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

The propagation of harmonic waves in a slightly compressible, finitely defo rmed, elastic plate is considered. The dispersion relation associated with harmonic waves propagating in a plate composed of such material with zero i ncremental surface traction is derived and asymptotic expansions, giving ph ase 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 provi de excellent approximation to the numerical solution and reveal a possible high wavenumber structure which differs significantly from the correspondin g unstrained case. These expansions have important application to numerical inversion of transform solutions used to determine the dynamic transient r esponse of a plate to surface, internal or edge loading. The paper conclude s with a discussion of the longitudinal wavefront as the bulk modulus incre ases. It is shown numerically that the contribution of this wavefront to tr ansient response decreases as the bulk modulus increases. (C) 2000 Elsevier Science Ltd. All rights reserved.