Response of a Rigid Spheroidal Inclusion to an Incident Plane Compressional Elastic Wave

TLDR: In this article, matched asymptotic expansions have been used to obtain a low-frequency solution for the diffraction of a plane compressional wave by a rigid spheroid embedded in an infinite homogeneous isotropic elastic medium.

Abstract: The method of matched asymptotic expansions has been used to obtain a low-frequency solution for the diffraction of a plane compressional wave by a rigid spheroid embedded in an infinite homogeneous isotropic elastic medium. In contrast to standard techniques such as separation of variables which are not effective in this case, the present method gives, in a systematic manner, both the “inner” and “outer” fields. Expansions have been carried out which are correct to $O(\varepsilon ^2 ),\varepsilon $ being a suitably defined nondimensional wave number. These results are then used to determine the motion of the inclusion as well as the stress distribution on the spheroid and the far-field displacement components. Numerical studies for these properties are presented in graphical form and the results compared with known results in various limiting cases.