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Shock and Vibration
Volume 2014 (2014), Article ID 572395, 25 pages
Research Article

Free Vibration Analysis of Moderately Thick Rectangular Plates with Variable Thickness and Arbitrary Boundary Conditions

1College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China
2Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang 621900, China
3College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China

Received 27 February 2014; Revised 30 May 2014; Accepted 16 June 2014; Published 14 July 2014

Academic Editor: Lei Zuo

Copyright © 2014 Dongyan Shi 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.


A generalized Fourier series solution based on the first-order shear deformation theory is presented for the free vibrations of moderately thick rectangular plates with variable thickness and arbitrary boundary conditions, a class of problem which is of practical interest and fundamental importance but rarely attempted in the literatures. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions, the current method can be generally applied to a wide range of boundary conditions with no need of modifying solution algorithms and procedures. Under the current framework, the one displacement and two rotation functions are generally sought, regardless of boundary conditions, as an improved trigonometric series in which several supplementary functions are introduced to remove the potential discontinuities with the displacement components and its derivatives at the edges and to accelerate the convergence of series representations. All the series expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh-Ritz technique. The effectiveness and reliability of the presented solution are demonstrated by comparing the present results with those results published in the literatures and finite element method (FEM) data, and numerous new results for moderately thick rectangular plates with nonuniform thickness and elastic restraints are presented, which may serve as benchmark solution for future researches.