Vibrations of inhomogeneous piezoelectric bodies in conditions of residual stress–strain state

Abstract

• The linearized statement for inhomogeneous piezoelectric prestressed body is derived. • The general variational principles and weak formulations of the original problem are described. • Particular boundary problems for rods and thin disk are investigated. • A formula for frequency change as a function of residual stress level is obtained. • An effect of residual stress on frequency response functions for a disk is estimated. In the article, we present the general linearized statement of the boundary problem on vibrations of inhomogeneous piezoelectric body under residual stress–strain state. We have derived the weak statement of the problem for the test functions satisfying the essential boundary conditions, formulated the general variational principle for a prestressed piezoelectric body and proposed several options for the potential energy representation. On the basis of the principles proposed, we have formulated and investigated a number of particular boundary problems on steady-state vibrations of inhomogeneous piezoelectric prestressed rods and thin prestressed disk polarized in the direction of thickness. The analysis of the residual stress levels on frequency response function for the bodies considered is provided.