欧拉-伯努利梁运动场的正交性及其能量传导特性分析

周俊; 饶柱石; 塔娜

doi:10.6052/0459-1879-14-116

欧拉-伯努利梁运动场的正交性及其能量传导特性分析

1.
上海交通大学振动、冲击、噪声研究所, 上海 200240
2. 上海交通大学, 机械系统与振动国家重点实验室, 上海 200240

基金项目: 国家重点基础研究发展计划资助项目(2014CB046302).

详细信息

作者简介:
饶柱石, 教授, 主要研究方向: 结构振动噪声分析与控制、生物力学、转子动力学.E-mail: tyuanhong@jnu.edu.cn

中图分类号: O32.7
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出版历程
- 收稿日期: 2014-04-24
- 修回日期: 2014-07-17
- 刊出日期: 2015-01-17

THE ORTHOGONALITY AND ENERGY TRANSMITION CHARACTERISTICS OF EULER-BERNOULLI BEAM DYNAMIC MOTION FIELD

1.
Institute of Vibration Shock & Noise, Shanghai Jiaotong University, Shanghai
2. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai 200240, China

Funds: The project was supported by the National Basic Research Program of China (2014CB046302).

摘要

摘要: 从无阻尼欧拉—伯努利梁振动方程解析解出发, 推导了有限长梁的关于谱系数的时间—空间平均能量和功率流表达式. 在此基础上, 从泛函分析观点, 探讨了弯曲运动场: 衰减振动、行波模式分解关于能量、功率泛函的正交性. 结果表明: 弯曲衰减振动模式和行波模式关于功率流、机械能时间—空间平均是相互独立的, 即关于场能和场功率互不干涉, 满足叠加原理; 衰减振动场导能与行波场导能的重要区别在于功率流关于右、左衰振动模式分解不满足叠加原理, 即弯曲衰减振动场间的相互"干涉"是使其具有能量传导能力的内在原因. 通过右端集中阻尼器支撑的梁的稳态功率流仿真分析计算, 表明低频区振动导能不可忽略, 同时, 衰减振动场和行波场间存在一定的能量交换现象, 但随着频率升高, 振动场传导能量不断下降, 同时能量传导效率也不断下降.
- 功率流 /
- 振导 /
- 正交性 /
- 欧拉—伯努利梁 /
- 泛函分析
Abstract: Based on analytical solution of undamped Euler-Bernoulli beam's equation of motion, the temporal & spatial average of mechanical energy and power flow's calculation formula are derived. The formula is related to spectral coefficients and based on finite length beam. From the view of functional analysis, the bending motion field, which can be decomposed into evanescent vibration and travelling wave mode, is investigated and the discussion focuses on orthogonality. The result shows that, the evanescent vibration mode is mutual independent of travelling wave mode with regard to energy and power flow functional. In another word, there is no interference between these two modes and the energy superposition principle is satisfied. The important difference between evanescent vibration and wave energy transfer is that the superposition principle is unsatisfied in the evanescent vibration energy transmit mode. That means the interference of two local vibration mode is the reason why the whole vibration field having the capability of energy conduction. The simulation result of a beam with damping at right end and harmonic exciting at middle length is given. The result exhibits that evanescent vibration energy transmit mode shouldn't be neglected in low-frequency range and it is existed that energy exchange between the two modes. But with the increase of frequency, evanescent vibration transmission mode decreases and the total efficiency of energy conducting also falls down.
- power flow /
- vibration guide /
- orthogonality /
- Euler-Bernoulli beam /
- functional analysis

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参考文献(25)

Lyon RH, Maidanik G. Power flow between linearly coupled oscillators. J Acoust Soc Am, 1962, 34(5): 632-639

游进, 孟光, 李鸿光. 声振系统中高频能量流分析法研究进展. 振动与冲击, 2012, 31(11): 62-69 (You Jin, Meng Guang, Li Hongguang. Review of mid-to-high frequency energy flow analysis method for vibro-acoustic systems. J Vib Shock, 2012, 31(11): 62-69 (in Chinese))

Lyon RH, Maidanik G. Statistical methods in vibration analysis. AIAA J, 1964, 2(6): 1015-1024

Lafont T, Totaro N, LeBot A. Review of statistical energy analysis hypotheses in vibroacoustics. Proc R Soc A, 2013, 470(2162)

Nefske DJ, Sung SH. Power flow finite element analysis of dynamic systems: basic theory and application to beams. J Vib Acoust, 111(1): 94-100

Wohlever JC, Bernhard RJ. Mechanical energy flow models of rods and beams. J Sound Vib, 1992, 153(1): 1-19

Cho PE, Bernard RJ. Energy flow analysis of coupled beams. J Sound Vib, 1998, 211(4): 593-605

张猛, 陈花玲, 祝丹晖等. 高频弯曲振动梁的随机参数能量有限元分析. 西安交通大学学报, 2013, 47(11) (Zhang Meng, Chen Hualing, Zhu Danhui, et al, Stochastic parameter energy finite element analysis of high-fequency flexural vibration beam. Journal of Xi'an Jiaotong University, 2013, 47(11) (in Chinese))

韩敬永. 基于统计能量及混合法的航天器有效载荷声振环境预示. [硕士论文]. 哈尔滨:哈尔滨工业大学, 2012 (Hang Jingyong. Research on vibro-acoutic environment prediction of space craft pay load based on statistical energy and hybrid method. [Master Thesis]. Harbin: Harbin Institute of Technology, 2012 (in Chinese))

Renno JM, Mace BR. Calculation of reflection and transmission coefficients of joints using a hybrid finite element/wave and finite element approach. J Vib Sound, 2013, 332(9):2149-2164.

姚煜中, 周俊, 饶柱石等. 充液管道能量传递途径及减振分析. 噪声与振动控制, 2011, 31(5): 13-16 (Yao Yuzhong, Zhou Jun, Rao Zhushi, et al. Analysis and assessment of vibration energy transmission of fluid-filled pipelines. Noise and Vibration Control, 2011, 31(5): 11-16 (in Chinese))

Goyder, HGD, White RG. Vibrational power flow from machines into built-up structures, part I: introduction and approximate analyses of beam and plate-like foundations. J Sound Vib, 1980, 68(1): 59-75

Miller, DW, von Flotow AH. A travelling wave approach to power flow in structural networks. J Sound Vib, 1989, 128(1): 145-162

Lase Y, Ichchou MN. Energy flow analysis of bars and beams: theoretical formulations. J Sound Vib, 1996, 192(1): 281-305

Mead DJ. Free wave propagation in periodically supported, infinite beams. J Sound Vib, 1970, 11(2): 181-197

Mead DJ. Wave propagation in continuous periodic structures: research contributions from Southampton, 1964-1995. J Sound Vib, 1996, 190(3): 495-524

von Flotow AH. Disturbance propagation in structural networks. J Sound Vib, 1986, 106(3):433-450

von Flotow AH. Traveling wave control for large space craft structures. Journal of Guidance, Control, and Dynamics, 1986, 9(4): 462-468

von Flotow AH.The acoustic limit of control of structural dynamics. In: Atluri SN, Amos AK, eds. Large Space Structures: Dynamics and Control. Berlin Heidelberg: Springer, 1988. 213-237.

程伟, 褚德超, 王大均. 梁传播的固有特性. 力学学报, 1997, 29(2): 175-181 (Cheng Wei, Zhu Dechao, Wang Dajun. Natural characteristics of wave propagation in beam. Acta Mechanica Sinica, 1997, 29(2): 175-181 (in Chinese))

朱桂东, 郑钢铁, 邵成勋. 框架结构模态分析的行波方法. 宇航学报, 1999, 20(3): 1-6 (Zhu Guidong, Zheng Gangtie, Shao Chengxun. Modal analysis for frame structures via traveling wave approach. Journal of Astronautics, 1999, 20(3): 1-6 (in Chinese))

田艳. 航天器空间桁架结构的振动特性研究. [硕士论文]. 哈尔滨: 哈尔滨工业大学, 2012 (Tian Yan. Study on vibration characteristic for space truss structure of space craft. [Master Thesis]. Harbin: Harbin Institute of Technology, 2012 (in Chinese))

周国良, 叶欣, 李小军等. 结构动力分析中多点激励问题的研究综述. 世界地震工程, 2009, 25(4): 25-32 (Zhou Guoliang, Ye Xin, Li Xiaojun, et al. Renew on dynamic analyses of structures under multi-support excitation. World Earthquake Engineering, 2009, 25(4): 25-32 (in Chinese))

Pavi? G. Vibration damping, energy and energy flow in rods and beams: governing formulae and semi-infinite systems. J Sound Vib, 2006, 291(3-5): 932-962

李思简. 大学工程力学手册. 上海: 上海交通大学出版社, 2000. 337-337 (Li Sijian. Handbook of University Engineering Mechanics. Shanghai: SJTU Press, 2000. 337-337 (in Chinese))