北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (8): 1359-1366.doi: 10.13700/j.bh.1001-5965.2014.0556

• 论文 • 上一篇    下一篇

梁纵向与横向耦合非线性振动分析

邢誉峰, 梁昆   

  1. 北京航空航天大学 固体力学研究所, 北京 100191
  • 收稿日期:2014-09-10 出版日期:2015-08-20 发布日期:2015-09-08
  • 通讯作者: 邢誉峰(1964-),男,吉林农安人,教授,xingyf@buaa.edu.cn,主要研究方向为结构动力学. E-mail:xingyf@buaa.edu.cn
  • 基金资助:
    国家自然科学基金(11372021,11172028);高等学校博士学科点专项科研基金(20131102110039)

Nonlinear vibration analysis of longitudinal-transverse coupled beam

XING Yufeng, LIANG Kun   

  1. Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2014-09-10 Online:2015-08-20 Published:2015-09-08

摘要: 纵向振动和横向振动耦合是捆绑火箭等结构中的典型振动现象.以Rayleigh梁为研究对象,通过Hamilton变分原理推导了考虑应变二次项的纵向振动与横向振动耦合控制方程,并用有限元方法对该非线性系统的行为进行了模拟.针对线性系统固有振动频率和非线性纵横耦合动态响应情况,把所得结果与NASTRAN结果进行了比较,二者结果吻合,证明了本方法的正确性.在此基础上,借助振动控制方程和模拟结果,讨论了非线性系统频率与模态的时变特性,非线性动态响应频率成分特性,横向振动和纵向振动相互影响以及共振现象等.研究结果为本方法的实际应用提供了理论基础.

关键词: 非线性, 纵横耦合, 振动, 有限元, Rayleigh梁

Abstract: The coupling phenomenon of longitudinal and transverse vibration is representative in boost rocket. Taking longitudinal and transverse vibration coupling into account by using the second order term of longitudinal strain, the governing differential equations of Rayleigh beam was derived through Hamilton variational principle, and the finite element method was employed to explore the behaviors of this nonlinear coupling system. As for the inherent frequency of the corresponding linear system and the dynamic responses of nonlinear longitudinal and transverse coupling system, the obtained results were in agreement with those of NASTRAN, which validated the correctness of present method and results. According to characteristics of the viberation governing equations and the results of finite element method, the analyses focused on the time-variable property of nonlinear system frequency, the amplitude-frequency characteristic of nonlinear dynamical responses, the mutual effects of the longitudinal and transverse vibration and resonant phenomenon when the combinations of frequencies of exciting forces are closer to the frequency of the nonlinear system. The results of present study lie the theoretical foundation for the practical application of the present method.

Key words: nonlinear, longitudinal and transverse coupling, vibration, finite element, Rayleigh beam

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