Subsonic Free Surface Waves in Linear Elasticity

TL;DR

This paper investigates Rayleigh-type surface waves in anisotropic elastic solids, providing spectral methods and asymptotic expansions to establish the existence of subsonic free surface waves in complex geometries.

Contribution

It introduces spectral factorization techniques and asymptotic analysis for inhomogeneous anisotropic bodies with curved surfaces, extending surface wave theory.

Findings

Existence of subsonic free surface waves in anisotropic solids.

Spectral factorization approach for matrix polynomials.

Asymptotic formulas for wave propagation and transport equations.

Abstract

For general anisotropic linear elastic solids with smooth boundaries, Rayleigh-type surface waves are studied. Using spectral factorizations of matrix polynomials, a self-contained exposition of the case of a homogeneous half-space is given first. The main result is about inhomogeneous anisotropic bodies with curved surfaces. The existence of subsonic free surface waves is shown by giving ray series asymptotic expansions, including formulas for the transport equation.