Wave based method (WBM) for free vibration analysis of cross-ply composite laminated cylindrical shells with arbitrary boundaries

In this paper, the wave based method (WBM) is presented to analyze the free vibration of composite laminated cylindrical shells with general classical and elastic restrained boundaries. The Reissner-Naghid's theory is adopted to establish the equations of the motion force and moments, the displacement functions of composite laminated cylindrical shells are extended to wave functions which can accurately satisfy the equations of motion and boundary conditions. According to the kinetic relationship of the composite laminated cylindrical shell, the final equation of the composite shell will be obtained to calculate the free vibration results. To validate its accuracy, the vibration results of composite laminated cylindrical shells subject to various boundary conditions including the classical cases, elastic restraints and their combinations by WBM are compared with those published in the literature. The numerical values of the errors are used to prove the high precision and wide application of WBM. Furthermore, the effects of several important parameters, including boundary conditions, length to radius ratio, and elastic modulus on natural frequencies are discussed. Compared with other existing numerical methods, the present solution has the characteristics of complete matrix assembly and high calculation accuracy. When the boundary conditions change, only the initial parameters of the matrix need modifying to adapt.