Vibration analysis of stepped rectangular plates using the extended Kantorovich method

In this study, vibration behaviors of stepped plates are investigated based on the variational principle of minimum total energy and the extended Kantorovich method. The out-of-plane displacement is represented by a separable function of parameters x and y. A set of governing equations, boundary conditions, and continuity conditions in the form of ordinary differential equations are derived from the energy condition. The natural frequency and out-of-plane displacement function can be determined numerically from the derived equations and conditions. Solutions from the proposed approach are in good agreement with results from past studies and those of the finite element method.