Analytical and Numerical Study of the Interaction of a “Weak Shock Wave” and an Immersed Elastic Structure

The present paper exposes an analytical and numerical study of the interaction between a weak shock wave and an immersed elastic structure. Several models of the problem are exposed and compared in the study: on the one hand, a semi-analytical method is proposed and on the other hand a numerical method is developed, based on a description of fluid-structure interaction through i) exact and ii) simplified interaction models. Comparison of the various approaches is exposed on a simple analytical case, namely that of a two-dimensional circular shell immersed in a two-dimensional compressible fluid and subjected to a spherical shock wave. Discussion of the various numerical results gives some practical guidance for the use of simplified fluid-structure interaction models in the context of industrial studies for underwater shock analysis.