纵向与横向振动耦合作用下轴向运动梁的非线性振动研究

Study on nonlinear vibration of an axially moving beam with coupled transverse and longitudinal motions

利用增量谐波平衡法(IHB法)研究轴向运动梁在纵向与横向振动耦合作用下的非线性振动,尤其是在横向第1,2固有频率之比ω1/ω2接近1∶3情况下的内部共振。首先利用哈密顿原理建立非惯性参考系下轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用Galerkin方法离散运动方程。再利用IHB法进行非线性振动的分析。典型算例获得了纵向振动与横向振动耦合时非线性振动复杂的频幅响应曲线,探讨了耦合情况下对系统振动的影响,揭示了很多复杂而有趣的非线性现象。

The Incremental Harmonic Balance （IHB） method was used in analysis of nonlinear vibration of the axially moving beam with coupled transverse and longitudinal motions. Attention was focused on the internal resonance in the neighborhood of the case when the eigen frequencies ratio of the first two transverse modes is 1 ： 3. The rnotioa equations of the axially moving beam were derived according to the Hamilton＇s principle and discretized by the Galerkin＇s method. Then, the IHB method was employed to solve the nonlinear vibration equations. Numerical results show the complicated frequency-amplitude response curves and the coupling effects on vibration of the axially moving beam and reveal the rich and interesting nonlinear phenomena.