Free vibration analysis of tapered rectangular plates by differential quadrature method: A semi-analytical approach

The particular type of thin rectangular plate configurations considered in the present work are the ones having two opposite edges simply supported and are of varying thickness between the other two edges. The boundary conditions at these two edges may be quite general. The plates may be isotropic or specially orthotropic. For the numerical solution to evaluate the free vibration characteristics of such plates, a semi-analytical approach is adopted. First, by using the trigonometric sine functions for the mode shape between the simply supported edges, the eigenvalue partial differential equation is reduced to an ordinary differential equation. The solution of the reduced equation is then carried out by the differential quadrature method. On the basis of comparison with the available results in the published literature, it is believed that this solution method is capable of yielding highly accurate results. Moreover, the very small computation times required for the evaluation of the vibration characteristics demonstrate the high computational efficiency of the method and point to its possible use in the real time analysis and design of vibrating plate systems. (C) 1996 Academic Press Limited