Bleustein-Gulyaev Surface Waves of Arbitrary Form

Abstract

The aim of this paper is to demonstrate that the theory of surface waves of arbitrary form, developed by FRIEDIANDER /1/, CHADWICK /2/, PARKER /3/, PARKER & TALBOT /4/, CLEMENTS /5/ for surface waves of Rayleigh-type in elastic materials, can be extended to the case of piezoelectric surface waves as well as to show that real Schwartz tempered distributions are admissible as the generalized wave profiles in this theory. For simplicity the analysis is performed for the case of the free-surface Bleustein-Gulyaev surface waves polarized along the sixfold symmetry axis in the 6mm hexagonal piezoelectric crystal. The solution to the governirrj equations and boundary conditions is assumed in the form of a travelling wave propagating without change of waveform at some subsonic speed in the direction corresponding to the respective space variable. Then we require the theory to predict the same propagation speed for all wave profiles and stipulate the existence, uniqueness and stability of the assumed solution. These assumptions are weaker than involved in /1,2,3,4,5/ and therefore enable us to derive the theory of surface waves of arbitrary form admitting the larger class of wave profiles and less restricted class of solutions. In the framework of this theory we prove that Bleustein-Gulyaev surface waves of S’(ℝ) profiles cannot propagate in the form of impulses.