Forced Vibration of the Pre-Stressed and Imperfectly Bonded Bi-Layered Plate Strip Resting on a Rigid Foundation

Abstract

Within the scope of the piecewise homogeneous body model with utilizing of the three dimensional linearized theory of elastic waves in initially stressed bodies the influence of the shear-spring type imperfection of the contact conditions between the layers of the pre-stressed bi-layered plate strip resting on the rigid foundation, on the frequency response of this plate strip is investigated. The corresponding mathematical problem is solved numerically by employing FEM and numerical results illustrating the influence of the parameter characterizing the degree of the mentioned imperfectness, on the frequency response of the normal stress acting on the interface planes between the layers and between the plate and rigid foundation are presented and discussed. In particular, it is established that an increase in the value of the shear-spring parameter the absolute values of the compressed normal stress decrease, but the values of the stretched normal stress increase and this parameter has an influence also on the character of the action of the initial stresses on the frequency response under consideration.