Strongly Nonlinear Elastic Surface Waves in Solids

Abstract

The possibility of the existence of a peculiar type of surface acoustic waves in solids due to elastic nonlinearity was considered in the paper¹. The calculations performed in this paper are mainly restricted to the cases of small amplitude waves for which the dependence of the wave amplitude on depth, U(Y), is described by sech function, and a particular limiting case of strongly nonlinear waves for which U(Y) is described by cosine function. To describe intermediate cases, it is necessary to calculate an integral containing two square roots with one being inserted into the other. We propose a procedure which allows to remove the inner square root and calculate the complete integral exactly. The solution includes both special cases mentioned above and describes the U(Y)-behaviour in the transitional region. To explain more detaily the subject of this research, we describe shortly some results of previous papers^{1, 2} in the next section.