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.

本文对简单支撑边界条件下的旋转薄圆柱壳的非线性行波振动进行了参数研究和稳定性分析。考虑到科里奥利力以及旋转引起的初始环向张力，利用拉格朗日方程建立了具有非线性的无穷大陀螺系统模型。在此模型的基础上，进行收敛分析，并识别出支配非线性行为的最高有效模式，以将其离散化为有限的多度数系统。然后，采用谐波平衡法结合电弧长度连续技术，对系统的周期解进行跟踪。此外，还进行了参数研究，以及转速的影响，研究了阻尼比和激励幅度对壳体非线性动力学行为的影响。同时，采用浮球理论对周期解进行稳定性分析。本文显示的结果说明了旋转薄圆柱壳时行波振动的非线性动力学演化。