The method of fundamental solutions for the high frequency acoustic-elastic problem and its relationship to a pure acoustic problem

Abstract

This paper firstly documents the method of fundamental solutions for the two dimensional high frequency acoustic-elastic interaction problem, and investigates its relationship to a pure acoustic problem with a sound-hard boundary. We approximate the displacements by the linear combination of the fundamental matrix tensors of the Navier equation. The acoustic scattered field outside the elastic solid is approximated by the linear combination of the fundamental solutions of the Helmholtz equation. At last, we give some examples using the real data in four cases, including the copper alloy in the water, in the oil, in the cork wood and in the air. Especially in the first example, an exact solution is available for checking the accuracy of the presented method. We also find that the acoustic-elastic interaction problem is close to a pure acoustic problem with a sound-hard boundary as the ratio of two medium density increasing.