Accurate variational approach for free vibration of simply supported anisotropic rectangular plates

The Ritz method is one of the most elegant and useful approximate methods for analyzing free vibration of laminated composite plates. It is simple to use and also straightforward to implement. However, the Ritz method has its own difficulty in determining the natural frequencies of simply supported laminated anisotropic plates. This is caused by the fact that the natural boundary conditions in the vibration of anisotropic plates can never be exactly satisfied by a solution in a variables separable form. As a result, the calculated natural frequencies would be expected to converge to solutions a little higher than true ones. To overcome this difficulty, this paper presents a simple variational formulation with Ritz procedure in which all the natural boundary conditions are implemented in an averaging manner. It is revealed that the proposed method can produce lower upper bound solutions compared with the conventional Ritz method where the geometric boundary conditions can only be satisfied by the assumed deflection functions.