Nonlinear mathematical theory of perforated viscoelastic thin plates with its applications

In this paper, the nonlinear mathematical theory of perforated viscoelastic thin plates, by the Karman's hypotheses of plates with large deflection an d the Boltzmann's constitutive law of linear viscoelastic materials, is est ablished. One could see that the governing equations, boundary conditions a nd constraining conditions generally are of nonlinear integro-differential operator types and that they further generalize the mathematical theory for perforated elastic thin plates and could be also reduced to the existing m athematical theory of viscoelastic thin plates without holes. As an applica tion, the nonlinear dynamical stability of a viscoelastic annular plate is analyzed and the effect of parameters on the stability is considered by usi ng Galerkin averaging method and numerical methods in nonlinear dynamics. S ome helpful conclusions are obtained. Specially, a new method calculating t he Lyapunov exponent spectrum of dynamical systems excited periodically is suggested. By using this method, the computation time can be greatly reduce d. (C) 2001 Elsevier Science Ltd. All rights reserved.