VIBRATION STUDY OF RECTANGULAR PLATES WITH CUTOUTS

Abstract

A numerical method based on the Rayleigh principle is developed for predicting the natural frequencies of either isotropic or orthotropic rectangular plates with rectangular cutouts. The plates under consideration are divided into smaller sub-domains based on the mode shapes and the locations of the cutouts. A suitable deflection function is assumed for each sub-domain. The Rayleigh method is then applied for estimating the natural frequency of the mode. The Classical plate theory and the dynamic equivalent of simplified Reissner theory are employed in the formulations. The method is first illustrated for isotropic rectangular plates having single and multiple rectangular cutouts. The predicted results are compared with the finite element results generated by PAFEC*and in some cases, with the reported finite element and finite difference results. The agreements are good except for rectangular plates with large cutouts and mode shapes with the nodal lines parallel to the longer sides of the cutouts. The predicted results for these cases can be improved by modifying the energy contribution from some of the sub-domains. The method is then applied for examining the effects of orthotropy, transverse shear deformation and rotary inertia. The predicted results compare favourably with the reported analytical and finite element results for plates with single cutout. Some new findings in regard of plates with multiple cutouts and the relative importance of the effects of transverse shear deformation and rotary inertia are also presented. The method is further extended to rectangular plates with cracks and simply supported plates with partially clamped edges. The predicted results are first compared with the available results for isotropic plates. The effects of special and general orthotropy are then examined for some selected cases.