Vol. 4, No. 3, 2011

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Rayleigh-type surface quasimodes in general linear elasticity

Sönke Hansen

Vol. 4 (2011), No. 3, 461–497

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.

Rayleigh surface waves, elastodynamics, anisotropy, quasimodes, microlocal analysis
Mathematical Subject Classification 2010
Primary: 35Q74
Secondary: 74J15, 35P20, 35S05
Received: 17 August 2010
Revised: 24 August 2010
Accepted: 3 June 2011
Published: 28 December 2011
Sönke Hansen
Institut für Mathematik
Universität Paderborn
33095 Paderborn