NONLINEAR FREE-VIBRATION OF HEATED ORTHOTROPIC RECTANGULAR-PLATES

An analytical analysis of free vibrations of a heated orthotropic rectangular thin plate under various boundary conditions is presented. The nonlinear governing equations are derived from von Karman plate theory and Berger's analysis separately; from them the Duffing-type nonlinear ordinary equations are then obtained by employing Galerkin's method using one-term approximation. The methods of successive approximation and complete elliptic cosine are applied to solve the nonlinear equations. The influence of temperature changes and large amplitudes on the period of free vibrations are established; also the buckling temperature is obtained. The analytical solutions are compared with numerical results from Runge-Kutta method. Two different approaches to linearize thermoelastic plate equations are considered and compared.