Abstract
In this paper, based on the theory of elastodynamics, applied the general solution proposed by Boussinesq-Galerkin and the operator theory of partial differential equations, the refined equations of elastodynamics of the thick plate including the effect of the transverse loading was obtained by using appropriate gauge conditions. The imaginary differential operator was firstly introduced in order to apply the spectrum decomposition theory of differential operators. The refined dynamic equations of plate bend and stretch were given, respectively. And the refined dynamic theory of thick plates was compared with the different classical theory of plates. Derivation of the dynamic equation was conducted without any priory assumption, so the proposed dynamic equation of plates is exact. The governing equation proposed by this paper can be used to analyze vibration of thick plates, evaluate the applicable condition of the engineering plate theory and exactly to design the active vibration control of thick plates.
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