Effect of Geometric Nonlinearities on Nonlinear Vibrations of Closed Cylindrical Shells

Geometrically nonlinear free vibrations of closed isotropic cylindrical shells are investigated through an analytical–numerical model. The method developed is a combination of Sanders–Koiter nonlinear shell theory and the finite element method. The cylindrical shell is subdivided into cylindrical finite elements and the displacement functions are derived from exact solutions of Sander's equations for thin cylindrical shells. Expressions for the mass, linear and nonlinear stiffness matrices are determined by exact analytical integration. Various boundary conditions of shell and in-plane effects are considered. Nonlinear responses are analyzed using the Runge–Kutta numerical method. The nonlinear frequency ratio is determined with respect to the amplitude thickness ratio of the motion for different study cases. Detailed numerical results are presented for various parameters for a closed isotropic shell, indicating either hardening or softening types of nonlinear behaviors, depending on the structure data. The present results show good agreement with the published ones for several cases of shells. This research clarifies the current disagreement about various types of cylindrical shells with geometric nonlinearities.