Parametric study and stability analysis on nonlinear traveling wave vibrations of rotating thin cylindrical shells

Parametric study and stability analysis on nonlinear traveling wave vibrations of rotating thin cylindrical shells with simply supported boundary conditions are carried out in the paper. Considering the Coriolis forces as well as the initial hoop tension due to rotation, an infinite-dimensional gyro system model with nonlinearity is established by using Lagrange equations. Based on this model, convergence analysis is performed and the most significant modes dominating the nonlinear behavior are recognized to discretize it to a finite multi-degree system. Then, the periodic solutions of the system are tracked by using harmonic balance method combined with arc length continuation technique. Furthermore, parametric studies are performed and the effects of rotating speed, damping ratio and the amplitude of excitation on the nonlinear dynamic behavior of the shell are investigated. Meanwhile, the Floquet theory is employed to carry out stability analysis of the periodic solutions. The results shown in this paper illustrate the nonlinear dynamic evolution of the traveling wave vibration for rotating thin cylindrical shells.