Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method

Abstract

This paper presents accurate three-dimensional elasticity solutions for free vibrations of six types of plates having free lateral surfaces, two opposite sides simply supported, and two other sides having combinations of simply supported, clamped, and free boundary conditions. The solution methodology adopted in the present work first reduces the spatial variables in the governing elasticity equations to two by using displacement functions in the forms which satisfy the boundary conditions of the assumed simply supported sides. The eigenvalue equations are then formulated from the reduced governing equations and the boundary conditions via the differential quadrature method. The numerical results include the first nine natural frequencies of the six plate configurations for combinations of three aspect ratios and two thickness ratios. These results are supported by appropriate convergence studies and comparisons with the results of other authors.