A generalized superposition method for accurate free vibration analysis of rectangular plates and assemblies.

A generalized superposition method is presented in this paper for free bending vibration analysis of single rectangular plates and assemblies of rectangular plates with arbitrary boundary conditions. The method was developed on the basis of the Levy method, the principle of superposition, and the uniform convergence of half-range Fourier cosine series for continuous functions in a closed interval. Numerical results, obtained using the proposed method for thin isotropic plates and plate assemblies, show that the proposed method is accurate and rapidly convergent. The proposed method can be extended to handle vibration of moderately thick plates made of isotropic and orthotropic materials.