The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space

Abstract

This paper deals with the three-dimensional analysis of the near-resonant regimes of a point load, moving steadily along the surface of a coated elastic half-space. The approach developed relies on a specialized hyperbolic–elliptic formulation for the wave field, established earlier by the authors. Straightforward integral solutions of the two-dimensional perturbed wave equation describing wave propagation along the surface are derived along with their far-field asymptotic expansions obtained using the uniform stationary phase method. Both sub-Rayleigh and super-Rayleigh cases are studied. It is shown that the singularities arising at the contour of the Mach cones typical of the super-Rayleigh case, are smoothed due to the dispersive effect of the coating.

Keywords

3D elasticity moving load Rayleigh wave thin coating uniform asymptotics

Get full access to this article

View all access options for this article.

References

Cao

Xia

. A semi-analytical/FEM model for predicting ground vibrations induced by high-speed train through continuous girder bridge. J Mech Sci Technol 2012; 26: 2485–2496.

Fryba

. Vibration of solids and structures under moving loads. London: Thomas Telford, 1999.

Georgiadis

Lykotrafitis

. A method based on the Radon transform for three-dimensional elastodynamic problems of moving loads. J Elast 2001; 65: 87–129.

Kaplunov

Zakharov

Prikazchikov

. Explicit models for elastic and piezoelastic surface waves. IMA J Appl Math 2006; 71: 768–782.

Dai

Kaplunov

Prikazchikov

. A long-wave model for the surface elastic wave in a coated half-space. Proc R Soc London, Ser A 2010; 466: 3097–3116.

Chadwick

. Surface and interfacial waves of arbitrary form in isotropic media. J Elast 1976; 6: 73–80.

Kiselev

Parker

. Omni-directional Rayleigh, Stoneley and Scholte waves with general time dependence. Proc R Soc London, Ser A 2010; 466: 2241–2258.

Kaplunov

Nolde

Prikazchikov

. A revisit to the moving load problem using an asymptotic model for the Rayleigh wave. Wave Motion 2010; 47: 440–451.

Kaplunov

Prikazchikov

Erbaş

Şahin

. On a 3D moving load problem for an elastic half space. Wave Motion 2013; 50: 1229–1238.

10.

Achenbach

Keshava

Herrmann

. Moving load on a plate resting on an elastic half-space. J Appl Mech 1967; 34: 910–914.

11.

Kalinchuk

Belyankova

Schmid

Tosecky

. Dynamic of layered half space under the action of moving and oscillating load. Bull South Res Cent RAS 2005; 1: 3–11.

12.

Kaplunov

Oblakova

Prikazchikov

. Near-resonant regimes of a moving load in the plane-strain problem for a coated elastic half-space. Mat Model Chislennye Metody 2014; 1: 57–67.

13.

Shuvalov

Every

. On the long-wave onset of dispersion of the surface-wave velocity in coated solids. Wave Motion 2008; 45: 857–863.

14.

Borovikov

. Uniform stationary phase method. London: Institution of Electrical Engineers, 1994.

15.

Abramowitz

Stegun

. Handbook of mathematical functions. New York: Dover Publications, 2012.

16.

Poruchikov

. Methods of the classical theory of elastodynamics. Berlin: Springer-Verlag, 1992.