Abstract
Propagation of stationary random waves in viscoelastic stratified transverse isotropic materials is investigated. The solid was considered multi-layered and located above the bedrock, which was assumed to be much stiffer than the soil, and the power spectrum density of the stationary random excitation was given at the bedrock. The governing differential equations are derived in frequency and wave-number domains and only a set of ordinary differential equations (ODEs) must be solved. The precise integration algorithm of two-point boundary value problem was applied to solve the ODEs. Thereafter, the recently developed pseudo-excitation method for structural random vibration is extended to the solution of the stratified solid responses.
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References
Ewing W M, Jardetzky W S, Press F.Elastic Waves in Layered Media [M]. McGral-Hill, New York, 1957.
Brekhovskikh L M.Waves in Layered Media [M]. Academic Press, New York, 1980.
Aki K, Richards P B.Quantitative Seismology[M]. W H Freeman and Company, San Francisco, 1980.
Timoshenko S P, Goodier J N.Theory of Elasticity[M]., McGraw-Hill, New York, 1951.
Graff L F.Wave Motion in Elastic Solids[M]. Clarendon Press Oxford, 1975.
Achenback, J D.Wave Propagation in Elastic Solids[M]. The North-Holland, Amsterdam, 1973.
Doyle J F.Wave Propagation in Structures[M]. Springer, New York, 1989.
Rizzi S A, Doyle J F. Spectral analysis of wave motion in plane solids with boundaries[J].Trans ASME Journal of Vibration and Acoustics, 1992.,114 (2): 133–140.
Rizzi S A, Doyle J F. Spectral element approach to wave motion in layered solids[J].Trans ASME Journal of Vibration and Acoustics, 1992,114(4): 569–577.
Alshaikh I A B U, Turhan D, Mengi Y. Two-dimensional transient wave propagation in viscoelastic layered media[J].Journal of Sound and Vibration, 2001,244 (5): 837–858.
Gulyayev V I, Lugovyy P Z, Ivanchenko G M. Discontinuous wave fronts propagation in anisotropic layered media[J].International Journal of Solids and Structures, 2003,40(1): 237–247.
Verma K L. On the propagation of waves in layered anisotropic media in generalized thermoelasticity [J].International Journal of Engineering Science, 2002,40 (20): 2077–2096.
Caviglia G, Morro A. Reflection and transmission in anisotropic dissipative multilayers[J].European Journal of Mechanics A/Solids, 2002,21(16): 1055–1067.
Caviglia, G, Morro A. Riccati equations for wave propagation in planarly-stratified solids[J].European Journal of Mechanics A/Solids, 2000,19 (4): 721–741.
Caviglia G, Morro A. Wave propagation in multilayered anisotropic solids[J].International Journal of Engineering Science, 2000,38 (8): 847–863.
Thomson C J. Modelling surface waves in anisotropic structures—I: Theory[J].Physics of Earth and Planetary Interiors, 1997,103 (3): 195–206.
Zhang Jianfeng, Li Youming. Numerical simulation of elastic wave propagation in inhomogeneous media[J].Wave Motion, 1997,25 (12): 109–125.
Vashishth A K, Khurana P. Inhomogeneous waves in anisotropic porous layered overlying solid bedrock[J].Journal of Sound and Vibration, 2002,258 (4): 577–594.
Khoury R A L, Scarpas A, Kasbergen C,et al. Spectral element technique for efficient parameter identification of layered media—Part III: Viscoelastic aspects[J].International Journal of Solids and Structures, 2002,39 (8): 2189–2201.
Khoury R A L, Kasbergen C, Scarpas A,et al. Poroelastic spectral element for wave propagation and parameter identification in multi-layer systems[J].International Journal of Solids and Structures, 2002,39 (15): 4073–4091.
Zhong Wanxie. The method of precise integration of finite strip and wave guide problems [A]. In: Lee P K K, Tham L G, Cheung Y K (eds).Proceeding of International Conference on Computational Methods in Structural and Geotechnical Engineering[C]. China Translation & Printing Services Ltd, Hong Kong, 1994, 51–59.
Lin Jiahao. A fast CQC algorithm of PSD matrices for random seismic responses[J].Computers and Structures, 1992,44 (3): 683–687.
Lin Jiahao, Williams F W, Zhang Wenshou. A new approach to multiphase-excitation stochastic seismic response[J].Microcomputers in Civil Engineering, 1993,8 (4): 283–290.
Williams F W, Bennett P N, Lin Jiahao. Localization investigation of stationary random wave transmission along damped ordered structural chains[J].Proc Inst Mech Engrs, Part C, 1997,211: 217–228.
Lin Jiahao, Fan Yue, Bennett P N,et al Propagation of stationary random waves along substructural chains[J].Journal of Vibration and Acoustics, 1995,180 (5): 757–767.
Lin Jiahao, Zhang Wenshou, Li Jianjun. Structural responses to arbitrarily coherent stationary random excitations[J].Computers and Structures, 1994,50 (5): 629–633.
Kennett B L N.Seismic Wave Propagation in Stratified Media[M]. Cambridge University Press, Cambridge, 1983.
Zhong Wanxie,Dual System in Applied Mechanics[M]. Science Press, Beijing, 2002 (in CHinese).
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Communicated by ZHONG Wan-xie
Project supported by the National Natural Science Foundation of China (No. 10472023) and the Special Fund for PhD Program of Education Ministry of China (No. 20040141020)
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Qiang, G., Jia-hao, L. Stationary random waves propagation in 3D viscoelastic stratified solid. Appl Math Mech 26, 785–796 (2005). https://doi.org/10.1007/BF02465430
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DOI: https://doi.org/10.1007/BF02465430