Vibration of Rectangular Plates of Variable Thickness

Abstract

In a previous paper the application of the finite element method to plate vibration problems was discussed. It was shown that the method gave good results when applied to the vibration of plates of uniform thickness. The present paper extends the method to include plates of variable thickness. In particular stiffness and inertia matrices are derived for an isotropic rectangular plate element of linearly variable thickness in one co-ordinate direction. These matrices are used to find the natural frequencies and mode shapes of a number of rectangular planform cantilever plates of non-uniform thickness. Experimental results provide a basis for comparison with the finite element results.