Application of a new differential quadrature methodology for free vibration analysis of plates

A new methodology is introduced in the di erential quadrature (DQ) analysis of plate problems. The proposed approach is distinct from other DQ methods by employing the multiple boundary conditions in a di erent manner. For structural and plate problems, the methodology employs the displacement within the domain as the only degree of freedom, whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co-ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem. Employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently. In order to demonstrate the capability of the new methodology, all cases of free vibration analysis of rectangular isotropic plates, in which the conventional DQ methods have had some sort of di culty to arrive at a converged or accurate solution, are carried out. Excellent convergence behaviour and accuracy in comparison with exact results and=or results obtained by other approximate methods were obtained. The analogous DQ formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised. It must be emphasized that the computational e orts of this new methodology are not more than for the conventional di erential quadrature methods