In-Plane Vibrations of Rectangular Plates with Rectangular Cutouts

摘要

This work presents accurate numerical values of the natural frequencies and mode shapes for the in plane vibrations of rectangular plates with rectangular cutouts. The solutions are obtained using the multi term extended Kantorovich method. In this method a solution is assumed in one direction of the plate, and this enables to transform the coupled partial differential equations of the plate equilibrium into an a set of ordinary differential equation. These equation are solved exactly by the exact element method, and an approximate natural frequency is obtained. In the second step, the derived solution is taken as the assumed solution in one direction, and the process is repeated to find an improved approximation of the natural frequency. This process converges with a small number of solution cycles. For plates with cutouts this process yields very accurate values even with 1 term expansion, and in some cases one can improve these values by adding additional functions in the expansion. Several examples are given and compared with solutions from finite element analysis.