In this paper, a new meshfree approach is proposed for the three-dimensional free vibration analysis of laminated composite elliptical and paraboloidal shells of revolution. The three-dimensional theory of elasticity has been applied to formulations for free vibration analysis of laminated composite elliptical and paraboloidal shells of revolution. The field function is approximated by a new Tchebychev-point interpolation method (TPIM) shape function that uses the Tchebychev polynomial as the basis for the point interpolation method (PIM) shape function. The governing equation and boundary conditions for laminated elliptical and paraboloidal shells are obtained by combining the governing equation and boundary conditions for individual layers using a continuous condition. The artificial spring technique is introduced to generalize the boundary and continuous conditions, and the type of boundary conditions is selected according to the stiffness of the spring. The accuracy and reliability of the proposed method is verified through comparison with the results of literature and ABAQUS software. Free vibration characteristics such as natural frequency and mode shape of laminated elliptical and paraboloidal shells of revolution under various boundary conditions are presented through numerical examples.

在本文中，提出了一种新的无网格方法用于层状复合材料椭圆和旋转抛物面壳的三维自由振动分析。三维弹性理论已应用于层状复合材料椭圆和旋转抛物面壳的自由振动分析公式。场函数由新的 Tchebychev 点插值法 (TPIM) 形状函数近似，该函数使用 Tchebychev 多项式作为点插值法 (PIM) 形状函数的基础。层状椭圆壳和抛物面壳的控制方程和边界条件是通过使用连续条件组合各个层的控制方程和边界条件而获得的。引入人工弹簧技术对边界条件和连续条件进行泛化，根据弹簧的刚度选择边界条件的类型。通过与文献和ABAQUS软件的结果对比，验证了所提方法的准确性和可靠性。通过数值算例给出了各种边界条件下的层状旋转椭圆壳和抛物面壳的固有频率和振型等自由振动特性。