In this paper, the free vibration behavior of inversely coupled composite laminated shells (ICCLSs) are studied using Haar wavelet discretization method (HWDM) for the first time. Two doubly-curved shells are inversely coupled on both end of cylindrical shell, in which the doubly-curved shell contains the elliptical, parabolic and hyperbolic shells. The individual shells are coupled by the continuous condition. The boundary condition is modeled by using the artificial spring technique. Based on the first order shear deformation theory (FSDT), the displacement field of coupled shell are established. All displacement functions containing the boundary and continuous conditions are expanded by Haar wavelet series in the meridional direction, and by trigonometric series in the circumferential direction. The boundary and continuous condition functions are contained to satisfy the constants expressed by Haar wavelet series integral form in the function of main system. The convergence and accuracy of current method for the proposed structure are verified by comparison with the finite element method (FEM). The results show that this method is very reasonable for analyzing the free vibration of ICCLSs. Then, the effects of geometric dimensions, fiber orientation angle and lamination type on the natural frequency of ICCLSs are investigated. In end, the new results on natural frequencies and mode shapes of ICCLS are presented, and they will be benchmark data for further research.

在本文中，首次使用哈尔小波离散化方法（HWDM）研究了反耦合复合层压壳（ICCLS）的自由振动行为。两个双曲壳在圆柱壳的两端反向耦合，其中双曲壳包含椭圆形、抛物线形和双曲形壳。单个壳通过连续条件耦合。边界条件是通过使用人工弹簧技术建模的。基于一阶剪切变形理论（FSDT），建立了耦合壳的位移场。所有包含边界和连续条件的位移函数在子午方向用 Haar 小波级数展开，在圆周方向用三角级数展开。主系统函数中包含边界条件函数和连续条件函数，满足以Haar小波级数积分形式表示的常数。通过与有限元方法 (FEM) 的比较，验证了当前方法对所提出结构的收敛性和准确性。结果表明，该方法对于分析ICCLS的自由振动是非常合理的。然后，研究了几何尺寸、纤维取向角和层压类型对 ICCLS 固有频率的影响。最后，给出了ICCLS固有频率和模态振型的新结果，它们将作为进一步研究的基准数据。通过与有限元方法 (FEM) 的比较，验证了当前方法对所提出结构的收敛性和准确性。结果表明，该方法对于分析ICCLS的自由振动是非常合理的。然后，研究了几何尺寸、纤维取向角和层压类型对 ICCLS 固有频率的影响。最后，给出了ICCLS固有频率和模态振型的新结果，它们将作为进一步研究的基准数据。通过与有限元方法 (FEM) 的比较，验证了当前方法对所提出结构的收敛性和准确性。结果表明，该方法对于分析ICCLS的自由振动是非常合理的。然后，研究了几何尺寸、纤维取向角和层压类型对 ICCLS 固有频率的影响。最后，给出了ICCLS固有频率和模态振型的新结果，它们将作为进一步研究的基准数据。