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Shock and Vibration
Volume 2014, Article ID 286710, 11 pages
Research Article

An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges

College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China

Received 4 March 2013; Accepted 19 September 2013; Published 25 February 2014

Academic Editor: Nuno Maia

Copyright © 2014 Xue Kai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An analysis method is proposed for the vibration analysis of the Mindlin rectangular plates with general elastically restrained edges, in which the vibration displacements and the cross-sectional rotations of the mid-plane are expressed as the linear combination of a double Fourier cosine series and four one-dimensional Fourier series. The use of these supplementary functions is to solve the possible discontinuities with first derivatives at each edge. So this method can be applied to get the exact solution for vibration of plates with general elastic boundary conditions. The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. The natural frequencies can be got through solving the matrix equation. Finally the numerical results are presented to validate the accuracy of the method.