Free vibration of stepped rectangular Mindlin plates with non-Levy boundary conditions

Dynamic properties of rectangular stepped Mindlin plates plates with non-Levy boundary conditions are investigated in this study. Plates are modelled based on the Rayleigh-Ritz method, whereas admissible functions are obtained using hierarchic high-order Timoshenko beam finite elements. The proposed method leads to reduced and step-independent error level compared with using uniform-beam admissible functions, and the boundary conditions are better approximated. Computation involved is significantly less than using the finite element method, thus suitable to be used in environments with limited computational power. The method is demonstrated numerically on cantilevered (CFFF), mixed (CFEF) and free (FFFF) plates and experimentally on FFFF plates. Compared with experimental results, natural frequency error of an FFFF plate is less than 1% and most of the mode assurance criterion (MAC) values are above 0.9.