Abstract

The dynamic motion of a prestressed compressible elastic layer having constrained boundaries is considered. The dispersion relations which relate wave speed and wave number are obtained for both symmetric and antisymmetric motions. Both motions can be considered by formulating the incremental boundary-value problem based on the theory of incremental elastic deformations, and using the propagator matrix technique. The limiting phase speed at the low wave number limit of symmetric and antisymmetric waves is obtained. At the low wave number limit, depending on the prestress, for symmetric motion with slipping boundaries and for antisymmetric motion with vertically unconstrained boundaries, a finite phase speed may exist for the fundamental mode. Numerical results are presented for a Blatz–Ko material. The effects of the constrained boundaries are clearly seen in the dispersion curves.

Keywords

wave propagation, prestress, dispersion curves, nonlinear elasticity

Authors