Free vibration analysis of thin functionally graded rectangular plates using the dynamic stiffness method

Abstract

In this paper, free vibration behavior of thin functionally graded rectangular plates is investigated by using the dynamic stiffness method (DSM). Classical plate theory along with the concept of physical neutral surface of the functionally graded plate is used to formulate the dynamic stiffness matrix. The dynamic stiffness matrix is finally solved by using the Wittrick-Williams algorithm to compute the natural frequencies. DSM frequencies are compared with those available in the literature. Some inaccurate published results are pointed out and possible reasons for these inaccuracies are discussed. Results for several plate parameters are given and the influence of these parameters on natural frequencies of the functionally graded plate is highlighted. The present study shows that the dynamic stiffness method provides very accurate results for vibration analysis of thin functionally graded plates and these results can be used as benchmark solutions for comparison purposes.