Vibration analysis of simply supported rectangular plates with unidirectionally, arbitrarily varying thickness

In this paper, a practical analytical method for the free vibration analysis of a simply supported rectangular plate with unidirectional, arbitrary thickness variation is proposed. First, the plate is divided into a number of regions of which the values of thickness are assumed to be constant and are given by the known thickness function of the plate. The close-form frequency function that yields the eigenvalues of the plate is extracted by considering the condition of continuity in displacement and slope between the regions and by considering the simply supported boundary condition of the plate. It is shown by several case studies that the proposed method has good convergence characteristics and yields accurate eigenvalues and mode shapes, compared with other analytical methods including FEM (ANSYS).