On the dynamical axisymmetric stress field in a finite pre-stretched bilayered slab resting on a rigid foundation

Abstract

The dynamic axisymmetric stress field in an initially finite pre-stretched bilayered slab resting on a rigid foundation is studied within the framework of the piecewise homogeneous body model. The three-dimensional linearized theory of elastic waves in initially stressed bodies is used. It is assumed that a time-harmonic point-located normal force acts on the free face plane of the slab. The considered problem is solved by employing the Hankel integral transformation. The materials of the layers are assumed to be incompressible, and the elastic relations are given through the Treloar potential. The formulation and solution to the problem coincide with the corresponding ones of classical linear theory of elasticity for an incompressible body in the case where there is no initial stretching in the layers. Numerical results are presented and these results involve stresses acting on the interface planes. In particular, it is established that stresses on the interface planes decrease as the pre-stretching is increased.