The development of the dynamic stiffness matrix for rectangular plate element undergoing in-plane vibration is presented in this paper. Gorman's superposition method is exploited to obtain the solution of the governing equations of motion. The dynamic stiffness matrix of completely free rectangular plate element is derived using the Projection method. Free vibration analysis of plate assemblies with arbitrary boundary conditions is carried out. The results obtained using the proposed method, are in very good agreement with the results obtained using exact solutions and finite element method. Modeling of plate assemblies using the spectral element method demonstrate high precision, accuracy and low memory cost in comparison with the finite element method.
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