非线性能量阱刚度优化计算与振动台试验

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摘要本文介绍了一种通过几何非线性产生非线性回复力的NES，并对它的宽频控制特性进行了研究。首先通过解析方式求得1:1共振下频率与能量之间的关系并绘制频率能量图，频率能量图直观的表达了当NES与线性振子连接到一起的时候，其相对于线性振子的振动频率与系统中能量水平有着直接关系。然后，在多自由度振动系统的模态空间中使用解析的方法将NES刚度与线性振子的能量、频率与振型建立起相关的表达式。由表达式得到振动系统在一定能量水平下，NES达到较优控制效果所需要的非线性刚度。根据较优刚度计算方法，设计了NES振动控制试验并进行振动台试验。为了试验NES宽频控制特性，振动台台面输入采用了针对频域测试的Chirp信号，试验过程中通过改变NES的弹簧刚度与增加被控框架质量来改变框架动力学特性的方法以检验NES宽频控制的效果。试验结果表明NES有较好的宽频控制效果，即使其刚度偏离优化值或被控对象动力学特性发生一定改变，NES依然能发挥较好的振动控制作用。

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	刘中坡1
	吕西林2
	王栋2
	乌建中1

关键词 ： NES, 振动控制, 振动台试验, 非线性振动

Abstract：

Nonlinear energy sink is proposed and its main feature that mitigating vibrations in broad frequency range is explored in this paper. First, the expressions of backbone branch S11± that represent 1:1 internal resonance is derived through use of analytical method. According to the expressions, the frequency-energy plot is got. The vibration frequency of the NES that attached to the linear oscillator and the energy levels in the linear oscillator has a direct relationship which is clearly illustrated in the frequency-energy plot. Then, the formulas that define the relationship between the stiffness of NES and the energy of MDOF linear oscillators are derived in modal space. So, the optimal solution of NES stiffness can be calculated with regard to the energy level of the target to be controlled. Based on the optimal computations of experimental target, the shaking table experiments that investigate the performance of NES vibration mitigation are designed and conducted. To validate the wide frequency vibration controlling attributes of NES, a set of springs with different stiffness are employed and dynamic properties of the experimental frame are modified in the tests. Experimental results demonstrate that NES has broad frequency band vibration controlling feature, it still works well even its stiffness deviate from the optimal value or there are some difference between the real and designing dynamic parameters of the experimental target.

Key words： NES vibration control shaking table experiment nonlinear vibration

收稿日期: 2015-10-28 出版日期: 2016-10-15

引用本文:

刘中坡1，吕西林2，王栋2，乌建中1 . 非线性能量阱刚度优化计算与振动台试验[J]. 振动与冲击, 2016, 35(20): 77-84.
Liu Zhongpo 1, LU Xilin 2, Wang Dong 2, WU Jianzhong1 . Stiffness Optimization of Nonlinear Energy Sink and Shaking Table Test. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(20): 77-84.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2016/V35/I20/77

[1] R.E. Roberson., Synthesis of a nonlinear dynamic vibration absorber [J]. Journal of the Franklin Institute, 1952, 254(3): 205-220.
[2] A.F. Vakakis, O. Gendelman. Energy pumping in nonlinear mechanical oscillators: part ii: resonance capture [J]. Journal of Applied Mechanics, 2001, 68(1): 42-48.
[3] A F. Vakakis. Inducing passive nonlinear energy sinks in vibrating systems [J]. Transactions-American Society of Mechanical Engineers Journal of Vibration and Acoustics, 2001, 123(3): 324-332.
[4] E. Gourdon, C.H. Lamarque. Energy pumping with various nonlinear structures: numerical evidences [J].Nonlinear Dynamics, 2005, 40(3): 281-307.
[5] Panagopoulos P N, A.F Vakakis, S. Tsakirtzis. Transient resonant interactions of finite linear chains with essentially nonlinear end attachments leading to passive energy pumping [J]. International Journal of Solids and Structures, 2004, 41(22): 6505-6528.
[6] O. Gendelman, L. Manevitch, A.F. Vakakis, et al. A degenerate bifurcation structure in the dynamics of coupled oscillators with essential stiffness nonlinearities [J]. Nonlinear Dynamics, 2003, 33(1): 1-10.
[7] Y.S. Lee, G. Kerschen, A.F. Vakakis, et al. Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment [J]. Physica D: Nonlinear Phenomena, 2005, 204(1):41-69.
[8] 张也弛,孔宪仁,杨正贤等.非线性吸振器的靶能量传递及参数设计[J].振动工程学报,2011, 34(2):111-117.
Zhang Ye-chi, Kong Xian-ren, Yang Zheng-xian, Zhang Hong-liang, et al. Targeted energy transfer and parameter design of a nonlinear vibration absorber [J]. Journal of Vibration Engineering, 2011, 34(2):111-117.
[9] 张也弛,孔宪仁，张红亮. 非线性耦合振子间的靶能量传递研究:保守系统中的完全能量传递[J].振动与冲击,2012, 31(1):150-155.
Zhang Ye-chi, Kong Xian-ren¸Zhang Hong-liang. Targeted energy transfer among coupled nonlinear oscillators:complete energy exchange in a conservative system [J]. Journal of Vibration and Shock, 2012, 31(1):150-155.
[10] 孔宪仁,张也弛.两自由度非线性吸振器在简谐激励下的振动抑制[J].航空学报, 2012, 33(6):1020-1029
Kong Xian-ren, Zhang Ye-chi. Vibration suppression of a two-degree-of-freedom nonlinear energy sink under harmonic excitation. Acta Aeronautica et Astronautica Sinica. 2012, 33(6):1020-1029.
[11] 陈勇，徐羿. 基于非线性能量吸振器的高耸结构减振分析[J].振动与冲击,2014, 33(9):27-32.
Chen Yong, Xu Yi. Vibration suppression analysis for a tall structure attached with a nonlinear energy sink absorber [J]. Journal of Vibration and Shock, 2014, 33(9):27-32.
[12] A. Carrella, M.J. Brennan, T.P. Waters. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic [J]. Journal of Sound and Vibration, 2007, 301(3-5):678-689.
[13] G. Kerschen, Y.S. Lee, A.F. Vakakis, et al. Irreversible passive energy transfer in coupled oscillators with essential nonlinearity [J]. SIAM Journal on Applied Mathematics, 2005, 66(2):648-679.
[14] G. Kerschen, M. Peeters, J.C. Golinval, et al. Nonlinear normal modes, Part I: A useful framework for the structural dynamicist [J]. Mechanical Systems and Signal Processing, 2009, 23(1):170-194.
[15] L. Manevitch, E. Gourdon, C.H. Lamarque. Towards the design of an optimal energetic sink in a strongly inhomogeneous two degree of freedom system [J]. Journal of Applied Mechanics, 2007, 74(6):1078-1086.
[16] V.N. Pilipchun, Transient mode localization in coupled strongly nonlinear exactly solvable oscillators [J]. Nonlinear Dynamics, 2008, 51(1): 245-258.
[17] O. Gendelman, Y. Starosvetsky, M. Feldman. Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: Description of response regimes [J]. Nonlinear Dynamics, 2008, 51(1-2):31-46.
[18] B. Vaurigaud, A.T. Savadkoohi, C.H. Lamarque. Efficient targeted energy transfer with parallel nonlinear energy sinks: theory and experiment [J]. Journal of Computational and Nonlinear Dynamics, 2011, 6(4):1-10.
[19] 熊怀,孔宪仁,刘源.阻尼对耦合非线性能量阱系统影响研究[J].振动与冲击,2015, 34(11):116-121.
Xiong Huai，Kong Xian-ren，Liu Yuan. Influence of structural damping on a system with nonlinear energy sinks [J]. Journal of Vibration and Shock, 2015, 34(11):116-121.