Generalised Differential Quadrature Method in the Study of Free Vibration Analysis of Monoclinic Rectangular Plates

Vibration characteristics of monoclinic rectangular plate of exponentially varying thickness resting on elastic foundation have been studied on the basis of classical plate theory. Following Lévy approach i.e. two parallel edges (y = 0 and b) are assumed to be simply-supported while the other two edges (x = 0 and a) may have either of three combinations C-C, C-S or C-F, where C, S and F stand for clamped, simply supported and free edge, respectively. Assuming the transverse displacement w to vary as sin (pπy/b), the partial differential equation which governs the motion of equation is reduced to an ordinary differential equation in x with variable coefficients. The resulting ordinary differential equation has been solved by Generalised Differential Quadrature Method (GDQM) for all the boundary conditions considered here. The effect of various plate parameters has been studied on the natural frequencies for the first three modes of vibration. Convergence studies have been carried out for four decimal exactitude. Mode shapes for all the three plates have been presented. The efficiency of generalized differential quadrature method for the natural frequencies of vibration of monoclinic rectangular plates has been examined.