On New Symplectic Approach for Exact Free Vibration Solutions of Moderately Thick Rectangular Plates with Two Opposite Edges Simply Supported

Abstract

The purpose of this paper is to report the effective application of a new symplectic approach for exact free vibration solutions of moderately thick rectangular plates. By way of a simple but rigorous derivation, the governing differential equations for free vibration of the plates are transferred into Hamilton canonical equations. The whole state variables are then separated. Using the method of eigenfunction expansion in the symplectic geometry, the free vibration analysis of moderately thick rectangular plates with two opposite edges simply supported is performed and exact vibration solutions are obtained. The method eliminates the need to pre-determine any trial functions hence more reasonable than other available methods. Comprehensive numerical results are presented to validate the approach proposed here by comparison with those established in the open literature

Keywords

• Moderately thick plate, free vibration, exact solution, symplectic approach

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