纵横向耦合轴向运动梁的自由振动响应研究

研究轴向运动梁在纵向与横向振动耦合下的自由振动响应,尤其是在横向第1,2固有频率之比ω1/ω2接近1:3内共振条件下的系统响应.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,得到了运动梁含有2次和3次非线性项的运动微分方程.利用增量谐波平衡法(IHB法)分析纵向与横向振动耦合时非线性振动复杂的频幅响应曲线,探讨了相互耦合下系统在横向前2阶固有频率附近没有横向外激励作用下的自由振动响应,揭示了很多复杂而有趣的非线性现象.

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

This paper studied the nonlinear vibration of an axially moving beam with coupled transverse and longitudinal motions,and the focus was on the internal resonance in the neighborhood of a 1:3 between the first two transverse modes.First,the motion equations of the axially moving beam were derived through the Hamilton's principle,and were discretized by the Galerkin's method to obtain the quadratic and cubic nonlinearities.Then,the IHB method was applied to analyze the complicated frequency-amplitude response...