【摘要】 高维动力系统的降阶方法一直以来是非线性动力系统领域的重要研究内容，对非线性振动系统、软体机器人和复杂结构系统的响应识别、计算及预测有着重要的意义.本文在基于参数化方法和弗洛凯理论的自激周期解不变流形降阶方法的基础上，建立了在外激励下的非自治自激振动系统的参数化降阶方法.通过采用摄动近似方法，得到了受激励下的自激系统的参数化降阶模型.依据本文所提的方法，对含有交叉耦合刚度的转子与定子碰摩模型的准周期解及其随着外激励频率变化的幅频曲线进行了预测.结果显示本文的降阶模型能够有效的预测自激振动系统的受迫情况下的动力学响应.更多还原

【Abstract】 Model reduction methods for high-dimensional dynamical systems have consistently constituted a significant research topic within the field of nonlinear dynamical systems, significantly influencing the response identification, computation, and prediction of nonlinear vibration systems, soft robots, and complex structural systems. Building upon the invariant manifold reduced method for autonomous self-excited vibration systems by parameterization method and Floquet theory, this paper establishes a parameterization method for reduced model on non-autonomous self-excited vibration systems. By employing a perturbation approximation technique, a parameterization reduced-order model for the forced self-excited system is derived. Using the proposed method, the quasi-periodic solutions and the amplitude-frequency curves varying with external excitation frequency are predicted for a rotor-stator rubbing model incorporating cross-coupled stiffness. The results show that the reduced-order model in this paper can effectively predict the dynamic response of the self-excited vibration system under external force.更多还原