Matching of asymptotic models in scattering of acoustic waves by elastic shells

Abstract

Scattering of stationary acoustic waves by elastic shells is considered. The approximate solution of the problem is synthesized by matching of asymptotic models having the limited ranges of applicability. In the vicinity of zero frequency the Kirchhoff-Love theory of shells or the refined Kirchhoff-Love theory is applied, in the vicinities of thickness resonance frequencies the long-wave high-frequency approximations are utilized and outside these vicinities the flat elastic layer model is applied. It is shown that the mentioned models have overlapping regions. As examples, the problems for scattering of a plane acoustic wave by circular cylindrical and spherical shells are considered. Numerical results of comparison with the relevant exact solution are presented.