Harmonic wave propagation along a non-principal direction in a pre-stressed elastic plate

In this paper harmonic wave propagation in a pre-stressed, incompressible e lastic plate is investigated. Specifically the problem in which one princip al direction of the primary deformation is normal to the plate and the dire ction of propagation is at an angle a to one of the in-plane principal dire ction is considered. The dispersion relation is derived in respect of a gen eral strain energy function and numerical solutions presented for a Mooney- Rivlin material. The dispersion curves are shown to be more complex in natu re than those associated with propagation along an in-plane principal direc tion, as the solution arising from the horizontally polarised sheer wave do es not uncouple. An asymptotic analysis, for high and low wave number, is c arried out with the high wave number expansions providing a good approximat ion to the numerical solution over a large wave number region. The paper al so includes an investigation of the effects of changes in the normal Cauchy stress and direction of propagation on the existence of surface waves. (C) 1999 Elsevier Science Ltd. All rights reserved.