Vol. 11, No. 4, 2016

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ISSN: 1559-3959
On the causality of the Rayleigh wave

Barış Erbaş and Onur Şahin

Vol. 11 (2016), No. 4, 449–461
DOI: 10.2140/jomms.2016.11.449
Abstract

An explicit hyperbolic-elliptic formulation for surface Rayleigh waves is analysed with an emphasis on the causality of obtained results. As an example, a 3D moving load problem for a distributed vertical load is considered. A simple approximate solution is derived for a near-resonant regime, and the related point load solution is recast as a limiting case. It is shown that causality is characteristic only for the longitudinal wave potential along the surface, where it is governed by a hyperbolic equation modelling the small dilatation disturbances propagating at the Rayleigh wave speed.

Keywords
moving load, causality, Rayleigh wave, hyperbolic-elliptic model
Milestones
Received: 13 January 2016
Revised: 13 February 2016
Accepted: 9 March 2016
Published: 4 August 2016
Authors
Barış Erbaş
Department of Mathematics
Anadolu University
Yunusemre Campus
26470 Eskişehir
Turkey
Onur Şahin
Department of Mathematics
Anadolu University
Yunusemre Campus
26470 Eskişehir
Turkey