Dynamical Response of Two Axially Pre-Strained System Comprising of a Covering Layer and a Half Space to Rectangular Time-Harmonic Forces

Abstract

The time-harmonic dynamical stress field in the system comprising two axially pre-stressed covering layer and two axially pre-stressed half space was studied under the action of uniformly distributed forces on free face plane of the covering layer. It is assumed that the forces are distributed within the rectangular area. The study was conducted within the scope of the piecewise homogeneous body model with the use of three-dimensional theory of elastic waves in an initially stressed bodies. The materials of the layer and half-space were assumed to be isotropic and homogeneous. The corresponding three-dimensional boundary-value-contact problem was solved by applying double Fourier exponential integral transformation. The numerical results were presented and discussed for the case where the material of the layer and half space were aluminum and steel, respectively. In this case, the main focus was the dependencies between the interfacial normal stress and frequency of the external forces. It was established that under the action of the statically equivalent forces in rectangular area the influence of the size of the area on the prescribed dependencies increased with increasing frequency of the forces. At the same time, it was shown that the influence of the pre-stretching of the covering layer on the stress was dependent on the frequency of the external forces. In particular, it was found that the influence became more significant as the frequency of the external forces approached the resonance frequency.