On the use of GDQ for vibration characteristic of non-homogeneous orthotropic rectangular plates of bilinearly varying thickness

The generalized differential quadrature (GDQ) method is used to analyze the effect of non-homogeneity, orthotropy, and thickness variation on the vibration characteristics of rectangular plates on the basis of Kirchhoff's plate theory. The non-homogeneity of the plate material is assumed to arise due to the exponential variations in Young's moduli, shear modulus, and density of the plate material with the in-plane coordinates. The thickness of the plate is taken as the Cartesian product of linear variations along two concurrent edges of the plate. In the GDQ method, the derivative of a function with respect to a space variable at a given grid point is approximated as a weighted linear sum of the function values at all of the grid points in the computational domain of that variable. Numerical results have been obtained for four different combinations of boundary conditions at the edges, namely: (1) fully clamped; (2) two opposite edges are clamped and the other two are simply supported; (3) two opposite edges are clamped and the other two are free; and (4) two opposite edges are simply supported and the other two are free. The effect of various plate parameters on the natural frequencies is studied for the first three modes of vibration. Three-dimensional mode shapes for a specified plate are plotted. A comparison of results obtained by the present method with those available in the literature is presented.