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Готові списки джерел за темами / Elastic rods and waves / Статті в журналах

Щоб переглянути інші типи публікацій з цієї теми, перейдіть за посиланням: Elastic rods and waves.

Статті в журналах з теми "Elastic rods and waves"

Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 29 січня 2023

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1

Coleman, Bernard D., and Ellis H. Dill. "Flexure waves in elastic rods." Journal of the Acoustical Society of America 91, no. 5 (May 1992): 2663–73. http://dx.doi.org/10.1121/1.402974.

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2

Lenells, Jonatan. "Traveling waves in compressible elastic rods." Discrete & Continuous Dynamical Systems - B 6, no. 1 (2006): 151–67. http://dx.doi.org/10.3934/dcdsb.2006.6.151.

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3

Borshch, E. I., E. V. Vashchilina, and V. I. Gulyaev. "Helical traveling waves in elastic rods." Mechanics of Solids 44, no. 2 (April 2009): 288–93. http://dx.doi.org/10.3103/s0025654409020149.

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4

Đuričković, Bojan, Alain Goriely, and Giuseppe Saccomandi. "Compact waves on planar elastic rods." International Journal of Non-Linear Mechanics 44, no. 5 (June 2009): 538–44. http://dx.doi.org/10.1016/j.ijnonlinmec.2008.10.007.

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5

Coleman, Bernard D., and Daniel C. Newman. "On waves in slender elastic rods." Archive for Rational Mechanics and Analysis 109, no. 1 (1990): 39–61. http://dx.doi.org/10.1007/bf00377978.

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6

Thurston, R. N. "Elastic waves in rods and optical fibers." Journal of the Acoustical Society of America 89, no. 4B (April 1991): 1901. http://dx.doi.org/10.1121/1.2029441.

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7

Soerensen, M. P., P. L. Christiansen, P. S. Lomdahl, and O. Skovgaard. "Solitary waves on nonlinear elastic rods. II." Journal of the Acoustical Society of America 81, no. 6 (June 1987): 1718–22. http://dx.doi.org/10.1121/1.394786.

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8

Thurston, R. N. "Elastic waves in rods and optical fibers." Journal of Sound and Vibration 159, no. 3 (December 1992): 441–67. http://dx.doi.org/10.1016/0022-460x(92)90752-j.

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9

Antman, Stuart S., and Gregory M. Crosswhite. "Planar Travelling Waves in Incompressible Elastic Rods." Methods and Applications of Analysis 11, no. 3 (2004): 431–46. http://dx.doi.org/10.4310/maa.2004.v11.n3.a13.

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10

Krishnaswamy, Shankar, and R. C. Batra. "On Extensional Oscillations and Waves in Elastic Rods." Mathematics and Mechanics of Solids 3, no. 3 (September 1998): 277–95. http://dx.doi.org/10.1177/108128659800300302.

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11

Cetin, Hakan, and Goksenin Yaralioglu. "Coriolis Effect on elastic waves propagating in rods." Journal of Sound and Vibration 485 (October 2020): 115545. http://dx.doi.org/10.1016/j.jsv.2020.115545.

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12

Martin, P. A. "On flexural waves in cylindrically anisotropic elastic rods." International Journal of Solids and Structures 42, no. 8 (April 2005): 2161–79. http://dx.doi.org/10.1016/j.ijsolstr.2004.09.015.

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13

Jian-gang, Guo, Zhou Li-jun, and Zhang Shan-yuan. "Geometrical nonlinear waves in finite deformation elastic rods." Applied Mathematics and Mechanics 26, no. 5 (May 2005): 667–74. http://dx.doi.org/10.1007/bf02466342.

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14

Hasan, M. Arif, Lazaro Calderin, Trevor Lata, Pierre Lucas, Keith Runge, and Pierre A. Deymier. "Directional Elastic Pseudospin and Nonseparability of Directional and Spatial Degrees of Freedom in Parallel Arrays of Coupled Waveguides." Applied Sciences 10, no. 9 (May 4, 2020): 3202. http://dx.doi.org/10.3390/app10093202.

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Анотація:

We experimentally and numerically investigated elastic waves in parallel arrays of elastically coupled one-dimensional acoustic waveguides composed of aluminum rods coupled along their length with epoxy. The elastic waves in each waveguide take the form of superpositions of states in the space of direction of propagation. The direction of propagation degrees of freedom is analogous to the polarization of a quantum spin; hence, these elastic waves behave as pseudospins. The amplitude in the different rods of a coupled array of waveguides (i.e., the spatial mode of the waveguide array) refer to the spatial degrees of freedom. The elastic waves in a parallel array of coupled waveguides are subsequently represented as tensor products of the elastic pseudospin and spatial degrees of freedom. We demonstrate the existence of elastic waves that are nonseparable linear combinations of tensor products states of pseudospin/ spatial degrees of freedom. These elastic waves are analogous to the so-called Bell states of quantum mechanics. The amplitude coefficients of the nonseparable linear combination of states are complex due to the Lorentzian character of the elastic resonances associated with these waves. By tuning through the amplitudes, we are able to navigate both experimentally and numerically a portion of the Bell state Hilbert space.

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15

Nielsen, R. B., and S. V. Sorokin. "Periodicity effects of axial waves in elastic compound rods." Journal of Sound and Vibration 353 (September 2015): 135–49. http://dx.doi.org/10.1016/j.jsv.2015.05.013.

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16

de Luna, Manuel Quezada, Bojan Đuričković, and Alain Goriely. "Non-linear waves in heterogeneous elastic rods via homogenization." International Journal of Non-Linear Mechanics 47, no. 2 (March 2012): 197–205. http://dx.doi.org/10.1016/j.ijnonlinmec.2011.05.005.

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17

Beliaev, Alexei, and Andrej Il'ichev. "Conditional stability of solitary waves propagating in elastic rods." Physica D: Nonlinear Phenomena 90, no. 1-2 (January 1996): 107–18. http://dx.doi.org/10.1016/0167-2789(95)00219-7.

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18

Wei, Dongming, Piotr Skrzypacz, and Xijun Yu. "Nonlinear Waves in Rods and Beams of Power-Law Materials." Journal of Applied Mathematics 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/2095425.

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Анотація:

Some novel traveling waves and special solutions to the 1D nonlinear dynamic equations of rod and beam of power-law materials are found in closed forms. The traveling solutions represent waves of high elevation that propagates without change of forms in time. These waves resemble the usual kink waves except that they do not possess bounded elevations. The special solutions satisfying certain boundary and initial conditions are presented to demonstrate the nonlinear behavior of the materials. This note demonstrates the apparent distinctions between linear elastic and nonlinear plastic waves.

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19

Krishnaswamy, Shankar, and R. C. Batra. "Addendum to "On Extensional Oscillations and Waves in Elastic Rods"." Mathematics and Mechanics of Solids 3, no. 3 (September 1998): 297–301. http://dx.doi.org/10.1177/108128659800300303.

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20

Ablowitz, M. J., V. Barone, S. De Lillo, and M. Sommacal. "Traveling Waves in Elastic Rods with Arbitrary Curvature and Torsion." Journal of Nonlinear Science 22, no. 6 (July 13, 2012): 1013–40. http://dx.doi.org/10.1007/s00332-012-9136-3.

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21

Zheng, J., P. Xu, Q. Fu, R. P. Taleyarkhan, and S. H. Kim. "Elastic stress waves of cylindrical rods subjected to rapid energy deposition." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 218, no. 4 (April 1, 2004): 359–68. http://dx.doi.org/10.1177/095440620421800401.

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Анотація:

Rapid energy deposition into targets and beam absorbers in a high-energy accelerator leads to a temperature rise at an enormous rate, giving rise to thermally induced stress waves. Understanding and predicting the resulting stresses are crucial for robust design and safe operation of such devices. In this paper, closed-form expressions for the induced stresses in cylindrical rods subjected to rapid partial energy deposition have been directly derived; they are then used to estimate the highest stress of long cylindrical absorbers and to test the accuracy of thermal shock simulation using finite element analysis (FEA) codes. Characteristics of such stresses were discussed in detail. It was found that ANSYS may produce accurate details in thermal shock simulation if element size and time step used in the simulation model meet the criteria proposed by Zheng and co-workers in another paper.

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22

Constantin, Adrian, and Walter A. Strauss. "Stability of a class of solitary waves in compressible elastic rods." Physics Letters A 270, no. 3-4 (May 2000): 140–48. http://dx.doi.org/10.1016/s0375-9601(00)00255-3.

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23

Garbuzov, F. E., K. R. Khusnutdinova, and I. V. Semenova. "On Boussinesq-type models for long longitudinal waves in elastic rods." Wave Motion 88 (May 2019): 129–43. http://dx.doi.org/10.1016/j.wavemoti.2019.02.004.

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24

de Billy, M. "Crossing of acoustic envelope solitary waves in homogeneous elastic rods: Experiments." Ultrasonics 72 (December 2016): 42–46. http://dx.doi.org/10.1016/j.ultras.2016.07.009.

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25

Coleman, B. D., and J. M. Xu. "On the interaction of solitary waves of flexure in elastic rods." Acta Mechanica 110, no. 1-4 (March 1995): 173–82. http://dx.doi.org/10.1007/bf01215423.

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26

Hayek, Alaa, Serge Nicaise, Zaynab Salloum, and Ali Wehbe. "Exponential and polynomial stability results for networks of elastic and thermo-elastic rods." Discrete & Continuous Dynamical Systems - S 15, no. 5 (2022): 1183. http://dx.doi.org/10.3934/dcdss.2021142.

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Анотація:

<p style='text-indent:20px;'>In this paper, we investigate a network of elastic and thermo-elastic materials. On each thermo-elastic edge, we consider two coupled wave equations such that one of them is damped via a coupling with a heat equation. On each elastic edge (undamped), we consider two coupled conservative wave equations. Under some conditions, we prove that the thermal damping is enough to stabilize the whole system. If the two waves propagate with the same speed on each thermo-elastic edge, we show that the energy of the system decays exponentially. Otherwise, a polynomial energy decay is attained. Finally, we present some other boundary conditions and show that under sufficient conditions on the lengths of some elastic edges, the energy of the system decays exponentially on some particular networks similar to the ones considered in [<xref ref-type="bibr" rid="b18">18</xref>].</p>

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27

Gau, W. H., and A. A. Shabana. "Use of the Finite Element Method in the Analysis of Impact-Induced Longitudinal Waves in Constrained Elastic Systems." Journal of Mechanical Design 117, no. 2A (June 1, 1995): 336–42. http://dx.doi.org/10.1115/1.2826144.

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Анотація:

In rotating elastic rods, dispersions occurs as the result of the finite rotations. By using Fourier method, it can be shown that the impact-induced longitudinal waves no longer travel with the same phase velocities. Furthermore, the speeds of the wave propagation are independent of the impact conditions including the value of the coefficient of restitution. In this investigation the use of the finite element method in the analysis of impact-induced longitudinal waves in rotating elastic rods is examined. The equations of motion are developed using the principle of virtual work in dynamics. Jump discontinuity in the system velocity vector as result of impact is predicted using the generalized impulse momentum equations. The solution obtained using the finite element method is compared with the solution obtained using Fourier method. Numerical results show that there is a good agreement between the solution obtained by using Fourier method and the finite element solution in the analysis of wave motion. However, discrepancies between the two solutions in the analysis of the velocity waves are observed and discussed in this paper.

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28

Miranda, Edson J. P. de, Edilson D. Nobrega, Leopoldo P. R. de Oliveira, and José M. C. Dos Santos. "Elastic wave propagation in metamaterial rods with periodic shunted piezo-patches." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 2 (August 1, 2021): 4303–11. http://dx.doi.org/10.3397/in-2021-2657.

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The wave propagation attenuation in low frequencies by using piezoelectric elastic metamaterials has been developed in recent years. These piezoelectric structures exhibit abnormal properties, different from those found in nature, through the artificial design of the topology or exploring the shunt circuit parameters. In this study, the wave propagation in a 1-D elastic metamaterial rod with periodic arrays of shunted piezo-patches is investigated. This piezoelectric metamaterial rod is capable of filtering the propagation of longitudinal elastic waves over a specified range of frequency, called band gaps. The complex dispersion diagrams are obtained by the extended plane wave expansion (EPWE) and wave finite element (WFE) approaches. The comparison between these methods shows good agreement. The Bragg-type and locally resonant band gaps are opened up. The shunt circuits influence significantly the propagating and the evanescent modes. The results can be used for elastic wave attenuation using piezoelectric periodic structures.

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29

Wang, Zijian, Jianxun Liu, Chen Fang, Kui Wang, Lianbo Wang, and Zhishen Wu. "Nondestructive measurements of elastic constants of thin rods based on guided waves." Mechanical Systems and Signal Processing 170 (May 2022): 108842. http://dx.doi.org/10.1016/j.ymssp.2022.108842.

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30

Saccomandi, Giuseppe. "Elastic rods, Weierstrass’ theory and special travelling waves solutions with compact support." International Journal of Non-Linear Mechanics 39, no. 2 (March 2004): 331–39. http://dx.doi.org/10.1016/s0020-7462(02)00192-0.

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31

Bayanov, E. V., and A. I. Gulidov. "Propagation of elastic waves in circular rods homogeneous over the cross section." Journal of Applied Mechanics and Technical Physics 52, no. 5 (September 2011): 808–14. http://dx.doi.org/10.1134/s0021894411050166.

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32

Zhang, Shan-yuan, and Zhi-fang Liu. "Three kinds of nonlinear dispersive waves in elastic rods with finite deformation." Applied Mathematics and Mechanics 29, no. 7 (July 2008): 909–17. http://dx.doi.org/10.1007/s10483-008-0709-2.

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33

Dai, H. H., and Y. Huo. "Asymptotically approximate model equations for nonlinear dispersive waves in incompressible elastic rods." Acta Mechanica 157, no. 1-4 (March 2002): 97–112. http://dx.doi.org/10.1007/bf01182157.

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34

Duan, Kai, De Shun Liu, Chang Yue Sun, and Zhi Gao Yang. "Study on Method and Experiment of Characteristics Impedance Calculation of Elastic Bars Based on Incident Wave and Reflected Wave." Advanced Materials Research 518-523 (May 2012): 3784–91. http://dx.doi.org/10.4028/www.scientific.net/amr.518-523.3784.

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Анотація:

Characteristics impedance is a very important physics parameter for many applications in rock fragmenting and percussive drilling. When the shape of the elastic bar is very complicate, it is difficult to calculate the characteristics impedance of the elastic bar with its definition. A method which uses the incident wave and reflected wave to calculate the characteristics impedance of elastic rods is presented. Firstly, the relationship of the incident wave, reflected wave and the characteristics impedance of elastic rods is studied on the basis of the reflection and transmission laws of elastic waves and, the resolution model is established; Then impact experiments were carried out in which a drilling bit with step cross-section was designed. The signal processing of eliminating polynomial trend item and discrete wavelet de-noising were done to stress signals before calculation to decrease the error. It is proved that the method is adequately accurate from the testing results.

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35

KOBAYASHI, Hidetoshi, Naoki NUMA, Kinya OGAWA, Keitaro HORIKAWA, and Ken-ichi TANIGAKI. "An Attempt to Lengthen Duration of Elastic Waves Propagating in Connected Stepped Rods." Journal of the Society of Materials Science, Japan 67, no. 11 (November 15, 2018): 957–63. http://dx.doi.org/10.2472/jsms.67.963.

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36

Kulikovskii, A. G., and A. P. Chugainova. "Discontinuity Structures of Solutions to Equations Describing Longitudinal–Torsional Waves in Elastic Rods." Doklady Physics 66, no. 4 (April 2021): 110–13. http://dx.doi.org/10.1134/s1028335821040017.

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37

TANAKA, Koichi, and Shigeiku ENOMOTO. "Dispersive waves along elastic rods subjected to local heating. (1st report. Analytical investigation)." Transactions of the Japan Society of Mechanical Engineers Series A 53, no. 496 (1987): 2313–17. http://dx.doi.org/10.1299/kikaia.53.2313.

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38

TANAKA, Koichi, Shigeiku ENOMOTO, Fujio ANDO, and Tomonori OHYA. "Dispersive waves along elastic rods subjected to local heating. (2nd report. Experimental investigation)." Transactions of the Japan Society of Mechanical Engineers Series A 53, no. 496 (1987): 2318–23. http://dx.doi.org/10.1299/kikaia.53.2318.

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39

Erofeev, V. I., and A. V. Leonteva. "Localized bending and longitudinal waves in rods interacting with external nonlinear elastic medium." Journal of Physics: Conference Series 1348 (December 2019): 012004. http://dx.doi.org/10.1088/1742-6596/1348/1/012004.

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40

Lundberg, B., J. Carlsson, and K. G. Sundin. "Analysis of elastic waves in non-uniform rods from two-point strain measurement." Journal of Sound and Vibration 137, no. 3 (March 1990): 483–93. http://dx.doi.org/10.1016/0022-460x(90)90813-f.

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41

Lu, Kuan, Yongjun Tian, Nansha Gao, Lizhou Li, Hongxia Lei, and Mingrang Yu. "Propagation of longitudinal waves in the broadband hybrid mechanism gradient elastic metamaterials rods." Applied Acoustics 171 (January 2021): 107571. http://dx.doi.org/10.1016/j.apacoust.2020.107571.

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42

Liu, Xiling, Feng Xiong, Qin Xie, Xiukun Yang, Daolong Chen, and Shaofeng Wang. "Research on the Attenuation Characteristics of High-Frequency Elastic Waves in Rock-Like Material." Materials 15, no. 19 (September 23, 2022): 6604. http://dx.doi.org/10.3390/ma15196604.

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Анотація:

In order to study the frequency-dependent attenuation characteristics of high-frequency elastic waves in rock-like materials, we conducted high-frequency elastic wave attenuation experiments on marble, granite, and red sandstone rods, and investigated the frequency dependence of the attenuation coefficient of high-frequency elastic waves and the frequency dependence of the attenuation of specific frequency components in elastic waves. The results show that, for the whole waveform packet of the elastic wave signal, the attenuation coefficient and the elastic wave frequency have an approximate power relationship, with the exponents of this power function being 0.408, 0.420, and 0.384 for marble, granite, and red sandstone, respectively, which are close to 1/2 the exponent value obtained theoretically by the Kelvin–Voigt viscoelastic model. However, when the specific frequency components are tracked during the elastic wave propagation, the exponents of the power relationship between the attenuation coefficient and frequency are 0.982, 1.523, and 0.860 for marble, granite, and red sandstone, respectively, which indicate that the relationship between the attenuation coefficient and frequency is rock-type dependent. Through the analysis of rock microstructure, we demonstrate that this rock-type-dependent relationship is mainly caused by the scattering attenuation component due to the small wavelength of the high-frequency elastic wave. Therefore, the scattering attenuation component may need to be considered when the Kelvin–Voigt model is used to describe high-frequency elastic wave attenuation in rock-like materials. The results of this research are of good help for further understanding the attenuation characteristics of high-frequency elastic waves in rock-like materials.

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43

Ghodake, Pravinkumar R. "Design optimization of metamaterials to control waves in cylindrical rods." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A56. http://dx.doi.org/10.1121/10.0010642.

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Анотація:

Metamaterials can control different modes of waves by tuning their bandgap structures. Various design strategies are implemented to obtain desired responses of metamaterials by solving multiple forward problems using parametric sweeps, topology, and shape optimization problems. This study focuses on the design of cylindrical metamaterials to control wave propagation in a cylindrical rod using a shape optimization approach. Topology optimization requires relatively more computational resources and time as well as it also gives relatively complex structures in comparison with shape optimization. Optimal widths of layered elastic materials arranged periodically along an axis, on subsurface, and an outer surface of cylindrical surface are obtained by solving multiple time-dependent shape optimization problems. Optimization problems are solved using the finite element method and non-gradient optimization algorithm. Single and multi-objective functions are defined to reduce only axial and both axial as well as radial displacements integrated over the end surface, and monochromatic Gaussian input pulse is considered in this study. Every design solution obtained during each design iteration can be easily manufactured as a weak constraint is applied to the total length of the metamaterial. Prior knowledge of possible bandgaps helps to set an effective optimization problem, but it is not a necessary condition.

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44

Khajehtourian, Romik, and Mahmoud I. Hussein. "Dispersion relation for harmonic generation in nonlinear elastic waves." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A40. http://dx.doi.org/10.1121/10.0010587.

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Анотація:

We present a theory for the dispersion of generated harmonics in a traveling nonlinear wave. The harmonics dispersion relation—derived by the theory—provides direct and exact prediction of the collective harmonics spectrum in the frequency-wavenumber domain and does so without prior knowledge of the spatial-temporal solution. The new relation is applicable to a family of initial wave functions characterized by an initial amplitude and wavenumber. We demonstrate the theory on nonlinear elastic waves in a homogeneous rod and demonstrate its extension to periodic rods. We investigate a thick elastic rod admitting longitudinal motion. In the linear limit, this rod is dispersive due to the effect of lateral inertia. The nonlinearity is introduced through either the stress–strain relation and/or the strain–displacementgradient relation. Using a theory we have developed earlier, we derive an exact general nonlinear dispersion relation for the thick rod. We then derive a special case of this relation and show that it provides an exact prediction of the generated harmonics spectrum, in frequency versus wavenumbers. Both relations are validated by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) for the general nonlinear dispersion relation and short-term, pre-breaking dispersion (by Fourier transformations) for both the general and specialized relation.

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45

Мокряков, Вячеслав Викторович. "Localization of maximal stresses in axisymmetric waves in elastic rods for positive Poisson’s ratio." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 2(44) (December 14, 2020): 95–100. http://dx.doi.org/10.37972/chgpu.2020.44.2.010.

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Анотація:

Рассмотрены максимальные напряжения в осесимметричных волнах в упругих стержнях для положительных значений коэффициента Пуассона. Обнаружена особая длина волны, для которой имеет место наибольшее значение максимального растяжения на оси по отношению к максимальному растяжению на поверхности. Показано, что и особая длина волна, и наибольшее значение отношений растяжений не зависят от коэффициента Пуассона. The maximum stresses in axisymmetric waves in elastic rods for positive values of the Poisson’s ratio are considered. A special wavelength has been found for which the ratio of axial maximal extension to surface maximal extension has the largest value. It is shown that both the special wavelength and the largest value of the extensions ratio are independent of the Poisson’s ratio.

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46

Ilyashenko, A. V., and S. V. Kuznetsov. "Longitudinal Pochhammer — Chree Waves in Mild Auxetics and Non-Auxetics." Journal of Mechanics 35, no. 3 (July 2, 2018): 327–34. http://dx.doi.org/10.1017/jmech.2018.13.

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ABSTRACTThe exact solutions of Pochhammer — Chree equation for propagating harmonic waves in isotropic elastic cylindrical rods, are analyzed. Spectral analysis of the matrix dispersion equation for the longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of the wave polarization due to variation of Poisson’s ratio for mild auxetics (Poisson’s ratio is greater than -0.5) is analyzed and compared with the non-auxetics. It is observed that polarization of the waves for both considered cases (auxetics and non-auxetics) exhibits abnormal behavior in the vicinity of the bulk shear wave speed.

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GAMA, R. M. S. "A NON-LINEAR PROBLEM ARISING FROM THE DESCRIPTION OF THE WAVE PROPAGATION IN LINEAR ELASTIC RODS." Latin American Applied Research - An international journal 49, no. 1 (January 31, 2019): 61–63. http://dx.doi.org/10.52292/j.laar.2019.286.

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In this work it is presented the modeling and the simulation of the dynamics of an elastic rod, taking into account the kinematic constraint arising from the Classical Continuum Mechanics. The simulation involves shock waves that consists of contact shocks when the kinematic constraint does not need to be imposed.

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48

Hu, Bin, Werner Schiehlen, and Peter Eberhard. "Comparison of Analytical and Experimental Results for Longitudinal Impacts on Elastic Rods." Journal of Vibration and Control 9, no. 1-2 (January 2003): 157–74. http://dx.doi.org/10.1177/107754603030745.

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In this paper, the dynamic problem of a rigid body colliding with an elastic rod is studied in some detail. Different contact theories for modeling impact responses are compared with experimental measurements. Based on an idea originally presented by Sears for collisions of two rods with rounded ends, a boundary approach combining Hertzian contact law and St. Venant's elastodynamics is developed to describe longitudinal waves in rods. It is shown that this boundary approach agrees very well with experimental results. For the simulation of long-term dynamic behavior after impact, a traditional rigid-body approach is advantageous because the elastic vibration of the rod will decay fast due to the structural damping and the elastic rod then moves like a rigid body. Hence, for modeling longitudinal impacts, it is suggested that both elastodynamics and rigid-body dynamics are combined into a two-timescale model. The short time behavior of wave propagation due to impacts is modeled using elastodynamics, and the state of the rigid-body mode is transferred to the rigid-body approach as the initial condition for the motion. The long-term behavior after impact is then computed using the rigid-body approach.

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49

Zeng, Yi, Liyun Cao, Sheng Wan, Tong Guo, Shuowei An, Yan-Feng Wang, Qiu-Jiao Du, Brice Vincent, Yue-Sheng Wang, and Badreddine Assouar. "Inertially amplified seismic metamaterial with an ultra-low-frequency bandgap." Applied Physics Letters 121, no. 8 (August 22, 2022): 081701. http://dx.doi.org/10.1063/5.0102821.

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In last two decades, it has been theoretically and experimentally demonstrated that seismic metamaterials are capable of isolating seismic surface waves. Inertial amplification mechanisms with small mass have been proposed to design metamaterials to isolate elastic waves in rods, beams, and plates at low frequencies. In this Letter, we propose an alternative type of seismic metamaterial providing an ultra-low-frequency bandgap induced by inertial amplification. A unique kind of inertially amplified metamaterial is first conceived and designed. Its bandgap characteristics for flexural waves are then numerically and experimentally demonstrated. Finally, the embedded inertial amplification mechanism is introduced on a soil substrate to design a seismic metamaterial capable of strongly attenuating seismic surface waves around a frequency of 4 Hz. This work provides a promising alternative way to conceive seismic metamaterials to steer and control surface waves.

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50

Oliynik, V. N. "The dispersion of waves in a system of elastic rods periodically supported with flexible elements." Reports of the National Academy of Sciences of Ukraine, no. 8 (August 22, 2017): 27–33. http://dx.doi.org/10.15407/dopovidi2017.08.027.

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