Free vibration of Mindlin plates based on the relative displacement plate element

In this paper, free vibration of Mindlin plates using the relative displacement element has been studied. Firstly, the governing equations of motion of Mindlin plates are reformulated using relative displacement concept rather than the rotational degrees of freedom, which has a good property of representation of the rotary inertia effect. Secondly, based on these formulations, the corresponding stiffness matrix and mass matrix are derived using isoparametric concept and assumed strain method, respectively. Finally, the natural frequencies of a circular plate are computed and in comparison with the theoretical solution, it is quite accurate in the numerical sense.