Free vibration analysis of rectangular Mindlin plates resting on uniform elastic edge supports by the superposition method.

Abstract

In the present study, it is demonstrated that the traditional superposition method lends itself successfully to obtaining of eigenvalues and mode shapes for rectangular shear deformable plates resting on uniform elastic edge supports. The effect of transverse shear deformation is taken into account by means of the first order shear deformation relationship developed by Mindlin. Uniform elastic rotational and translational supports of any stiffness magnitudes are considered to act simultaneously along the four edges. The effects of twisting edge restraint are investigated for the first time. The governing differential equations are satisfied exactly throughout the plate domain. Eigenvalues are tabulated for the first six vibration modes of square plates with identical stiffnesses along all edges. It is shown that all the three classical boundary conditions, namely, free, simply supported, and clamped, are approached when the stiffness coefficients are allowed to take on appropriate limits. These appear to be the first analytical solutions to these important elastically supported plate vibration problems obtained by the superposition method.