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

黄建亮; 陈树辉

振动与冲击 ›› 2011, Vol. 30 ›› Issue (8) : 24-27,5.

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PDF(1220 KB)
振动与冲击 ›› 2011, Vol. 30 ›› Issue (8) : 24-27,5.
论文

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

  • 黄建亮; 陈树辉
作者信息 +

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

  • Huang Jian-liang;Chen Shu-hui
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文章历史 +

摘要

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1/2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。

Abstract

In this paper, the Incremental Harmonic Balance (IHB) method is used to analysis of nonlinear vibration of the axially moving beam with coupled transverse and longitudinal motions, attention is focused 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 are derived through the Hamilton’s Principle and discretized by the Galerkin’s method. Then, the IHB method is employed to solve the nonlinear vibration equations. Numerical results show the complicated frequency-amplitude response curves and effects on vibration of the axially moving beam with coupled transverse and longitudinal motions and reveal the rich and interesting nonlinear phenomena.

关键词

轴向运动梁 / 非线性振动 / IHB法 / 耦合 / 内部共振

Key words

Axially moving beam / nonlinear vibration / IHB method / coupled / internal resonance

引用本文

导出引用
黄建亮; 陈树辉. 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[J]. 振动与冲击, 2011, 30(8): 24-27,5
Huang Jian-liang;Chen Shu-hui . Study on nonlinear vibration of an axially moving beam with coupled transverse and longitudinal motions[J]. Journal of Vibration and Shock, 2011, 30(8): 24-27,5

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