Dynamics analysis of rotating shells with arbitrary boundary conditions

This study investigates the free-vibration characteristics of cylindrical shells subjected to complex boundary conditions utilizing the Ritz method. Arbitrary boundary conditions are simulated by introducing elastic springs at both ends of the shell, and an analytical derivation is provided for the variation law of spring potential energy under different constraints. The convergence behavior of the system is influenced by both the stiffness values of the springs and the selection of admissible functions. The accuracy of the proposed theoretical model is validated through numerical simulations and experimental tests, demonstrating excellent agreement among theoretical, numerical, and experimental results. For nonlinear vibration characteristics, this article focuses on analyzing how transverse excitation amplitude, in-plane excitation amplitude, and damping coefficient affect the bifurcation behavior within the system. It is observed that under identical parameter conditions, there exists a significant difference in nonlinear dynamic behavior between two resonance states. As both damping coefficient and excitation amplitude increase, complex phenomena such as period-doubling bifurcations emerge. Dynamic responses, including bifurcation diagrams, phase portraits, and Poincaré maps, are numerically obtained using the Runge-Kutta method, revealing the complex nonlinear behaviors of the system. These findings provide valuable insights for addressing nonlinear vibration challenges in metallic shells with arbitrary boundary constraints.