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An advanced theory of moderately thick plate vibrations

In thick plate vibration theory, the governing equations are stated with a system of three partial differential equations of motion with total deflection, which consists of bending deflection and shear contribution, and angles of rotation as fundamental variables. Most of the methods deal with these three equations, some of them with two, and recently a solution based on one equation has been offered. In the present paper, a system of three equations for a moderately thick plate is reduced to a single equation in terms of bending deflection only as a fundamental variable. Shear deflection and angles of rotation depend on bending deflection as a potential function. A simple formula for natural frequencies of a simply supported plate is derived. A characteristic equation is also obtained for a plate with simply supported two opposite edges. Numerical results for a simply supported plate and a plate clamped on the two remaining opposite edges are compared with those known in literature, for different aspect ratios and relative thickness, and very good agreement is achieved.

Mindlin plate; differential equation; free vibration; eigenpair; analytical solutions

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