Natural Characteristics of Thin-Walled Cylindrical Shells Made with Functional Gradient Materials under Interval Constraints

The vibration characteristics of the thin-walled functional gradient material cylindrical shell with complex boundary conditions are studied in this paper. The dynamical model of the cylindrical shell is established by the orthogonal polynomial and trigonometric function where the interval rigid constraints on the side generatrix and both bottom rings of the cylindrical shell are considered. To describe the interval constraint, the power series multiplier polynomial method is proposed, then the constraining expression is constructed by combining with the admissible function. The characteristic equation of the constrained cylindrical shell is derived by the Rayleigh–Ritz method, and natural frequencies are obtained. The validation of the proposed method is verified by comparing with the result of the traditional method and the finite-element method. Numerical simulations, including the material property, structural parameter, and constraining parameter, show the dynamic characteristic of the cylindrical shell. Results show that the power series multiplier polynomial is more feasible on the traditional constraint and superior on the interval constraint. The proposed method resolves the limitation that the traditional Lagrange multiplier can only construct the point constraint. It provides a new idea for the structural design of cylindrical shells with complex boundaries conditions in the aerospace field.