Stability of parametric vibrations of an isolated symmetric cross-ply laminated plate

Abstract

The stochastic stability of parametric vibrations of an isolated symmetric cross-ply laminated plate system is investigated in this paper. The mechanical model of the plate system is given as a symmetric cross-ply laminated plate viscoelastically connected with two additional thin plates in order to satisfy necessary isolation (mechanical, thermal, acoustical, etc.) or structural requirements. Several important applications of the model are given in the introduction of the study. The investigated model is new and the adapted procedure is based on the analytical determination of the variable stability conditions as a consequence of the plate system being under the influences of the in-plane stochastic forces. The dynamic equilibrium equations are derived on the basis of the first-order shear deformation theory for laminated plates and Kirchhoff-Love plate theory for thin external plate-isolators. The stochastic stability of the coupled system, under parametric excitation of white noise, is investigated analytically through the moment Lyapunov exponents and Lyapunov exponents. The system of stochastic differential equations of motion is decoupled by using the contact transformation method. Then an intensive analytical procedure is continued through the perturbation method which is used in order to obtain the explicit asymptotic expressions for these exponents for the class of problems with three-degrees-of-freedom stochastic systems. The moment, almost-sure stability boundaries and critical excitation are presented and discussed for varying system parameters. The influences of the laminated plate parameters, damping coefficients and spectral density are taken into consideration in numerical examples. It is shown that thin plate-isolators could improve stochastic stability performances of composite laminated plates.