Using Mathematica for the Galerkin Representation of Nonlinear Plate Equations

Jon Lee
AF Research Lab

By the Galerkin procedure we have previously derived modal equations from the von Karman type of nonlinear equations for a heated plate. Although the procedure is straightforward, the devil is in the detail. This is because the modal equations entail cubic convolutions and there also arises a convolution of the displacement and temperature field. It is not hard to write down the convolution sums in analytical form, yet enumerating them for practical computation calls for the help of computers. In this paper we use Mathematica to do the complete Galerkin procedure, and the simply supported and clamped plates are handled by similar syntactic commands but by different basis functions.