Analysis of non-uniform residual stress state in plates with in-plane and transverse heterogeneities

Abstract

In the present paper, we describe a model of a prestressed inhomogeneous body and provide the variational and weak statements. On its basis, we study a problem of mixed vibrations of a non-uniform plate with inclusions and a sandwich-structured three-ply plate under the conditions of the residual stress-strain state. We build the numerical finite-element solution on the basis of the weak problem statement and analyze the effect of the prestress states on its frequency response functions. In addition, we identify the prestress level in the middle layer of the composite plate by the data on frequency characteristics measurements.