Free Vibration Analysis of Curvilinear Quadrilateral Plates by the Differential Quadrature Method

A methodology for applying the differential quadrature (DQ) method to the free vibration analysis of arbitrary quadrilateral plates is developed. In our approach, the irregular physical domain is transformed into a rectangular domain in the computational space. The governing equation and the boundary conditions are also transformed into relevant forms in the computational space. Then all the computations are based on the computational domain. As compared to the approach proposed by C. W. Bert and M. Malik (Int. J. Mech. Sci.38, 589 (1996)), the present approach requires much less computational effort and virtual storage. In addition, the present work uses a simple and convenient way to implement clamped and simply supported boundary conditions. An exact mapping technique is used to perform the coordinate transformation in this study. Some numerical examples are provided to show the computational efficiency of the present scheme.