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

Abstract

Vibrat ion 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. t wo parallel edges (y = 0 and b) are assumed to be simp ly-supported while the other two edges (x = 0 and a) may have either of three co mbinations C-C, C-S or C-F, where C, S and F stand for clamped, simp ly supported and free edge, respectively. Assuming the transverse displacement w to vary as sin (p y/b), the part ial differential equation wh ich governs the motion of equation is reduced to an ordinary differential equation in x with variab le 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 vibrat ion of monoclin ic rectangular p lates has been examined.

Propagation of Flexural Waves in Anisotropic Fluid-Conveying Cylindrical Shells

“…Tornabene [23] analyzed free vibrational characteristics of anisotropic laminated composite doubly-curved shells within the framework of FSDT in conjunction with GDQM. Classical plate theory has been utilized by Singhal and Bindal [24] in order to solve the vibration problem of an embedded monoclinic rectangular plate. The nonlinear vibration response of anisotropic laminated cylindrical shells resting on the Pasternak medium within the framework of HSDT has been investigated by Shen [25].…”

New Frequency‐Dependent Trigonometric Interpolation Functions for the Dynamic Finite Element Analysis of Thin Rectangular Plates

“…Despite these advantages, one of the major drawbacks of this method is that it is difficult to apply to problems involving differential equations with multiple end conditions at the system (line) boundaries such as the fourth-order differential equation for thin plates [15]. Another disadvantage of the DQ method is that its accuracy drops when applied to study the vibration behaviour of complicated geometries [16].…”