In this paper, a new and an efficient solution method based on local gradient smoothing method has been applied to free vibration problem of open composite laminated cylindrical and conical shells with elastic boundary conditions. The theoretical model is formulated by the first-order shear deformation theory, and the motion equation is obtained by the Hamilton’s principle. The motion equation is discretized by meshless shape function; in this process, the derivatives of the shape function are approximated by local gradient smoothing method. The accuracy, applicability and efficiency of this method are demonstrated for free vibrations of open composite laminated cylindrical and conical shells with different geometric, material parameters and boundary condition. The numerical results show good convergence characteristics and good agreement between the present method and the existing literature. And through several numerical examples, some useful results for free vibration results of open composite laminated cylindrical and conical shells are obtained, which may serve as a benchmark solutions for researchers to check their analytical and numerical methods.

本文将基于局部梯度平滑法的一种新的有效的求解方法应用于具有弹性边界条件的开口复合叠层圆柱壳和圆锥壳的自由振动问题。通过一阶剪切变形理论建立理论模型，并根据汉密尔顿原理获得运动方程。运动方程通过无网格形状函数离散化；在这个过程中，形状函数的导数通过局部梯度平滑法来近似。证明了该方法在具有不同几何，材料参数和边界条件的开放复合叠层圆柱壳和圆锥壳的自由振动下的准确性，适用性和效率。数值结果表明，该方法具有很好的收敛性，并且与现有文献具有很好的一致性。并通过几个数值例子，获得了开放复合材料层合圆柱壳和圆锥壳自由振动结果的一些有用结果，可作为研究人员检查其解析和数值方法的基准解决方案。