Wave based method for free vibration characteristics of functionally graded cylindrical shells with arbitrary boundary conditions

The wave based method (WBM) is used to analyze the free vibration characteristics of functionally graded material (FGM) cylindrical shell with arbitrary boundary conditions. The motion relationship is described by the first-order shear deformation shell theory (FSDST). The displacement components and transverse rotations are expressed as wave function expansions. In accordance with the dynamic relationship, the final governing equation and global matrix are assembled by incorporating the boundary matrices. The natural frequency of the system is obtained by solving the determinant of the global matrix. By comparing the results with those in the literature, the validity of the proposed method is verified. In addition, the influences of power-law exponents and boundary conditions on natural frequencies are analyzed. The effects of geometric parameters including the ratio of thickness to radius and the ratio of length to the radius on natural frequencies are discussed. The purpose of this paper is to demonstrate the ease of application of the WBM for the free vibration of FGM cylindrical shells with arbitrary boundary conditions. Furthermore, the advantage of the WBM are: (1) the global matrix is easy to construct; (2) different boundary conditions can be conveniently adjusted; (3) it is with high computational efficiency and precision.