Free Vibration Analysis of Rotating Functionally Graded Joined Cylindrical-Conical-Cylindrical Shells with Arbitrary Boundary Conditions

In order to promote the application of functionally graded materials in engineering fields, this paper focuses on analyzing the traveling wave vibration characteristics of rotating functionally graded joined cylindrical-conical-cylindrical shells. Firstly, the material properties of the shell are established based on the Voigt model. The energy equation of the shell is derived by utilizing Donnell’s thin shell theory. Then, the boundary conditions and continuity conditions between the shells are simulated using artificial springs. Additionally, the displacement function is constructed by using Chebyshev polynomials, and the modal frequency equations of the cylindrical-conical-cylindrical joined shells are solved using the Rayleigh–Ritz method. The results show that the traveling wave frequency increases with an increase in the gradient exponent. The stronger the constraint effect of the boundary conditions, the more stable the structure becomes. Axial springs have a greater impact on the frequency of traveling waves in the structure compared to other springs.