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多阶梯梁系统的3:1内共振

A·特金 E·奥兹卡亚 S·M·巴哥达德利

A·特金, E·奥兹卡亚, S·M·巴哥达德利. 多阶梯梁系统的3:1内共振[J]. 应用数学和力学, 2009, 30(9): 1057-1068. doi: 10.3879/j.issn.1000-0887.2009.09.007
引用本文: A·特金, E·奥兹卡亚, S·M·巴哥达德利. 多阶梯梁系统的3:1内共振[J]. 应用数学和力学, 2009, 30(9): 1057-1068. doi: 10.3879/j.issn.1000-0887.2009.09.007
A. Tekin, E. Özkaya, S. M. BagdatlL. 3: 1 Internal Resonance in Multiple Stepped Beam Systems[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1057-1068. doi: 10.3879/j.issn.1000-0887.2009.09.007
Citation: A. Tekin, E. Özkaya, S. M. BagdatlL. 3: 1 Internal Resonance in Multiple Stepped Beam Systems[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1057-1068. doi: 10.3879/j.issn.1000-0887.2009.09.007

多阶梯梁系统的3:1内共振

doi: 10.3879/j.issn.1000-0887.2009.09.007
基金项目: 土耳其科学技术研究委员会(TUBITAK)资助项目(104M427)
详细信息
  • 中图分类号: O322;O175.29

3: 1 Internal Resonance in Multiple Stepped Beam Systems

  • 摘要: 研究了具有三次非线性项的多阶梯梁的振动.讨论了该系统3∶1内共振情况.运用多重尺度法,即一种摄动技术,得到该问题的一般近似解,并得到两种模型的振幅和相位调制方程.这些方程组用来确定稳态解及其稳定性.假设外加的强迫频率接近于较低的频率.在研究的数值部分,讨论固有频率中的3∶1情况.对两端固支和一端固支另一端简支,观测到的频率位于第一和第二固有频率之间;对两端简支,观测到的频率位于第二和第三固有频率之间.最后,利用数值算法求解3∶1内共振.第一模型为两端固支和一端固支另一端简支梁的外激励模型;第二模型为两端简支梁的外激励模型.然后,当外激励第一模型时,研究第一、二模型的振幅.当外激励第二模型时,研究第二、三模型的振幅.对振动的内共振模型,画出强迫响应、阻尼响应和频率响应曲线.同时进行这些曲线的稳定性分析.
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出版历程
  • 收稿日期:  2009-01-20
  • 修回日期:  2009-06-19
  • 刊出日期:  2009-09-15

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