Approximate Solutions for the Fundamental Frequency of Square Plates with Variable Thickness.

A perturbation method was used to approximate the fundamental frequency and mode shape of variable thickness, square, simply supported plates. The study was divided into two major phases development of the necessary equations from perturbation theory and application of the equations to specific examples. The perturbation equations developed were found to be quite general, since the frequency of a plate of any thickness shape could be evaluated without reformulation of the equations in a different form. The only requirement necessary to use the equations is that the thickness of the plate be representable as a continuous function with continuous first derivatives. Modified author abstract