Rayleigh-type surface quasimodes in general linear elasticity

Hansen, Sönke

doi:10.2140/apde.2011.4.461

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Rayleigh-type surface quasimodes in general linear elasticity

Sönke Hansen

Vol. 4 (2011), No. 3, 461–497

DOI: 10.2140/apde.2011.4.461

Abstract

Rayleigh-type surface waves correspond to the characteristic variety, in the elliptic boundary region, of the displacement-to-traction map. In this paper, surface quasimodes are constructed for the reduced elastic wave equation, anisotropic in general, with traction-free boundary. Assuming a global variant of a condition of Barnett and Lothe, the construction is reduced to an eigenvalue problem for a selfadjoint scalar first order pseudodifferential operator on the boundary. The principal and the subprincipal symbol of this operator are computed. The formula for the subprincipal symbol seems to be new even in the isotropic case.

Keywords

Rayleigh surface waves, elastodynamics, anisotropy, quasimodes, microlocal analysis

Mathematical Subject Classification 2010

Primary: 35Q74

Secondary: 74J15, 35P20, 35S05

Milestones

Received: 17 August 2010

Revised: 24 August 2010

Accepted: 3 June 2011

Published: 28 December 2011

Authors

Sönke Hansen
Institut für Mathematik Universität Paderborn 33095 Paderborn Germany
http://www.math.upb.de/~soenke/

Vol. 4, No. 3, 2011