In this paper free vibration analysis of two rectangular isotropic plates, which are connected to each other by two translational and rotational springs along the edges, are investigated. The equation of motion and associated boundary and continuity conditions are derived using the extended Hamilton principle. To solve the eigenvalue problem, the Ritz method is utilized. Numerical investigations are presented to show some applications of this method. In this research two types of problems are investigated: first, vibration of a continuous plate and second, free vibration of two hinged plates. This approach is usually referred to as the artificial spring method, which can be regarded as a variant of the classical penalty method. In order to validate the results, the achieved results are compared to results which are presented in literatures.
