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.

提出了一种基于无网格理论框架的局部梯度平滑法(LGSM)，用于对封闭叠层圆锥、圆柱壳和环形板进行振动分析。基于一阶层状结构的理论假设，推导出旋转结构单元的控制方程和边界条件方程，并对所研究结构的离散振动特征方程进行数值离散。然后，采用无网格方法求解复合材料层合壳的振动特性，其中位移变量的导数采用 LGSM 近似。在此基础上，详细研究了所涉及的离散节点的数量和与局部平滑域相关的维数系数对解收敛的影响。同时，为了检验 LGSM 的适用性，将所提出的方法模拟的几个数值结果与一些已发表的文献以及有限元模型的数值结果进行了比较。此外，还分析了结构边界条件、几何尺寸和纤维角度对复合材料层合壳振动行为的影响的一些参数研究。结果表明，所开发的 LGSM 无网格方法在阐明这种层状结构的振动现象方面具有良好的应用潜力。通过所提出的方法模拟的几个数值结果与一些已发表的文献以及有限元模型的结果进行了比较。此外，还分析了结构边界条件、几何尺寸和纤维角度对复合材料层合壳振动行为的影响的一些参数研究。结果表明，所开发的 LGSM 无网格方法在阐明这种层状结构的振动现象方面具有良好的应用潜力。通过所提出的方法模拟的几个数值结果与一些已发表的文献以及有限元模型的结果进行了比较。此外，还分析了结构边界条件、几何尺寸和纤维角度对复合材料层合壳振动行为的影响的一些参数研究。结果表明，所开发的 LGSM 无网格方法在阐明这种层状结构的振动现象方面具有良好的应用潜力。