组合刚度非线性能量阱减震性能研究

PDF(4153 KB)

振动与冲击 ›› 2025, Vol. 44 ›› Issue (9) : 203-213.

地震科学与结构抗震

组合刚度非线性能量阱减震性能研究

吴梦南1，宁西占*1,2，张洪福3

作者信息 +

Seismic mitigation performance of combined stiffness nonlinear energy sink

WU Mengnan1, NING Xizhan*1,2, ZHANG Hongfu3

Author information +

文章历史 +

摘要

为解决常规非线性能量阱(nonlinear energy sink,NES)在低能量输入时难以触发靶向能量传递的问题，在立方刚度NES的基础上引入低阶非线性刚度项，提出一种组合刚度NES，以提高NES减震性能的鲁棒性。提出考虑不同层级能量输入的NES参数优化策略，采用遗传算法对组合刚度NES、立方刚度NES和调谐质量阻尼器(tuned mass damper,TMD)进行参数数值寻优，对比分析了不同阻尼器的减震性能。结果表明，组合刚度NES的减震性能全面优于立方刚度NES，对不同层级能量输入的鲁棒性几乎与TMD相当，而对主结构频率变化的鲁棒性则优于TMD。利用数值小波变换对地震响应的功率谱进行分析，揭示了组合刚度NES能在较宽频带与主结构产生强烈的瞬时内共振俘获行为，由此表明其具有极强的频率鲁棒性。对能量在受控系统中不同部分间的传递分析表明，高阶非线性刚度仅在高能量输入时转移主结构能量，而低阶非线性刚度在低能量输入时仍可有效转移主结构能量，揭示了组合刚度NES具有良好的能量输入鲁棒性。

Abstract

To address the issue that conventional Nonlinear Energy Sink (NES) has difficulty in triggering targeted energy transfer at low energy input, a combined stiffness NES is proposed by introducing a low-order nonlinear stiffness term into the cubic stiffness NES to improve its seismic mitigation performance robustness. An optimization strategy considering different energy input levels is proposed, and the genetic algorithm is used to optimize the parameters of the combined stiffness NES, cubic stiffness NES, and TMD. The seismic mitigation performances of different dampers are compared and analyzed. The results show that the seismic mitigation performance of the combined stiffness NES is comprehensively superior to that of the cubic stiffness NES, and its robustness to energy input is similar to TMD, while its robustness to the frequency change of the main structure is better. By analyzing the power spectrum of the seismic response with the numerical wavelet transform, it is revealed that the combined stiffness NES can generate a strong instantaneous internal resonance capture behavior with the main structure in a wider frequency band, indicating that it has extremely strong frequency robustness. The analysis of the transfer of energy between different parts in the controlled system shows that the high-order nonlinear stiffness only transfers the energy of the main structure at high energy input, while the low-order nonlinear stiffness can still effectively transfer the energy of the main structure at low energy input, revealing that the combined stiffness NES has good energy input robustness.

导出引用

吴梦南1, 宁西占1, 2, 张洪福3. 组合刚度非线性能量阱减震性能研究[J]. 振动与冲击, 2025, 44(9): 203-213

WU Mengnan1, NING Xizhan1, 2, ZHANG Hongfu3. Seismic mitigation performance of combined stiffness nonlinear energy sink[J]. Journal of Vibration and Shock, 2025, 44(9): 203-213

参考文献

[1] 李春祥, 刘艳霞, 王肇民. 质量阻尼器的发展[J]. 力学进展, 2003, 33(2): 194-206.
LI Chunxiang, LIU Yanxia, WANG Zhaomin. A review on mass dampers [J]. Advances in Mechanics, 2003, 33(2): 194-206.
[2] 鲁正, 王自欣, 吕西林. 非线性能量阱技术研究综述[J]. 振动与冲击, 2020, 39(04): 1-16.
LU Zheng, WANG Zixin, LÜ Xilin. A review on nonlinear energy sink technology [J]. Journal of Vibration and Shock, 2020, 39(04): 1-16.
[3] Sapsis T P, Vakakis A F, Gendelman O V, et al. Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1: 1 resonance captures: Part II, analytical study [J]. Journal of Sound and Vibration, 2009, 325(1-2): 297-320.
[4] Gendelman O V. Targeted energy transfer in systems with non-polynomial nonlinearity [J]. Journal of Sound and Vibration, 2008, 315(3): 732-745.
[5] Gendelman O V, Starosvetsky Y, Feldman M. Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: description of response regimes [J]. Nonlinear Dynamics, 2008, 51: 31-46.
[6] Al-Shudeifat M A. Highly efficient nonlinear energy sink [J]. Nonlinear Dynamics, 2014, 76: 1905-1920.
[7] Gendelman O, Manevitch L I, Vakakis A F, et al. Energy pumping in nonlinear mechanical oscillators: part I—dynamics of the underlying Hamiltonian systems [J].Journal of Applied Mechanics,2001, 68(1): 34-41.
[8] 谭平, 刘良坤, 陈洋洋, 等. 非线性能量阱减振系统受基底简谐激励的分岔特性分析[J]. 工程力学, 2017, 34(12): 67-74.
TAN Ping, LIU Liangkun, CHEN Yangyang, et al. Bifurcation analysis of nonlinear energy sink absorption system under ground harmonic excitation [J]. Engineering Mechanics, 2017, 34(12): 67-74.
[9] 刘良坤, 潘兆东, 谭平, 等. 非线性能量阱系统受基底简谐激励的参数优化分析[J]. 振动与冲击, 2019, 38(22): 36-43.
LIU Liangkun, PAN Zhaodong, TAN Ping, et al. Parameter optimization analysis of a nonlinear energy sink system under base harmonic excitation [J]. Journal of Vibration and Shock, 2019, 38(22): 36-43.
[10] 隋鹏, 申永军, 王晓娜. 复变量平均法与其他近似方法的异同[J]. 振动与冲击, 2023, 42(10): 289-296.
SUI Peng, SHEN Yongjun, WANG Xiaona. Similarities and differences between the complexification-averaging method and other approximation methods [J]. Journal of Vibration and Shock, 2023, 42(10): 289-296.
[11] McFarland D M, Bergman L A, Vakakis A F. Experimental study of non-linear energy pumping occurring at a single fast frequency [J]. International Journal of Non-Linear Mechanics, 2005, 40(6): 891-899.
[12] 陈洋洋, 陈凯, 谭平等. 负刚度非线性能量阱减震控制性能研究[J]. 工程力学, 2019, 36(03): 149-158.
CHEN Yangyang, CHEN Kai, TAN Ping, et al. A study on structural seismic control performance by nonlinear energy sinks with negative stiffness [J]. Engineering Mechanics, 2019, 36(3): 149-158.
[13] Wang J, Wierschem N, Spencer Jr B F, et al. Experimental study of track nonlinear energy sinks for dynamic response reduction [J]. Engineering Structures, 2015, 94: 9-15.
[14] 王菁菁, 浩文明, 吕西林. 单边碰振轨道非线性能量阱减震性能及碰撞参数研究[J]. 振动与冲击, 2019, 38(16): 64-70.
WANG Jingjing, HAO Wenming, LÜ Xilin. A parametric study of single-sided vibro-impact track nonlinear energy sink for seismic response reduction [J]. Journal of Vibration and Shock, 2019, 38(16): 64-70.
[15] 刘中坡, 吕西林, 鲁正, 等. 轨道型非线性能量阱振动控制的振动台试验研究[J]. 建筑结构学报, 2016, 37(11): 1-9.
LIU Zhongpo, LÜ Xilin, LU Zheng, et al. Experimental inerstigation on vibration control effect of track nonlinear energy sink [J]. Journal of Building Structures, 2016, 37(11): 1-9.
[16] Dekemele K, Van Torre P, Loccufier M. Design, construction and experimental performance of a nonlinear energy sink in mitigating multi-modal vibrations [J]. Journal of Sound and Vibration, 2020, 473: 115243.
[17] 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[J]. 振动与冲击, 2022, 41(13): 103-111.
ZHANG Yunfa, KONG Xianren, YUE Chengfei. Dynamic analysis of linear oscillator with coupled combined stiffness NES [J]. Journal of Vibration and Shock, 2022, 41(13): 103-111.
[18] 刘良坤, 谭平, 闫维明, 等. 一种NES与TMD的混合控制方案研究[J]. 工程力学, 2017, 34(09): 64-72.
LIU Liangkun, TAN Ping, YAN Weiming, et a1. Analysis of a hybrid scheme comprised of nonlinear energy sink and tuned mass damper [J]. Engineering Mechanics, 2017, 34(09): 64-72.
[19] 郑雨强, 王菁菁. 一种内部碰撞型三质量阻尼器试验验证及数值模拟分析[J]. 振动与冲击, 2023, 42(14):84-91.
ZHENG Yuqing, WANG Jingjing. Experimental validation and numerical analyses of a novel type of vibro-impact tri-mass damper [J]. Journal of Vibration and Shock, 2023, 42(14): 84-91.
[20] 陈建恩, 张维兴, 刘军, 等. 多尺度串联非线性能量阱的减振效能及阻尼连接方式研究[J]. 振动与冲击, 2022, 41(10): 147-153.
CHEN Jianen, ZHANG Weixing, LIU Jun, et al. Vibration reduction efficiency and damping connection type of multi-scale series nonlinear energy sinks [J]. Journal of Vibration and Shock, 2022, 41(10): 147-153.
[21] 王菁菁, 张超, 刘志彬, 等. 非对称非线性质量阻尼器试验研究及鲁棒性分析[J]. 振动与冲击, 2022, 41(03): 176-182.
WANG Jingjing, ZHANG Chao, LIU Zhibin, et al. Tests and robustness analysis for asymmetric NES [J]. Journal of Vibration and Shock, 2022, 41(03): 176-182.
[22] 刘志彬, 谭平, 王菁菁, 等. 新型非对称惯容NES减震控制性能研究[J]. 振动与冲击, 2023, 42(02): 116-125.
LIU Zhibin, TAN Ping, WANG Jingjing, et al. Performance analysis of a novel asymmetric inerter NES for seismic response mitigation [J]. Journal of Vibration and Shock, 2023, 42(02): 116-125.
[23] 宁西占, 吴梦南, 张洪福, 等. 一种可实现任意阶刚度和能量收集的非线性能量阱装置[P]. 中国: CN202410136119.5, 2024-03-29.
NING Xizhan, WU Mengnan, ZHANG Hongfu, et al. A nonlinear energy sink device capable of achieving arbitrary-order stiffness and energy harvesting[P]. China, CN202410136119.5, 2024-03-29.
[24] Zhang S, Zhou J, Ding H, et al. Dual-power nonlinear energy sink for targeted energy transfer in ultra-wide range of impulsive energy[J]. International Journal of Non-Linear Mechanics, 2024, 159: 104623.