Acta Mechanica Solida Sinica

, Volume 24, Issue 6, pp 556–567 | Cite as

Exact Solutions for Free In-Plane Vibrations of Rectangular Plates

Article

Abstract

All possible exact solutions are successfully obtained in terms of 10 sets of distinct eigensolutions for the free in-plane vibration of isotropic rectangular plates. The plates have simply supported condition at two opposite edges and any combination of classical boundary conditions at the other two edges. The exact solutions are validated through both mathematical proof and comparisons with the solutions of differential quadrature method. Some unusual phenomena are revealed in free in-plane vibrations of rectangular plates due to one of the eigenvalues being zero. This work constitutes an improved version of very recent corresponding work by the same authors [Int. J. Mech. Sci., 2009, 51: 246–255]. Both the solution forms and solving procedures in the previous work are substantially simplified. Some new results are also given, which are useful for validation purpose in future.

Key words

rectangular plate in-pane free vibration frequency mode shape exact solution 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2011

Authors and Affiliations

  1. 1.The Solid Mechanics Research CenterBeijing University of Aeronautics and AstronauticsBeijingChina

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