噪声与振动控制

噪声与振动控制 ›› 2013, Vol. 33 ›› Issue (3): 16-20.DOI: 10.3969/j.issn.1006-1335.2013.03.004

• 2.振动理论与数值解法 • 上一篇    下一篇

黏弹性轴向运动变张力梁非线性动力学

严巧赟，丁 虎，陈立群   

  1. ( 1. 上海大学  上海市应用数学和力学研究所，  上海  200072；2. 上海大学  力学系，  上海  200444 )
  • 收稿日期:2012-06-25 修回日期:2012-09-04 出版日期:2013-06-18 发布日期:2013-06-18
  • 通讯作者: 丁虎
  • 基金资助:

    国家自然科学基金项目(10902064);上海市青年科技启明星计划(11QA1402300); 上海市教育委员会科研创新项目(12YZ028)

Nonlinear Dynamic Behaviors of Axially Moving Viscoelastic Beams with Varying Tensions

  • Received:2012-06-25 Revised:2012-09-04 Online:2013-06-18 Published:2013-06-18
  • Contact: Ding DING

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摘要： 在黏弹性轴向运动梁横向参数振动的非线性动力学行为研究中，首次计入因速度变化引起的、沿梁的径向变化的、轴向变张力的影响。给出描述变张力轴向运动梁横向非线性振动的偏微分—积分控制方程。基于微分求积法给出轴向运动梁横向非线性参数振动的数值解，通过观察梁中点的位移、速度随时间变化的历程，识别轴向运动系统的非线性动力学行为。同时，通过从数值解中提取的相图、Poincaré映射图和频谱分析，考察轴向运动梁横向振动的分岔与混沌特性，揭示了工程应用中的非线性轴向运动系统的混沌动力学行为。

关键词: 振动与波, 轴向运动梁, 非线性振动, 微分求积法, 分岔, 混沌

Abstract: In this paper, nonlinear dynamical behavior is investigated for the transverse vibration of axially moving viscoelastic beams for the first time with varying tensions due to varying speed. The longitudinally varying tension is introduced to establish the integro-partial-differential governing equations describing the the transverse vibration of beams. Based on the numerical solutions by the differential quadrature method, the nonlinear dynamical behaviors like chaos are identified by the observation of the cources of displacement and velocity with time changing of the midpoint of the beam. Meanwhile the phase plane, the Poincaré map and the spectral analysis method are used to indicate the bifurcation and chaotic motions occurring in the transverse vibration of the axially accelerating viscoelastic beam. The paper reveals the chaotic dynamics of nonlinear axially moving systems in engineering applications.

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