In this paper, for the first time, the free vibration characteristics of a joined shell structure in which three shells of revolution made of functionally graded material are elastically bonded are reported. The structure of the joined shell is formed by elastically bonding double-curved shells to both sides of the cylindrical shell in the middle, and the hyperbolic shells have elliptic, parabolic, and hyperbolic shapes. The Haar wavelet discretization method (HWDM), one of the effective, convenient and accurate numerical solution methods, is applied to investigate the free vibration behavior of various elastically joined functionally graded shells (EJFGSs). The theoretical model of the EJFGSs is formulated based on first-order shear deformation theory (FSDT). The displacement and rotation of arbitrary point of the EJFGS are expended as Haar wavelet series in the meridian direction and as a Fourier series in the circumferential direction. The boundary condition at both ends of the EJFGS and the continuous condition between its shells are modeled by the spring stiffness technique. By solving the governing equation of the whole system, the vibration characteristics of the EJFGS such as the natural frequency and the corresponding mode shape can be obtained. Through the comparisons with the previous literature and finite element method (FEM) results, the accuracy and reliability of our method are verified. Finally, new free vibration analysis results of various EJFGSs, which can be used as benchmark data for researchers in this field, are reported with parameter study.

本文首次报道了由功能梯度材料制成的三个旋转壳弹性结合的连接壳结构的自由振动特性。连接壳的结构是由双曲壳在中间的圆柱壳两侧弹性粘合而成，双曲壳有椭圆形、抛物线形和双曲线形。Haar 小波离散化方法 (HWDM) 是一种有效、方便和准确的数值求解方法，用于研究各种弹性连接功能梯度壳 (EJFGS) 的自由振动行为。EJFGS 的理论模型是基于一阶剪切变形理论 (FSDT) 制定的。EJFGS任意点的位移和旋转在子午方向上展开为Haar小波级数，在圆周方向上展开为傅里叶级数。EJFGS 两端的边界条件及其壳之间的连续条件通过弹簧刚度技术建模。通过求解整个系统的控制方程，可以得到EJFGS的固有频率和相应的模态振型等振动特性。通过与以往文献和有限元法（FEM）结果的比较，验证了我们方法的准确性和可靠性。最后，通过参数研究报告了各种 EJFGS 的新自由振动分析结果，可作为该领域研究人员的基准数据。