Vibration analysis of moderately thick rectangular plates with elastically restrained edges

Abstract

In this paper, an improved Fourier series method is proposed for the free vibration analysis of moderately thick rectangular plates with uniform elastic restraints along each edge. The effect of shear deformation is considered by using Mindlin plate theory (namely, the first order shear deformation theory). The transverse deflection and rotation displacement functions are invariantly expressed as the superposition of a double Fourier cosine series and four supplementary functions in the form of the product of a polynomial function and a single cosine series expansion introduced to ensure (accelerate) the uniform and absolute convergence (rate) of the series representation on the plate including four edges. The unknown expansion coefficients are determined using the Rayleigh-Ritz procedure in conjunction with the energy formulation of Mindlin plate system. Several numerical examples are presented to demonstrate the effectiveness and reliability of the proposed method for predicting the modal parameters of rectangular Mindlin plates with various thickness-length ratios under different boundary conditions. Although the constraint is considered uniformly distributed over each edge, the current method can be readily extended to the general cases when the spatial variation of the restraining stiffness is of interest.