梁纵向与横向耦合非线性振动分析

邢誉峰; 梁昆

doi:10.13700/j.bh.1001-5965.2014.0556

梁纵向与横向耦合非线性振动分析

doi: 10.13700/j.bh.1001-5965.2014.0556

邢誉峰^,,
梁昆

北京航空航天大学固体力学研究所, 北京 100191

基金项目: 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)

详细信息

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.

中图分类号: O322;V414.3
计量
- 文章访问数: 1501
- HTML全文浏览量: 114
- PDF下载量: 1111
- 被引次数: 0
出版历程
- 收稿日期: 2014-09-10
- 网络出版日期: 2015-08-20

Nonlinear vibration analysis of longitudinal-transverse coupled beam

XING Yufeng^,,
LIANG Kun

Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

摘要

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.
- 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.
- nonlinear /
- longitudinal and transverse coupling /
- vibration /
- finite element /
- Rayleigh beam

HTML全文

参考文献(15)

[1]	邢誉峰,谢珂, 潘忠文.纵向过载环境下变质量欧拉梁动特性分析方法[J].北京航空航天大学学报,2013,39(8):999-1003. Xing Y F,Xie K,Pan Z W.Dynamic analysis methods of variable-mass Euler beam under longitudinal overload[J].Journal of Beijing University of Aeronautics and Astronautics,2013,39(8): 999-1003(in Chinese).
[2]	邢誉峰,谢珂, 潘忠文.变质量系统振动分析的两种方法[J].北京航空航天大学学报,2013,39(7):858-862. Xing Y F,Xie K,Pan Z W.Two methods for vibration analysis of variable-mass systems[J].Journal of Beijing University of Aeronautics and Astronautics,2013,39(7):858-862(in Chinese).
[3]	夏品奇, Pun D.纵横向耦合梁的谐波响应分析[J].振动工程学报,1995,8(1):67-72. Xia P Q,Pun D.Harmonic responses of beams with longitudinal and transversal coupling[J].Journal of Vibration Engineering,1995,8(1):67-72(in Chinese).
[4]	奈弗A H,穆克D T. 非线性振动(上)[M].北京:高等教育出版社,1990:215-242. Nayfeh A H,Mook D T.Nonlinear oscillations volumel 1[M].Beijing:Higher Education Press,1990:215-242(in Chinese).
[5]	奈弗A H, 穆克D T.非线性振动(下)[M].北京:高等教育出版社,1990:93-140. Nayfeh A H,Mook D T.Nonlinear oscillations volume 2[M].Beijing:Higher Education Press,1990:93-140(in Chinese).
[6]	Han S M, Benaroya H.Non-linear coupled transverse and axial vibration of a compliant structure,Part 1:Formulation and free vibration[J].Journal of Sound and Vibration,2000,237(5):837-873.
[7]	Han S M, Benaroya H.Non-linear coupled transverse and axial vibration of a compliant structure,Part 2:Forced vibration[J].Journal of Sound and Vibration,2000,237(5):875-900.
[8]	胡义,杨建国. 梁纵横耦合振动研究[J].武汉理工大学学报:交通科学与工程版,2010,34(3):537-541. Hu Y,Yang J G.Studies on the longitudinal and lateral coupled vibration of beam[J].Journal of Wuhan University of Technology:Transportation Science & Engineering,2010,34(3):537-541(in Chinese).
[9]	黄建亮,陈树辉. 纵横向耦合轴向运动梁的自由振动响应研究[J].动力学与控制学报,2010,8(4):316-321. Huang J L,Chen S H.Study on vibration of an axially moving beam with coupled transverse and longitudinal motions[J].Journal of Dynamics and Control,2010,8(4):316-321(in Chinese).
[10]	Kuchnicki S N, Benaroya H.Coupled transverse and axial motion of a compliant structure in response to vortex-shedding loads[J].Journal of Sound and Vibration,2002,257(5):903-929.
[11]	Xu X X, Jiao S J,Cheng J L,et al.Study and test of coupled axial and transverse vibrations on drillpipe for rotary drilling rig[J].Applied Mechanics and Materials,2014,472:73-78.
[12]	张雷,王永. 尾部有推力自由梁的振动分析[J].弹道学报,2010,22(1):83-86. Zhang L,Wang Y.Vibration analysis of free-free beam with end rocket thrust[J].Journal of Ballistics,2014,22(1):83-86(in Chinese).
[13]	邢誉峰,李敏. 计算固体力学原理与方法[M].北京:北京航空航天大学出版社,2011:51-59. Xing Y F,Li M.The principle and method of computational solid mechanics[M].Beijing:Beihang University Press,2011:51-59(in Chinese).
[14]	徐荣桥. 结构分析有限元法与MATLAB程序设计[M].北京:人民交通出版社,2011:32-40. Xu R Q.Structural analysis and MATLAB program design of the finite element method[M].Beijing:China Communications Press,2006:32-40(in Chinese).
[15]	邢誉峰,李敏. 工程振动基础[M].2版.北京:北京航空航天大学出版社,2011:199-210. Xing Y F,Li M.Foundation of engineering vibration[M].2nd ed.Beijing:Beihang University Press,2011:199-210(in Chinese).