Quintic Splines in the Study of Buckling and Vibration of Non-homogeneous Orthotropic Rectangular Plates with Variable Thickness

Buckling and vibrational behaviour of non-homogeneous orthotropic rectangular plates of variable thickness having two opposite edges (y = 0 and b) simply supported and these are subjected to constant in-plane force have been analyzed on the basis of classical plate theory. The other two edges (x = 0 and a) may be clamped, simply supported or free. For nonhomogeneity of the plate material, Young’s moduli and density are assumed to vary exponentially along one direction. The use of trigonometric sine function for the mode shapes between the simply supported edges reduces the governing partial differential equation of motion for such plates to an ordinary differential equation in x with variable coefficients. Applying boundary conditions at the edges x = 0 and a, frequency equations for three different combinations of boundary conditions have been solved numerically employing quintic splines interpolation technique. The effect of in-plane force parameter together with orthotropy, non-homogeneity, aspect ratio and thickness variation on the natural frequencies of vibration is illustrated for the first three modes of vibration. Normalized displacements are presented for specified plates. By allowing the frequency to approach zero, the critical buckling loads in compression for various values of plate parameters have been computed. A comparison of results has been presented.