Nonlinear global dynamic characteristics and experimental validation of a cylindrical shell
Abstract
Based on first-order shear deformation theory and the Rayleigh-Ritz method, this paper establishes the dynamic model for a cylindrical shell with various boundary conditions (fixed, simply supported, free or elastically supported etc.) by means of Chebyshev polynomials and the artificial boundary spring method. To validate the proposed approach, a comparative study is first conducted with existing literature, finite element simulations, and experimental modal tests. The results demonstrate that the method can accurately predict the natural frequencies and mode shapes of the shell. Subsequently, the method of multiple scales is introduced to perform a perturbation analysis of the nonlinear governing equations. Through polar coordinate transformations, the four-dimensional averaged equations of the system are derived. Finally, based on the averaged equations, the amplitude–frequency response characteristics are systematically analyzed, revealing typical nonlinear phenomena such as multi-valued solutions, jump instabilities, and softening–hardening spring behaviors. Furthermore, the Runge–Kutta algorithm is employed to obtain the bifurcation diagrams, phase portraits, Poincaré maps, and maximum Lyapunov exponents. The results indicate that the external excitation amplitude acts as the dominant parameter inducing bifurcations and chaos, whereas the detuning parameter exhibits a weakly sensitive local perturbation effect.