half-space." Journal of Intelligent Material Systems and Structures 30, no. 13 (May 23, 2019): 1932–50. http://dx.doi.org/10.1177/1045389x19849286.

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Modeling layered systems with dislocations is very challenging; yet, it is important since most smart structures are made of multilayers to make best use of the combined effective property. As such, during the manufactures, defects, such as dislocations, could be introduced in the multilayers. In this article, we analytically find, for the first time, the response of three-dimensional multilayered magneto-electro-elastic systems due to time-harmonic dislocations. The dislocations are the most general, containing the elastic dislocations and discontinuity of the electric potential and/or magnetic potential over a circular region in any layer in the medium. The fully coupled partial differential equations of motion and the Gauss law for the magneto-electro-elastic materials are solved in terms of cylindrical system of vector functions, and the dual variable and position method is further introduced to treat the multilayers. Numerical examples are carried out based on the derived analytical solution to demonstrate the effects of the time-harmonic dislocations on the induced magneto-electro-elastic fields. This analytical solution is important in both electrodynamics and elastodynamics, with possible applications in material sciences and physics. The numerical results are useful in design process of smart devices made of magneto-electro-elastic solids applicable to other engineering fields like renewable energy.

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38

Ben‐Menahem, Ari, and Sergio Kostek. "The equivalent force system of a monopole source in a fluid‐filled open borehole." GEOPHYSICS 56, no. 9 (September 1991): 1477–81. http://dx.doi.org/10.1190/1.1443168.

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One of the major contributors to the complexity of boundary‐value problems pertaining to theoretical modeling of exploration elastodynamics is the presence of both vertical and horizontal discontinuities. It has been known for a long time that it is sometimes possible to replace certain boundaries by a system of images, provided the extra stresses and displacements induced by these images could indeed mimic the discontinuities caused by the said boundaries (e.g., Ben‐Menahem and Singh, 1981). In this vein, we show that part of the field created by a monopole source acting on the axis of a fluid‐filled open borehole surrounded by a homogeneous and isotropic formation, can be reconstructed with the aid of an equivalent force system (EFS) that mimics the geometrodynamic effects of the borehole. The advantages of the EFS are twofold. In the first place, it simplifies the physical setup and brings many seemingly different problems into a common denominator in a sense that they are reduced to fields of known basic force systems. Second, and this is not less important, much computer time is saved and numerical complexities are avoided.

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39

Tortorelli, Daniel A., Stephen C.-Y. Lu, and Robert B. Haber. "Design Sensitivity Analysis for Elastodynamic Systems*." Mechanics Based Design of Structures and Machines 18, no. 1 (March 1, 1990): 77–106. http://dx.doi.org/10.1080/08905459008915660.

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40

Afferrante, L., M. Ciavarella, and J. R. Barber. "Sliding thermoelastodynamic instability." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2071 (March 6, 2006): 2161–76. http://dx.doi.org/10.1098/rspa.2006.1676.

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Numerous mechanisms can give rise to instabilities and vibrations in sliding systems. These can generally be characterized as either elastodynamic (e.g. ‘brake squeal’) or thermoelastic. The time-scales of these processes differ considerably, so it is usual to neglect coupling between them, i.e. to neglect thermal effects in elastodynamic analyses and to use the quasi-static approximation in thermoelastic analyses. In the present paper, we consider the potential coupling between them in the simplest possible context—a thermoelastodynamic layer sliding against a rigid plane and constrained to one-dimensional displacements. The results show that although the coupling is extremely weak, it has a destabilizing effect on the natural elastodynamic vibration of the layer at arbitrarily low sliding speeds. A numerical solution of the transient equations below the quasi-static critical speed shows that an initial disturbance grows exponentially until periods of separation develop, after which the system approaches asymptotically to a steady state involving periods of contact and separation alternating at the lowest natural frequency of the elastodynamic system. With increasing sliding speed, the proportion of the cycle spent in contact is reduced and the maximum contact pressure increases. It is important to note that neither a quasi-static thermoelastic analysis, nor an elastodynamic analysis neglecting thermal expansion would predict instability in this speed range. Similar instabilities due to thermoelastodynamic coupling are almost certain to occur in more complex practical sliding systems such as brakes and clutches, implying the need for the incorporation of these effects in commercial analysis software. The proposed mechanism might also provide an explanation of reported experimental observations of vibrations normal to the contact interface during frictional sliding.

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41

Geib, Nathan, Bogdan-Ioan Popa, and Karl Grosh. "Breaking reciprocity through nonlocal coupling in elastodynamic systems." Journal of the Acoustical Society of America 150, no. 4 (October 2021): A108. http://dx.doi.org/10.1121/10.0007784.

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42

Schiehlen, W., and R. Seifried. "Three Approaches for Elastodynamic Contact in Multibody Systems." Multibody System Dynamics 12, no. 1 (August 2004): 1–16. http://dx.doi.org/10.1023/b:mubo.0000042930.24911.bf.

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43

Gandhi, M. V., B. S. Thompson, S. B. Choi, and S. Shakir. "Electro-Rheological-Fluid-Based Articulating Robotic Systems." Journal of Mechanisms, Transmissions, and Automation in Design 111, no. 3 (September 1, 1989): 328–36. http://dx.doi.org/10.1115/1.3259003.

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The limitations of the current generation of robotic systems has triggered a new research thrust for predicting the elastodynamic response of assemblages of articulating flexible-bodied systems. This research thrust is extended herein by proposing the fabrication of robotic systems in either monolithic or ultra-advanced composite laminated high-strength, high-stiffness materials in which are incorporated electro-rheological fluids. These multiphase fluid systems, which change their rheological behavior instantaneously when subjected to an externally applied electrical field, provide a potential for tailoring the vibrational characteristics of these hybrid materials from which the structural members of the proposed robotic systems are fabricated. This paper is focused on developing the necessary design tools for predicting the vibrational response of flexible multibodied articulating systems fabricated with this new class of advanced materials. A variational theorem is developed herein as a basis for finite element formulations which can be employed to predict the elastodynamic response of these systems. A coherent combination of experimental and theoretical work on cantilevered beams is presented to demonstrate the viability of the proposed design methodology. In addition, computer simulation results are presented to demonstrate the potential payoffs in terms of superior performance characteristics of a new generation of robotic systems capitalizing on this innovative and revolutionary design philosophy.

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44

Alabau, Fatiha, and Vilmos Komornik. "Boundary Observability, Controllability, and Stabilization of Linear Elastodynamic Systems." SIAM Journal on Control and Optimization 37, no. 2 (January 1999): 521–42. http://dx.doi.org/10.1137/s0363012996313835.

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45

Tebou, Louis. "Stabilization of some elastodynamic systems with localized Kelvin-Voigt damping." Discrete and Continuous Dynamical Systems 36, no. 12 (October 2016): 7117–36. http://dx.doi.org/10.3934/dcds.2016110.

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46

Higuera, María, José M. Perales, María-Luisa Rapún, and José M. Vega. "Non-Invasive Testing of Physical Systems Using Topological Sensitivity." Applied Sciences 11, no. 3 (February 2, 2021): 1341. http://dx.doi.org/10.3390/app11031341.

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Анотація:

A review of available results on non-destructive testing of physical systems, using the concept of topological sensitivity, is presented. This mathematical tool estimates the sensitivity of a set of measurements in some given sensors, distributed along the system, to defects/flaws that produce a degradation of the system. Such degradation manifests itself on the properties of the system. The good performance of this general purpose post-processing method is reviewed and illustrated in some applications involving non-destructive testing. These applications include structural health monitoring, considering both elastodynamic ultrasonic guided Lamb waves and active infrared thermography. Related methods can also be used in other fields, such as diagnosis/prognosis of engineering devices, which is also considered.

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47

Zhao, Yongjie. "Kineto-Elastodynamic Characteristics of the Six-Degree-of-Freedom Parallel Structure Seismic Simulator." Journal of Robotics 2011 (2011): 1–17. http://dx.doi.org/10.1155/2011/489695.

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Based on the kineto-elastodynamic assumptions, the dynamic model of the six-degree-of-freedom parallel structure seismic simulator is developed by virtue of the finite element method and the substructure synthesis technique. The kineto-elastodynamic characteristics represented by the natural frequency, the sensitivity analysis, the energy ratios, and the displacement response of the moving platform are investigated. It is shown that the second-order natural frequency is much higher than the first-order natural frequency, and the first-order natural frequency is sensitive to the radius of the strut and the radius of the lead screw. In order to improve the dynamic characteristic of the manipulator, the mass of the moving platform should be reduced or the stiffness of the strut should be increased especially for the sixth strut. For the investigated trajectory, the displacement response of the moving platform along thexdirection is smaller than these displacement responses along theydirection and along thezdirection. The angular displacement response of the moving platform rotating aboutz-axis is slightly larger than those angular displacement responses rotating about thex-axis and about they-axis.

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48

Brossard, R., and J. P. Lohéac. "Boundary stabilization of elastodynamic systems, II. The case of a linear feedback." Journal of Dynamical and Control Systems 16, no. 3 (July 2010): 355–75. http://dx.doi.org/10.1007/s10883-010-9097-5.

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49

Parvini, Mehdi, and Dieter FE Stolle. "Interpretation of pavement deflection measurement data using an elastodynamic stochastic approach." Canadian Journal of Civil Engineering 25, no. 1 (January 1, 1998): 151–60. http://dx.doi.org/10.1139/l97-074.

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Pavement deflection measurements, together with backcalculation procedures, are widely used to estimate the layer moduli of pavement-subgrade systems. Sensitivity analysis of a sample problem indicates that conclusions drawn from static analyses with regards to deflection sensitivity to variation in layer moduli may apply when characterizing uncertainty associated with the interpretation of the falling weight deflectometer (FWD) data. The uncertainty associated with the values of the backcalculated parameters from deflection data is investigated in this paper using an elastodynamic, stochastic finite element approach. The results of the simulations indicate that, in order to properly estimate surface layer moduli, loading frequencies higher than that of excitation by typical FWD loading are required. The low sensitivity of deflection uncertainty to random variations in surface modulus, when compared with that associated with subgrade modulus, is demonstrated to contribute to high variations in backcalculated surface modulus from measured surface deflections. Although focus is placed on uncertainties in elastic modulus and deflection, the methodology presented in the paper can be used to quantify uncertainties associated with other layer properties and pavement responses.Key words: stochastic, finite element, pavement deflection, elastodynamic, backcalculation, layer moduli, falling weight deflectometer test.

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50

Fryer, Gerard J., and L. Neil Frazer. "Seismic waves in stratified anisotropic media - II. Elastodynamic eigensolutions for some anisotropic systems." Geophysical Journal International 91, no. 1 (October 1987): 73–101. http://dx.doi.org/10.1111/j.1365-246x.1987.tb05214.x.

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