High accuracy mixed finite element-Ritz formulation for free vibration analysis of plates with general boundary conditions

A high order accurate mixed finite element-Ritz method is introduced and developed to study the vibration problem of plates with general boundary conditions. The finite element method (FEM) with higher order interpolation functions is first used to discretize the spatial partial derivatives with respect to a co-ordinate direction of the plate. The Ritz method is then employed to analogize the resulting system of ordinary differential equations. A novel technique is also presented to exactly satisfy the mixed natural boundary conditions. The proposed method is applied here to solve some benchmark vibration problems of plates including isotropic and anisotropic rectangular plates, variable thickness rectangular plates, multi-span rectangular plates, and skew plates. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can yield highly accurate results for vibration problem of plates involving free edges, free corners and irregular boundaries using a small number of finite elements and Ritz terms.