Dynamic Analysis of T-Shaped Plate with General Boundary Conditions

Abstract

In this investigation, an analytical method is proposed for the dynamic analysis of T-shaped plates with general boundary conditions. Four types of springs are uniformly distributed along each edge, which are used to simulate the transverse shearing forces, bending moments, in-plane longitudinal forces and in-plane shearing forces, respectively. Arbitrary boundary conditions can be readily realized by setting the stiffness of the four types restraining springs. The interactions between the plates have been taken into account at the junction with four types of coupling springs. The in-plane and out-of-plane displacements are invariantly expressed, regardless of boundary conditions, as a new form of double Fourier series with a drastically improved convergence as compared with the traditional Fourier series. The expansion coefficients are considered as the generalized coordinates, and determined using the Rayleigh-Ritz technique. Numerical examples are presented to validate the accuracy and reliability of the proposed method. A good agreement is observed between the current results and FEA results. The present method can be directly extended to more complicated structures with any number of plates.