Thermal shock of orthotropic rectangular plates

The dynamic response of homogeneous, orthotropic plates having two parallel, simply supported edges and exposed to rapid surface heating is examined. Uncoupled, thin-plate theory is used to determine the inducedflexural vibrations. The solution is obtained as the superposition of two displacement fields, representing the quasi-static and the dynamic behaviors. An exact Levy-type solution is derived for the quasi-static problem. For the dynamic case, the governing partial differential equation is first reduced to a system of ordinary differential equations in time by means of the Galerkin method. For special situations in which the latter equations are uncoupled (e.g., plates having all edges simply supported), the solution is obtained using the Laplace transform. For cases involving more general support conditions, the equations are integrated numerically using the Runge-Kutta-Gill technique. Numerical results are presented for both isotropic and orthotropic plates having various combinations of edge cond...