Variational principles on static-dynamic analysis of viscoelastic thin plates with applications

Abstract

In this paper, according to the integral-type constitutive relation of linear viscoelastic materials, the initial-boundary-value problem on the static-dynamic analysis of viscoelastic thin plates is established by introducing a “structural function”. The corresponding variational principles are presented by means of convolution bilinear forms. As applications, we consider the quasi-static responses of a simply-supported square plate with three different load histories in which the classical Ritz method on the spatial response and the interpolation technique of Legendre polynomials on the temporal response are used. The obtained results are compared with the analytical solutions given in this paper. One can see that the approximate solutions agree well with the analytical solutions.