Some dynamic properties of a pre-stressed, nearly incompressible (rubber-like) elastic layer

Abstract

The propagation of harmonic waves in a slightly compressible, finitely deformed, elastic plate is considered. The dispersion relation associated with harmonic waves propagating in a plate composed of such material with zero incremental surface traction is derived and asymptotic expansions, giving phase speed as a function of wave number, harmonic number and pre-stress, are obtained for high and low wave number. These expansions are shown to provide excellent approximation to the numerical solution and reveal a possible high wave number structure which differs significantly from the corresponding unstrained case. These expansions have important application to numerical inversion of transform solutions used to determine the dynamic transient response of a plate to surface, internal or edge loading. The paper concludes with a discussion of the longitudinal wavefront as the bulk modulus increases. It is shown numerically that the contribution of this wavefront to transient response decreases as the bulk modulus increases.