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轴向变速黏弹性Timoshenko梁的非线性振动

唐有绮

唐有绮. 轴向变速黏弹性Timoshenko梁的非线性振动[J]. 力学学报, 2013, 45(6): 965-973. doi: 10.6052/0459-1879-13-099
引用本文: 唐有绮. 轴向变速黏弹性Timoshenko梁的非线性振动[J]. 力学学报, 2013, 45(6): 965-973. doi: 10.6052/0459-1879-13-099
Tang Youqi. NONLINEAR VIBRATIONS OF AXIALLY ACCELERATING VISCOELASTIC TIMOSHENKO BEAMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(6): 965-973. doi: 10.6052/0459-1879-13-099
Citation: Tang Youqi. NONLINEAR VIBRATIONS OF AXIALLY ACCELERATING VISCOELASTIC TIMOSHENKO BEAMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(6): 965-973. doi: 10.6052/0459-1879-13-099

轴向变速黏弹性Timoshenko梁的非线性振动

doi: 10.6052/0459-1879-13-099
基金项目: 国家自然科学基金青年基金(11202135)和上海应用技术学院引进人才科研启动项目(YJ2012-13)资助项目.
详细信息
    通讯作者:

    唐有绮,讲师,主要研究方向:非线性动力学与振动控制。E-mail:tangyouqi2000@163.com

  • 中图分类号: O316

NONLINEAR VIBRATIONS OF AXIALLY ACCELERATING VISCOELASTIC TIMOSHENKO BEAMS

Funds: The project was supported by the National Natural Science Foundation of China (11202135) and the Introduction of Talents Scientific Research Project of Shanghai Institute of Technology (YJ2012-13).
  • 摘要: 研究了轴向加速黏弹性Timoshenko梁的非线性参数振动。参数激励是由径向变化张力和轴向速度波动引起的。引入了取决于轴向加速度的径向变化张力,同时还考虑了有限支撑刚度对张力的影响。应用广义哈密尔顿原理建立了Timoshenko梁耦合平面运动的控制方程和相关的边界条件。黏弹性本构关系采用Kelvin模型并引入物质时间导数。耦合方程简化为具有随时间和空间变化系数的积分-偏微分型非线性方程。采用直接多尺度法分析了Timoshenko梁的组合参数共振。根据可解性条件得到了Timoshenko梁的稳态响应,并应用Routh-Hurvitz判据确定了稳态响应的稳定性。最后通过一系列数值例子描述了黏弹性系数、平均轴向速度、剪切变形系数、转动惯量系数、速度脉动幅值、有限支撑刚度参数以及非线性系数对稳态响应的影响。

     

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出版历程
  • 收稿日期:  2013-04-01
  • 修回日期:  2013-05-09
  • 刊出日期:  2013-11-18

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