Fundamental frequency analysis of single specially orthotropic, generally orthotropic and anisotropic rectangular layered plates by the differential quadrature method

A differential quadrature method is presented for computation of the fundamental frequency of a thin single-layer specially orthotropic and anisotropic rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomial functions for the differential operators. By doing this, the uncoupled and coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations. The results for the eigenvalue (or fundamental frequency) for all the cases analyzed are compared with solutions obtained by another numerical method. Effects of level of discretization, boundary conditions, aspect ratio and taper ratio on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use much less computer time.