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Zhang Yunfa, Kong Xianren. Analysis on vibration suppression response of nonlinear energy sink with combined nonlinear damping. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 355-364 doi: 10.6052/0459-1879-22-563
 Citation: Zhang Yunfa, Kong Xianren. Analysis on vibration suppression response of nonlinear energy sink with combined nonlinear damping. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 355-364

# ANALYSIS ON VIBRATION SUPPRESSION RESPONSE OF NONLINEAR ENERGY SINK WITH COMBINED NONLINEAR DAMPING

##### doi: 10.6052/0459-1879-22-563
• Accepted Date: 2023-01-06
• Available Online: 2023-01-07
• Nonlinear energy sink is a kind of vibration energy absorption device, which plays an important role in vibration suppression of structure. In this paper, the correlation analysis of vibration suppression for a system with combined nonlinear damping nonlinear energy sink is carried out. Firstly, the theoretical model of the system with combined nonlinear damping nonlinear energy sink is described. The motion equations of the system model are derived by using the complex variable average method, and the slow variable equations of the system are obtained. Secondly, the slow variable equations of the system are analyzed by using the multi-scale method. By studying the slow invariant manifold and phase trajectories of the system, the condition basis of the strongly modulated response of the system is described. In addition, the influence law of the external excitation amplitude on the frequency detuning coefficient interval in the presence of the strongly modulated response is revealed by analyzing the system with one-dimensional mapping. Finally, the energy spectrum, time response and Poincare mapping are applied to study the vibration suppression of the system with combined nonlinear damping nonlinear energy sink, the influence law of different damping ratio, damping and stiffness of nonlinear energy sink on its vibration suppression effect is revealed. Meanwhile, it is found that the response of the nonlinear energy sink with combined nonlinear damping is consistent with that of the main structure. In addition, it is verified that the nonlinear energy sink with combined nonlinear damping proposed in this study has good vibration suppression ability.

•  [1] Xie F, Aly AM. Structural control and vibration issues in wind turbines: A review. Engineering Structures, 2020, 210: 110087 [2] Lu Z, Wang Z, Zhou Y, et al. Nonlinear dissipative devices in structural vibration control: A review. Journal of Sound & Vibration, 2018, 423: 18-49 [3] Zang J, Zhang YW, Ding H, et al. The evaluation of a nonlinear energy sink absorber based on the transmissibility. Mechanical Systems and Signal Processing, 2018, 125: 99-122 [4] Geng XF, Ding H. Two-modal resonance control with an encapsulated nonlinear energy sink. Journal of Sound and Vibration, 2022, 520: 116667 [5] 陆泽琦, 陈立群. 非线性被动隔振的若干进展. 力学学报, 2017, 49(3): 15 (Lu Zeqi, Chen Liqun. Some recent progresses in nonlinear passive isolations of vibrations. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 15 (in Chinese) [6] Vakakis AF, Gendelman OV, Bergman LA, et al. Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems I. Springer, 2008 [7] 熊怀, 孔宪仁, 刘源. 阻尼对耦合非线性能量阱系统影响研究. 振动与冲击, 2015, 34(11): 116-121 (Xiong Huai, Kong Xianren, Liu Yuan. Influence of structural damping on a system with nonlinear energy sinks. Journal of Vibration and Shock, 2015, 34(11): 116-121 (in Chinese) [8] Barredo E, Rojas GL, Mayén J, et al. Innovative negative-stiffness inerter-based mechanical networks. International Journal of Mechanical Sciences, 2021, 205: 106597 [9] Weiss M, Savadkoohi AT, Gendelman OV, et al. Dynamical behavior of a mechanical system including Saint-Venant component coupled to a non-linear energy sink. International Journal of Non-Linear Mechanics, 2014, 63: 10-18 [10] Sarmeili M, Ashtiani H, Rabiee AH. Nonlinear energy sinks with nonlinear control strategies in fluid-structure simulations framework for passive and active FIV control of sprung cylinders. Communications in Nonlinear Science and Numerical Simulation, 2021, 97: 105725 [11] Kopidakis G, Gp, T, Aubry S. Targeted energy transfer through discrete breathers in nonlinear systems. Physical Review Letters, 2001, 87: 165501 [12] Al-Shudeifat MA. Highly efficient nonlinear energy sink. Nonlinear Dynamics, 2014, 76(4): 1905-1920 [13] Xu KF, Zhang YW, Zang J, et al. Integration of vibration control and energy harvesting for whole-spacecraft: Experiments and theory. Mechanical Systems and Signal Processing, 2021, 161: 107956 [14] Fang B, Timo T, Krack M, et al. Vibration suppression and modal energy transfers in a linear beam with attached vibro-impact nonlinear energy sinks. Communications in Nonlinear Science and Numerical Simulation, 2020, 91: 105415 [15] Wang J, Wang B, Liu Z, et al. Experimental and numerical studies of a novel asymmetric nonlinear mass damper for seismic response mitigation. Structural Control and Health Monitoring, 2020, 27(4): e2513 [16] 范舒铜, 申永军. 简谐激励下黏弹性非线性能量阱的研究. 力学学报, 2022, 54(9): 2567-2576 (Fan Shutong, Shen Yongjun. Research on a viscoelastic nonlinear energy sink under harmonic excitation. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2567-2576 (in Chinese) [17] Zang J, Cao RQ, Zhang YW. Steady-state response of a viscoelastic beam with asymmetric elastic supports coupled to a lever-type nonlinear energy sink. Nonlinear Dynamics, 2021, 105: 1327-1341 [18] Wang J, Wierschem N, Spencer BF, et al. Experimental study of track nonlinear energy sinks for dynamic response reduction. Engineering Structures, 2015, 94: 9-15 [19] Al-Shudeifat MA. Nonlinear energy sinks with piecewise-linear nonlinearities. Journal of Computational and Nonlinear Dynamics, 2019, 14(12): 124501 [20] Chen YY, Qian ZC, Zhao W, et al. A magnetic Bi-stable nonlinear energy sink for structural seismic control. Journal of Sound and Vibration, 2020, 473: 115233 [21] 吕嘉琳, 牛江川, 申永军等. 动力吸振器复合非线性能量阱对线性镗杆系统的振动控制. 力学学报, 2021, 53(11): 3124-3133 (Lü Jialin, Niu Jiangchuan, Shen Yongjun, et al. Vibration control of linear boring bar by dynamic vibration absorber combined with nonlinear energy sink. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(11): 3124-3133 (in Chinese) [22] Wang GX, Ding H, Chen LQ. Nonlinear normal modes and optimization of a square root nonlinear energy sink. Nonlinear Dynamics, 2021, 104(2): 1069-1096 [23] Geng XF, Ding H, Mao XY, et al. Nonlinear energy sink with limited vibration amplitude. Mechanical Systems and Signal Processing, 2021, 156: 107625 [24] 张运法, 孔宪仁, 岳程斐. 耦合组合刚度非线性能量阱的线性振子动力学分析. 振动与冲击, 2022, 41(13): 10 (Zhang Yunfa, Kong Xianren, Yue Chengfei. Dynamic analysis of linear oscillator with combined stiffness nonlinear energy sink. Journal of Vibration and Shock, 2022, 41(13): 10 (in Chinese) [25] Zhang Y, Cao Q. The recent advances for an archetypal smooth and discontinuous oscillator. International Journal of Mechanical Sciences, 2022, 214: 106904 [26] Gendelman OV, Starosvetsky Y. Quasi-periodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing. Journal of Applied Mechanics, 2007, 74(2): 325-331 [27] Savadkoohi AT, Lamarque CH, Dimitrijevic Z. Vibratory energy exchange between a linear and a nonsmooth system in the presence of the gravity. Nonlinear Dynamics, 2012, 70(2): 1473-1483 [28] Wang C, Moore KJ. On nonlinear energy flows in nonlinearly coupled oscillators with equal mass. Nonlinear Dynamics, 2021, 103(1): 343-366 [29] Gendelman OV, Starosvetsky Y, Feldman M. Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: Description of response regimes. Nonlinear Dynamics, 2008, 51(1): 31-46 [30] Xiong H, Kong X, Yang Z, et al. Response regimes of narrow-band stochastic excited linear oscillator coupled to nonlinear energy sink. Chinese Journal of Aeronautics, 2015, 28(2): 457-468 [31] Theurich T, Vakakis AF, Krack M. Predictive design of impact absorbers for mitigating resonances of flexible structures using a semi-analytical approach. Journal of Sound and Vibration, 2022, 516: 116527 [32] Abdollahi A, Khadem SE, Khazaee M, et al. On the analysis of a passive vibration absorber for submerged beams under hydrodynamic forces: An optimal design. Engineering Structures, 2020, 220: 110986 [33] Kong X, Li H, Wu C. Dynamics of 1-dof and 2-dof energy sink with geometrically nonlinear damping: application to vibration suppression. Nonlinear Dynamics, 2018, 91(1): 733-754 [34] Starosvetsky Y, Gendelman OV. Vibration absorption in systems with a nonlinear energy sink: nonlinear damping. Journal of Sound and Vibration, 2009, 324(3-5): 916-939 [35] Liu Y, Chen G, Tan X. Dynamic analysis of the nonlinear energy sink with local and global potentials: geometrically nonlinear damping. Nonlinear Dynamics, 2020, 101(4): 2157-2180 [36] Tehrani MG, Elliott SJ. Extending the dynamic range of an energy harvester using nonlinear damping. Journal of Sound and Vibration, 2014, 333(3): 623-629 [37] Mallik AK, Kher V, Puri M, et al. On the modelling of non-linear elastomeric vibration isolators. Journal of Sound and Vibration, 1999, 219(2): 239-253 [38] Elliott SJ, Tehrani MG, Langley RS. Nonlinear damping and quasi-linear modelling. Philosophical Transactions of the Royal Society A:Mathematical, Physical and Engineering Sciences, 2015, 373(2051): 20140402 [39] Gendelman OV, Gourdon E, Lamarque CH. Quasiperiodic energy pumping in coupled oscillators under periodic forcing. Journal of Sound and Vibration, 2006, 294(4-5): 651-662 [40] Zhang Y, Kong X, Yue C, et al. Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness. Nonlinear Dynamics, 2021, 105(1): 167-190

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###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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