Vibration analysis of closed laminate conical, cylindrical shells and annular plates using meshfree method

A local gradient smoothing method(LGSM) in the framework of meshless theory is developed for implementing vibration analysis of closed laminate conical, cylindrical shells and annular plates. Based on the theoretical assumptions of the first-order laminated structure, the governing equations and boundary condition equations of the structure elements of revolution are derived and numerically discretized for the discrete vibration characteristic equations of the studied structures. Then, the meshless method is used to solve the vibration characteristic of the composite laminated shell, in which the derivatives of the displacement variables are approximated by employing LGSM. On this basis, the effects of the number of the involved discrete nodes and the dimensional coefficient related to the local smooth domain on the solution convergence are examined in detail. Meanwhile, for sake of checking the applicability of LGSM, several numerical results simulated by the presented method are compared with those from some published literature as well as FEM models. Moreover, some parametric studies with regard to the influence of structural boundary conditions, geometric dimensions, and fiber angle on the vibration behaviors of composite laminated shells are analyze. The results reveal that the developed LGSM meshless method has a good application potential in clarifying vibration phenomena of such laminated structure.