Research Article
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Year 2020, Volume: 69 Issue: 1, 158 - 171, 30.06.2020
https://doi.org/10.31801/cfsuasmas.532747

Abstract

References

  • 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.

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

Year 2020, Volume: 69 Issue: 1, 158 - 171, 30.06.2020
https://doi.org/10.31801/cfsuasmas.532747

Abstract

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.

References

  • 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.
There are 25 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Onur Şahin 0000-0001-5389-9855

Publication Date June 30, 2020
Submission Date February 26, 2019
Acceptance Date September 30, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Şahin, O. (2020). Analysis of the Rayleigh wave field due to a tangential load applied on the surface of a coated elastic half-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 158-171. https://doi.org/10.31801/cfsuasmas.532747
AMA Şahin O. Analysis of the Rayleigh wave field due to a tangential load applied on the surface of a coated elastic half-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):158-171. doi:10.31801/cfsuasmas.532747
Chicago Şahin, Onur. “Analysis of the Rayleigh Wave Field Due to a Tangential Load Applied on the Surface of a Coated Elastic Half-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 158-71. https://doi.org/10.31801/cfsuasmas.532747.
EndNote Şahin O (June 1, 2020) Analysis of the Rayleigh wave field due to a tangential load applied on the surface of a coated elastic half-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 158–171.
IEEE O. Şahin, “Analysis of the Rayleigh wave field due to a tangential load applied on the surface of a coated elastic half-space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 158–171, 2020, doi: 10.31801/cfsuasmas.532747.
ISNAD Şahin, Onur. “Analysis of the Rayleigh Wave Field Due to a Tangential Load Applied on the Surface of a Coated Elastic Half-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 158-171. https://doi.org/10.31801/cfsuasmas.532747.
JAMA Şahin O. Analysis of the Rayleigh wave field due to a tangential load applied on the surface of a coated elastic half-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:158–171.
MLA Şahin, Onur. “Analysis of the Rayleigh Wave Field Due to a Tangential Load Applied on the Surface of a Coated Elastic Half-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 158-71, doi:10.31801/cfsuasmas.532747.
Vancouver Şahin O. Analysis of the Rayleigh wave field due to a tangential load applied on the surface of a coated elastic half-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):158-71.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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