A new identity for the surface–impedance matrix and its application to the determination of surface-wave speeds

Abstract

It is well known in surface–wave theory that the secular equation for the surface–wave speedυcan be written as det M = 0 in terms of the surface–impedance matrix M. It is shown in this paper that M satisfies the simple identity(M-iR)T-1(M+iRT)-Q+υ2I=0 in the usual notation in the Stroh formalism. This identity provides an efficient method for calculating the wave speed of surface waves in unstressed or pre–stressed elastic half–spaces. The method is explained and illustrated by examples. It is also shown that the buckling/wrinkling pre–stress for a pre–stressed elastic half–space can be calculated using the same procedure but with pre–stress playing the role of υ.