A spring-layer model for a bi-layered plate-strip with initial stress through imperfect contact interface

Abstract

In this paper, we present our report on the forced vibration of a bi-layered plate-strip with initial stress resting on a rigid foundation induced by a time-harmonic force. The investigation is carried out according to the piecewise homogeneous body model with utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB). The materials of the body are chosen to be linearly elastic, homogeneous, and isotropic. The interface between the layers is assumed to be imperfect, and is simulated by the spring-layer model. A similar degree of imperfection on the interface is realized in the normal and tangential directions. The mathematical model for the problem under consideration is designed, and the system of the equations of motion is approximately solved by employing the finite element method (FEM). The numerical results explaining the influence of the parameter that characterizes the degree of corresponding imperfectness on the dynamic response of the plate-strip are presented. In particular, we demonstrate that the distributions of the normal stress become flat, as the normal-spring parameter increases.