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Shock and Vibration
Volume 2014, Article ID 517946, 11 pages
Research Article

Vibration Analysis of Annular Sector Plates under Different Boundary Conditions

1College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China
2Department of Mechanical Engineering, Wayne State University, Detroit, MI 48201, USA
3Luoyang Sunrui Special Equipment Co., Ltd., Luoyang 471003, China

Received 18 October 2013; Accepted 18 May 2014; Published 9 June 2014

Academic Editor: Hassan Haddadpour

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.


An analytical framework is developed for the vibration analysis of annular sector plates with general elastic restraints along each edge of plates. Regardless of boundary conditions, the displacement solution is invariably expressed as a new form of trigonometric expansion with accelerated convergence. The expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling annular sector plates under a variety of boundary conditions and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. Of equal importance, the proposed approach is universally applicable to annular sector plates of any inclusion angles up to 2π. The reliability and accuracy of the current method are adequately validated through numerical examples.