Analysis of the Rayleigh wave field due to a tangential load applied on the surface of a coated elastic half-space

Yıl 2020, Cilt: 69 Sayı: 1, 158 - 171, 30.06.2020

Onur Şahin

https://doi.org/10.31801/cfsuasmas.532747

Cited By: 2

Öz

The paper deals with 3D dynamic response of a coated elastic half space subject to in-plane surface loading.  The problem is formulated by a pair of elliptic equations over the interior and a two dimensional singularly perturbed hyperbolic equation expressed in terms of shear wave potentials along the interface. As an example, a point force acting one of the in-plane axis is considered and the integral solution of the normal displacement along the interface is derived through the use of the relation between the wave potentials.

Anahtar Kelimeler

Rayleigh wave, thin coating, asymptotic model

Kaynakça

• Rayleigh, J. W. S., On waves propagated along the plane surface of an elastic solid, Proc. Lond. Math. Soc. 17, (1885), 4–11.
• Friedlander, F. G., On the total reflection of plane waves, Quart. J. Mech. Appl. Math, 1, (1948), 376–384.
• Chadwick, P., Surface and interfacial waves of arbitrary form in isotropic elastic media, J. Elast, 6, (1976), 73–80.
• Kiselev, A. P. and Parker, D. F., Omni-directional Rayleigh, Stoneley and Schlte waves with general time dependence, Proc. R. Soc. Lond. A, 466(2120), (2010), 2241–2258.
• Knowles, J. K., A note on elastic surface waves, J. Geophys. Res., 71, (1966), 5480–5481.
• Kaplunov, J. D. and Kossovich, L. Y., Asymptotic model of Rayleigh waves in the far-field zone in an elastic half-plane, Dokl. Phys., 49, (2004), 234–236.
• Kaplunov, J. D., Kossovich, L., and Zakharov, A., An explicit asymptotic model for the Bleustein-Gulyaev wave, C. R. Mecanique, 332, (2004), 487–492.
• Kaplunov J., Zakharov A. and Prikazchikov D. A., Explicit models for elastic and piezoelastic surface waves, IMA J. Appl. Math., 71, (2006), 768–782.
• Dai, H. H., Kaplunov J. and Prikazchikov D.A., A long-wave model for the surface elastic wave in a coated half-space, Proc. R. Soc. A., 466, (2010), 3097–3116.
• Ege, N., Erbaş, B., and Prikazchikov, D. A., On the 3D Rayleigh wave field on an elastic half-space subject to tangential surface loads, ZAMM Journal of Applied Mathematics and Mechanics/Zeitschrift fr Angewandte Mathematik und Mechanik, 95(12), (2015), 1558–1565.
• Cole, J., Huth, J., Stresses produced in a half plane by moving loads, J. Appl. Mech., 25, (1958), 43–436.
• Freund, L.B., Wave motion in an elastic solid due to a nonuniformly moving line load, Quart. Appl. Math., 30, (1972), 27–281.
• Agostinacchio, M., Ciampa, D., Diomedi, M. and Olita, S., Parametrical analysis of the railways dynamic response at high speed moving loads, J. Mod. Transp., 21(3), (2013), 169–181.
• Cao, Y., Xia, H. and Li, Z., A semi-analytical/FEM model for predicting ground vibrations induced by high- speed train through continuous girder bridge, J. Mech. Sci. Technol., 26(8), (2012), 2485–2496.
• Kaplunov, J. D., Prikazchikov, D. A., Erbaş, B., and Şahin, O., On a 3D moving load problem for an elastic half space, Wave Motion, 50(8), (2013), 1229–1238.
• Erbaş, B., Kaplunov, J., Prikazchikov, D. A., and Şahin, O., The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space, Mathematics and Mechanics of Solids, 22(1), (2017), 89–100.
• Erbaş, B. and Şahin, O., On the causality of the Rayleigh wave, Journal of mechanics of materials and structures 11(4), (2016), 449–461.
• Ege, N., Şahin, O., and Erbaş, B., Response of a 3D elastic half-space to a distributed moving load, Hacettepe Journal of Mathematics and Statistics, 46(5), (2017), 817–828.
• Şahin, O., and Ege, N., Surface displacement field of a coated elastic half-space under the Influence of a moving distributional load, Anadolu U ̈niversitesi Bilim Ve Teknoloji Dergisi-B Teorik Bilimler, 5(1), (2017), 77–90.
• Achenbach, J.D., Wave propagation in elastic solids, North-Holland, Amsterdam, 1973.
• Georgiadis, H. G. and Lykotrafitis, G., A method based on the Radon transform for three-dimensional elastodynamic problems of moving loads, J. Elast., 65, (2001), 87–129.
• Polyanin, A. D., and Nazaikinskii, V. E., Handbook of linear partial differential equations for engineers and scientists. Chapman and hall/crc., 2015.
• Prikazchikov, D. A., Rayleigh waves of arbitrary profile in anisotropic media, Mechanics Research Communications, 50, (2013), 83–86.
• Shuvalov, A. L., and Every, A. G., On the long-wave onset of dispersion of the surface-wave velocity in coated solids, Wave Motion, 45(6), (2008), 857–863.
• Romeo, M., Rayleigh waves on a viscoelastic solid half-space, J. Acoust. Soc. Am., 110, (2001), 59–67.