On the Interaction and Reflection of Shocks in Hyperelastic Strings

Abstract

Governing equations for finite amplitude wave propagation in stretched hyperelastic strings are given in recent papers, (Beatty and Haddow, 1985), along with similarity solutions for symmetrically plucked and impacted strings. The similarity solutions are valid until the first reflections at the fixed ends and in this paper we consider symmetrically plucked Mooney-Rivlin strings and investigate the response after reflections. The method of characteristics is applied to extend the results of the similarity solutions and to obtain solutions for the interaction of a reflected longitudinal shock and incident transverse shock and the reflection of an incident transverse shock. A deformed shape, which is not intuitively obvious, is predicted by the solution of the interaction problem and is confirmed by an experimental study. A finite difference scheme is used to obtain numerical solutions, which are valid after multiple wave interactions and reflections occur. Solutions obtained by the method of characteristics are used as a partial check on the numerical results.