Further Modification of Bolotin Method in Vibration Analysis of Rectangular Plates

Abstract

A further modification of the Bolotin method for the determination of the natural frequencies and mode shapes of isotropic and orthotropic rectangular plates with various types of boundary conditions is given. Unlike the Bolotin method (BM) or the modified Bolotin method (MBM), the present approach does not postulate the formula for the eigenfrequency, but rather is based on the condition that the frequency obtained from the governing differential equations has to be equal to that yielded by Rayleigh's method. This modification is shown to be more straightforward and faster in computation, and the mode shapes derived are valid on a larger portion of the plate. Furthermore, the proposed modification easily provides a solution for boundary conditions for which the BM and MBM cannot provide a solution. Problems with two different sets of boundary conditions were solved in this study: a rectangular orthotropic plate with all edges clamped and rectangular isotropic and orthotropic plates clamped along one pair of opposite edges and free along the other pair. The results obtained for the first set compared favorably with those yielded by the MBM and Rayleigh methods, whereas in the second case the BM and MBM failed to predict the beam-like modes of vibration, while the present modification treats the problem satisfactorily.