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.