动力吸振技术及其创新设计研究进展

doi:10.3901/JME.2025.21.002

摘要/Abstract

摘要： 动力吸振作为解决结构振动问题的有效手段之一，其性能瓶颈的突破对航空航天、国防军工等国之重器领域的高端装备可靠性跃升具有重要战略意义。以构型创新为主线，系统梳理了单自由度、组合式单自由度、多自由度、可调谐及非线性五大类型动力吸振器的研究进展。单自由度吸振器结构简单、稳定可靠、便于实现，是当下实际工程中应用最为广泛的结构形式，但其窄频特性短板催生了组合式与多自由度设计；组合式吸振器通过并联/串联拓扑拓展频带，实现了频带拓展与工程实现难度的平衡；多自由度吸振器通过对质量单元多个空间自由度的充分利用，实现了多维或多模态振动的高效抑制；可调谐吸振器结合调谐机构与半主动控制，解决了主振结构动态特性变化工况下的最优适配难题；非线性吸振器则利用靶能量传递机制，在宽频抑振中展现出独特优势。对比分析表明，构型创新通过自由度扩展、参数自适应调整及刚度非线性化，显著提升了吸振器的抑振性能与环境适应性，设计方法也经历了从传统参数优化向构型创新驱动的范式转变。同时，基于柔性元件的刚度单元重构，为构型驱动的性能跃升提供了理论基石。未来，动力吸振器的抑振性能将向更高层次突破：更高幅值抑制率、更优动态适应性、更大抑振带宽以及更多抑振自由度。此外，研究有望推动振动控制技术向“抑振－储能－感知”一体化方向演进，为航空航天、高端制造装备等尖端领域振动抑制提供理论支撑与技术范式。

关键词: 动力吸振, 柔性机构, 构型创新, 多自由度

Abstract: As an effective solution for structural vibration suppression, the breakthrough in performance bottlenecks of dynamic vibration absorbers (DVAs) holds significant strategic importance for enhancing the reliability of high-end equipment in national strategic sectors such as aerospace and defense. The research progress in five major DVA types is systematically reviewed: single-degree-of-freedom (SDOF) DVAs, multiple DVAs, multi-DOF DVAs, tunable DVAs, and nonlinear DVAs, with a focus on structural innovation. SDOF DVAs, characterized by their structural simplicity, stability, and easy implementation, remain the most widely used configuration in engineering, nevertheless their narrowband limitations have spurred the development of combined and multi-DOF designs. Multiple SDOF DVAs achieve broad bandwidth through parallel/serial topological configurations, balancing bandwidth enhancement with engineering feasibility. Multi-DOF DVAs leverage spatial freedom of mass units to enable efficient multi-dimensional or multi-mode vibration suppression. Tunable DVAs integrate tuning mechanisms with semi-active control to address optimal adaptation under time-varying structural dynamics. Nonlinear DVAs demonstrate unique advantages in broadband vibration control via targeted energy transfer mechanisms. Comparative analysis reveals that structural innovations, including freedom-degree expansion, parameter adaptive tuning, and nonlinear stiffness design, have substantially improved vibration suppression performance and environmental adaptability, driving a paradigm shift from traditional parameter optimization to configuration-driven design. Simultaneously, the reconfiguration of stiffness units based on flexures has established a theoretical cornerstone for configuration-driven performance enhancement of DVAs. Future advancements are expected to achieve higher vibration attenuation amplitudes, superior dynamic adaptability, broader suppression bandwidths, and multi-directional vibration control. Furthermore, this field is poised to catalyze the evolution of integrated vibration suppression, energy harvesting and sensing technologies, providing theoretical foundations and technical frameworks for vibration control in aerospace and advanced manufacturing systems.

Key words: dynamic vibration absorber, compliant mechanism, type innovation, multi-degree-of-freedom

中图分类号:

O328
TH112

马文硕, 朱昊宽, 杨毅青, 于靖军. 动力吸振技术及其创新设计研究进展[J]. 机械工程学报, 2025, 61(21): 2-17.

MA Wenshuo, ZHU Haokuan, YANG Yiqing, YU Jingjun. State of the Art of Dynamic Vibration Absorption[J]. Journal of Mechanical Engineering, 2025, 61(21): 2-17.

参考文献

[1] KRENK S，HOGSBERG J. Tuned mass absorber on a flexible structure[J]. Journal of Sound and Vibration，2014，333(6)：1577-1595.
[2] WAN M，LIANG X，YANG Y，et al. Suppressing vibrations in milling-trimming process of the plate-like workpiece by optimizing the location of vibration absorber[J]. Journal of Materials Processing Technology，2020，278：116499.
[3] YAMADA K，ASAMI T. Passive vibration suppression using 2-degree-of-freedom vibration absorber consisting of a beam and piezoelectric elements[J]. Journal of Sound and Vibration，2022，532：116997.
[4] AIDA T，ASO T，NAKAMOTO K，et al. Vibration control of shallow shell structures using a shell-type dynamic vibration absorber[J]. Journal of Sound and Vibration，1998，218(2)：245-267.
[5] ABD M Y，PUTRA A，JALIL N A A，et al. Effects of structural parameters on the dynamics of a beam structure with a beam-type vibration absorber[J]. Advances in Acoustics and Vibration，2012，2012：1-10.
[6] BAE J，HWANG J，ROH J，et al. Vibration suppression of a cantilever beam using magnetically tuned-mass- damper[J]. Journal of Sound and Vibration，2012，331(26)：5669-5684.
[7] SCHMITZ T，HONEYCUTT A，GOMEZ M，et al. Multi-point coupling for tool point receptance prediction[J]. Journal of Manufacturing Processes，2019，43：2-11.
[8] LIAO J，YU D，ZHANG J，et al. An efficient experimental approach to identify tool point frf by improved receptance coupling technique[J]. The International Journal of Advanced Manufacturing Technology，2017，94(1-4)：1451-1460.
[9] JI Y，BI Q，ZHANG S，et al. A new receptance coupling substructure analysis methodology to predict tool tip dynamics[J]. International Journal of Machine Tools and Manufacture，2018，126：18-26.
[10] STĂNCIOIU D，OUYANG H. Structural modification formula and iterative design method using multiple tuned mass dampers for structures subjected to moving loads[J]. Mechanical Systems and Signal Processing，2011，28：542-560.
[11] OZER M B，ROYSTON T J. Extending den hartog’s vibration absorber technique to multi-degree-of-freedom systems[J]. Journal of Vibration and Acoustics，2004，127(4)：341-350.
[12] WONG W O，CHEUNG Y L. Optimal design of a damped dynamic vibration absorber for vibration control of structure excited by ground motion[J]. Engineering Structures，2008，30(1)：282-286.
[13] WANG X，HE T，SHEN Y，et al. Parameters optimization and performance evaluation for the novel inerter-based dynamic vibration absorbers with negative stiffness[J]. Journal of Sound and Vibration，2019，463：114941.
[14] 隋鹏，申永军，杨绍普. 一种含惯容和接地刚度的动力吸振器参数优化[J]. 力学学报，2021，53(5)：1412-1422.SUI Peng，SHEN Yongjun，YANG Shaopu. Parameters optimization of a dynamic vibration absorber with inerter and grounded stiffness[J]. Chinese Journal of Theoretical and Applied Mechanics，2021，53(5)：1412-1422.
[15] 范盛喆，孙汝奇，赵轩，等. 阻尼调控下两类动力吸振器的H∞设计与试验[J]. 力学学报，202456(11)：3324- 3332.FAN Shengzhe，SUN Ruqi，ZHAO Xuan，et al. H∞ design and experimental study of two types of dynamic vibration absorbers with tunable damping[J]. Chinese Journal of Theoretical and Applied Mechanics，2024，56(11)：3324-3332.
[16] BROWN B，SINGH T. Minimax design of vibration absorbers for linear damped systems[J]. Journal of Sound and Vibration，2011，330(11)：2437-2448.
[17] BIAN J，JING X. A nonlinear x-shaped structure based tuned mass damper with multi-variable optimization (x-absorber)[J]. Communications in Nonlinear Science and Numerical Simulation，2021，99：105829.
[18] DOU J，YAO H，CAO Y，et al. Enhancement of bistable nonlinear energy sink based on particle damper[J]. Journal of Sound and Vibration，2022，547：117547.
[19] ZENG Y，DING H，DU R，et al. Micro-amplitude vibration suppression of a bistable nonlinear energy sink constructed by a buckling beam[J]. Nonlinear Dynamics，2022，108(4)：3185-3207.
[20] LIU Q，LIU H，ZHANG J. Optimization of nonlinear energy sink using euler-buckled beams combined with piezoelectric energy harvester[J]. Mechanical Systems and Signal Processing，2025，223：111812.
[21] ZUO L，NAYFEH S A. Minimax optimization of multi-degree-of-freedom tuned-mass dampers[J]. Journal of Sound and Vibration，2003，272(3-5)：893-908.
[22] 刘辛军，于靖军. 机器人机构学[M]. 北京：机械工业出版社，2021.LIU Xinjun，YU Jingjun. Robot mechanism science[M]. Beijing：China Machine Press，2021.
[23] DEN HARTOG J P. Mechanical vibration[M]. New York：McGraw-Hill，1940.
[24] CRANDALL S H，MARK W D. Random vibration in mechanical systems[M]. Pittsburgh：Academic Press，1963.
[25] YAMAGUCHI H. Damping of transient vibration by a dynamic absorber[J]. Transactions of the Japan Society of Mechanical Engineers Series C，1988，54(499)：561-568.
[26] FRAHM H. Device for damping vibrations of bodies：U.S. Patent，989958[P]. 1909-03-05.
[27] ORMONDROYD J，DEN HARTOG I P. The theory of thedynamic vibration absorber[J]. ASME Joural of AppliedMechanics，1928，50：9-22.
[28] KAWASHIMA T. Vibration prevention by a three-element dynamic vibration absorber[J]. Transactions of the Japan Society of Mechanical Engineers Series C，1992，58(548)：1024-1029.
[29] ASAMI T，NISHIHARA O. H2 optimization of the three-element type dynamic vibration absorbers[J]. Journal of Vibration and Acoustics，2002，124(4)：583-592.
[30] REN M Z. A variant design of the dynamic vibration absorber[J]. Journal of Sound and Vibration，2001，245(4)：762-770.
[31] SHEN Y，CHEN L，YANG X，et al. Improved design of dynamic vibration absorber by using the inerter and its application in vehicle suspension[J]. Journal of Sound and Vibration，2015，361：148-158.
[32] ZHANG Z，LU Z，DING H，et al. An inertial nonlinear energy sink[J]. Journal of Sound and Vibration，2019，450：199-213.
[33] DOGAN H，SIMS N D，WAGG D J. Implementation of inerter-based dynamic vibration absorber for chatter suppression[J]. Journal of Manufacturing Science and Engineering，2023，145(8)：084502.
[34] LIANG Q，LI L. Optimal design for a novel inerter-based clutching tuned mass damper system[J]. Journal of Vibration and Control，2020，26(21-22)：2050-2059.
[35] HA S I，YOON G H. Numerical and experimental studies of pendulum dynamic vibration absorber for structural vibration[J]. Journal of Vibration and Acoustics，2020，143(1)：011013.
[36] LEE H M，HAN S J，KIM D，et al. Optimization of structural design with pendulum dynamic vibration absorber using genetic algorithm[J]. Journal of Vibration and Control，2022，29(13-14)：3038-3051.
[37] YANG Y，XU D，LIU Q. Milling vibration attenuation by eddy current damping[J]. The International Journal of Advanced Manufacturing Technology，2015，81(1-4)：445-454.
[38] XU D，LU X，XU B. Design and modeling of a passive magnetic vibration absorber for robotic polishing process[J]. Journal of Manufacturing Processes，2023，95：204-216.
[39] DUNCAN G S，TUMMOND M F，SCHMITZ T L. An investigation of the dynamic absorber effect in high-speed machining[J]. International Journal of Machine Tools and Manufacture，2005，45(4-5)：497-507.
[40] WANG M，ZAN T，YANG Y，et al. Design and implementation of nonlinear tmd for chatter suppression：An application in turning processes[J]. International Journal of Machine Tools and Manufacture，2010，50(5)：474-479.
[41] YANG Y，GAO H，MA W，et al. Design of a turning cutting tool with large length-diameter ratio based on three-element type vibration absorber[J]. Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture，2020，234(6-7)：1032-1043.
[42] 张明华，杨国庆，杨毅青，等. 内置动力吸振器的宽频减振车刀设计及试验[J]. 振动与冲击，2023，42(18)：338-344.ZHANG Minghua，YANG Guoqing，YANG Yiqing，et al. Design and experiment of a broadband vibration- damping turning tool with a built-in dynamic vibration absorber[J]. Journal of Vibration and Shock，2023，42(18)：338-344
[43] SNOWDON J C，JONES D I G. Vibration and shock in damped mechanical systems[J]. Journal of Applied Mechanics，1969，36(2)：383-383.
[44] XU K，IGUSA T. Dynamic characteristics of multiple substructures with closely spaced frequencies[J]. Earthquake Engineering & Structural Dynamics，1992，21(12)：1059-1070.
[45] IGUSA T，XU K. Vibration control using multiple tuned mass dampers[J]. Journal of Sound and Vibration，1994，175(4)：491-503.
[46] HOANG N，WARNITCHAI P. Design of multiple tuned mass dampers by using a numerical optimizer[J]. Earthquake Engineering & Structural Dynamics，2004，34(2)：125-144.
[47] ZUO L，NAYFEH S A. Optimization of the individual stiffness and damping parameters in multiple-tuned-mass- damper systems[J]. Journal of Vibration and Acoustics，2005，127(1)：77-83.
[48] 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. Development of mass dampers[J]. Advances in Mechanics，2003，33(2)：194-206.
[49] ZUO L. Effective and robust vibration control using series multiple tuned-mass dampers[J]. Journal of Vibration and Acoustics，2009，131(3)：031003.
[50] ZHU X，CHEN Z，JIAO Y. Optimizations of distributed dynamic vibration absorbers for suppressing vibrations in plates[J]. Journal of Low Frequency Noise，Vibration and Active Control，2018，37(4)：1188-1200.
[51] LI C. Performance of dual-layer multiple tuned mass dampers for structures under ground excitations[J]. International Journal of Structural Stability and Dynamics，2006，6(4)：541-557.
[52] LEE J，KIM C J，LEE C，et al. Optimal design of multiple tuned mass dampers to reduce vibrations of a ram-type structure with varying dynamics via a control theoretic framework[J]. Journal of Manufacturing Science and Engineering，2019，142(2)：021009.
[53] BRECHER C，SCHMIDT S，FEY M. Analytic tuning of robust multi-mass dampers[J]. CIRP Annals，2016，65(1)：365-368.
[54] ZHANG J，XIE F，MA Z，et al. Design of parallel multiple tuned mass dampers for the vibration suppression of a parallel machining robot[J]. Mechanical Systems and Signal Processing，2023，200：110506.
[55] WANG M，ZAN T，GAO X，et al. Suppression of the time-varying vibration of ball screws induced from the continuous movement of the nut using multiple tuned mass dampers[J]. International Journal of Machine Tools and Manufacture，2016，107：41-49.
[56] 白鸿柏，陈毅鹏，任志英，等. 用于高温管道的二重动力吸振器设计及力学性能试验[J]. 郑州大学学报，2024，45(5)：37-44.BAI Hongbai，CHEN Yipeng，REN Zhiying，et al. Design and mechanical performance testing of a dual dynamic vibration absorber for high-temperature pipelines[J]. Journal of Zhengzhou University，2024，45(5)：37-44.
[57] 王帅，孙磊，吴君，等. 失谐整体叶盘多模态振动抑制的吸振器阵列方法[J]. 力学学报，2023，55(10)：2261-2273.WANG Shuai，SUN Lei，WU Jun，et al. Vibration absorber array method for multi-mode vibration suppression of detuned integral bladed disks[J]. Chinese Journal of Theoretical and Applied Mechanics，2023，55(10)：2261-2273.
[58] YANG Y，MUÑOA J，ALTINTAS Y. Optimization of multiple tuned mass dampers to suppress machine tool chatter[J]. International Journal of Machine Tools and Manufacture，2010，50(9)：834-842.
[59] 杨毅青，刘强，王民. 面向车削颤振抑制的多重阻尼器优化设计[J]. 振动工程学报，2010，23(4)：468-474.YANG Yiqing，LIU Qiang，WANG Min. Optimization of multiple dampers for chatter suppression in turning[J]. Journal of Vibration Engineering，2010，23(4)：468-474.
[60] MA W，YANG Y，YU J. Design and optimization of multiple single-dof tuned mass dampers based on flexure design theory[C]//Proceedings of the ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference，Quebec：ASME，2018：1-8.
[61] NAKANO Y，TAKAHARA H，KONDO E. Countermeasure against chatter in end milling operations using multiple dynamic absorbers[J]. Journal of Sound and Vibration，2012，332(6)：1626-1638.
[62] 王军，雷鸿飞，余业龙，等. 一种双自由度动力减振镗杆：中国，CN201710422257.X[P]. 2017-11-10.WANG Jun，LEI Hongfei，YU Yelong，et al. A dual- degree-of-freedom dynamic vibration damping boring bar：China，CN201710422257.X[P]. 2017-11-10.
[63] 韩锋. 多频动力吸振器优化设计技术研究[D]. 南京：南京航空航天大学，2014.HAN Feng. Research on optimization design technology of multi-frequency dynamic vibration absorbers[D]. Nanjing：Nanjing University of Aeronautics and Astronautics，2014.
[64] MA W，JIN X，YU J，et al. Oppositely oriented series multiple tuned mass dampers and application on a parallel machine tool[J]. Mechanical Systems and Signal Processing，2022，163：108196.
[65] REN H，LIU S，DONG L，et al. A multimodal dynamic vibration absorber for controlling longitudinal vibration of propulsion shafting system[J]. Applied Ocean Research，2024，148：104011.
[66] YIN L，XU W，HU Z，et al. A novel dynamic vibration absorber for vibration control of piping systems under multi-frequency harmonic excitations[J]. Scientific Reports，2025，15(1)：2086.
[67] VERDIRAME J M，NAYFEH S A，ZUO L. Design of multi-degree-of-freedom tuned-mass dampers[C]//Proceedings of the SPIE's 9th Annual International Symposium on Smart Structures and Materials，San Diego：SPIE，2002：98-108.
[68] ZUO L，NAYFEH S A. The two-degree-of-freedom tuned-mass damper for suppression of single-mode vibration under random and harmonic excitation[J]. Journal of Vibration and Acoustics，2005，128(1)：56-65.
[69] JANG S J，BRENNAN M J，Rustighi E，et al. A simple method for choosing the parameters of a two degree-of-freedom tuned vibration absorber[J]. Journal of Sound and Vibration，2012，331(21)：4658-4667.
[70] REZAZADEH H，JAFARZADEH V，ATABAKHSH S，et al. A novel passive nonlinear two-dof internal resonance-based tuned mass damper[J]. Mechanical Systems and Signal Processing，2023，204：110788.
[71] MA W，YU J，YANG Y. Graphical design methodology of multi-degrees-of-freedom tuned mass damper for suppressing multiple modes[J]. Journal of Vibration and Acoustics，2020，143(1).
[72] 于靖军，裴旭，宗光华. 机械装置的图谱化创新设计[M]. 北京：科学出版社，2014.YU Jingjun，PEI Xu，ZONG Guanghua. Graphical design and innovation of mechanical devices[M]. Beijing：Science Press，2014.
[73] 于靖军，毕树生，裴旭，等. 柔性设计[M]. 北京：高等教育出版社，2018.YU Jingjun，BI Shusheng，PEI Xu，et al. Flexible design：Analysis and synthesis of compliant mechanisms[M]. Beijing：Higher Education Press，2018.
[74] MOKRANI B，TIAN Z，ALALUF D，et al. Passive damping of suspension bridges using multi-degree of freedom tuned mass dampers[J]. Engineering Structures，2017，153：749-756.
[75] YANG Y，DAI W，LIU Q. Design and implementation of two-degree-of-freedom tuned mass damper in milling vibration mitigation[J]. Journal of Sound and Vibration，2015，335：78-88.
[76] 杨毅青，代巍. 两自由度被动阻尼器设计及数控加工应用[J]. 计算机集成制造系统，2015，21(10)：2653-2658.YANG Yiqing，DAI Wei. Design and CNC machining application of a two-degree-of-freedom passive damper[J]. Computer Integrated Manufacturing Systems，2015，21(10)：2653-2658.
[77] YANG Y，DAI W，LIU Q. Design and machining application of a two-dof magnetic tuned mass damper[J]. The International Journal of Advanced Manufacturing Technology，2016，89(5-8)：1635-1643.
[78] MA W，YU J，YANG Y，et al. Optimization and tuning of passive tuned mass damper embedded in milling tool for chatter mitigation[J]. Journal of Manufacturing and Materials Processing，2020，5(1)：2.
[79] MENG F，WAN J，XIA Y，et al. A multi-degree of freedom tuned mass damper design for vibration mitigation of a suspension bridge[J]. Applied Sciences，2020，10(2)：457-457.
[80] MA W，YANG Y，JIN X. Chatter suppression in micro-milling using shank-mounted two-dof tuned mass damper[J]. Precision Engineering，2021，72：144-157.
[81] MA W，YANG Y，YU J. General routine of suppressing single vibration mode by multi-dof tuned mass damper：Application of three-dof[J]. Mechanical Systems and Signal Processing，2019，121：77-96.
[82] SUN C，JAHANGIRI V. Bi-directional vibration control of offshore wind turbines using a 3D pendulum tuned mass damper[J]. Mechanical Systems and Signal Processing，2017，105：338-360.
[83] D’IMPERIO S，BERRUTI T M，GASTALDI C，et al. Tunable vibration absorber design for a high-precision cartesian robot[J]. Robotics，2022，11(5)：103-103.
[84] MANZONI S，BERARDENGO M，BOCCUTO F，et al. Piezoelectric-shunt-based approach for multi-mode adaptive tuned mass dampers[J]. Mechanical Systems and Signal Processing，2023，200：110537.
[85] CHATZIATHANASIOU G M，CHRYSOCHOIDIS N A，REKATSINAS C S，et al. A semi-active shunted piezoelectric tuned-mass-damper for multi-modal vibration control of large flexible structures[J]. Journal of Sound and Vibration，2022，537：117222.
[86] CHATZIATHANASIOU G M，CHRYSOCHOIDIS N A，SARAVANOS D A. A semi-active shunted piezoelectric tuned mass damper for robust vibration control[J]. Journal of Vibration and Control，2021，28(21-22)：2969-2983.
[87] 高普，刘辉，项昌乐，等. 面向实车动力传动系统的隔振与吸振综合减振技术研究[J]. 机械工程学报，2021，57(14)：244-252.GAO Pu，LIU Hui，XIANG Changle，et al. Integrated vibration reduction technology for real-vehicle powertrain systems：Combining isolation and absorption[J]. Journal of Mechanical Engineering，2021，57(14)：244-252.
[88] GAO P，XIANG C，LIU H，et al. Reducing variable frequency vibrations in a powertrain system with an adaptive tuned vibration absorber group[J]. Journal of Sound and Vibration，2018，425：82-101.
[89] PARK J E，LEE J，KIM Y K. Design of model-free reinforcement learning control for tunable vibration absorber system based on magnetorheological elastomer[J]. Smart Materials and Structures，2021，30(5)：055016.
[90] YANG Z，QIN C，RAO Z，et al. Design and analyses of axial semi-active dynamic vibration absorbers based on magnetorheological elastomers[J]. Journal of Intelligent Material Systems and Structures，2014，25(17)：2199-2207.
[91] MANI Y，SENTHILKUMAR M. Shape memory alloy-based adaptive-passive dynamic vibration absorber for vibration control in piping applications[J]. Journal of Vibration and Control，2013，21(9)：1838-1847.
[92] LEE C Y，PAI C A. Design and implementation of tunable multi-degree-of-freedom vibration absorber made of hybrid shape memory helical springs[J]. Journal of Intelligent Material Systems and Structures，2015，27(8)：1047-1060.
[93] 姚红良，王重阳，陈子冬，等. 转子系统永磁变刚度抑振及吸振研究[J]. 机械工程学报，2017，53(9)：66-72.YAO Hongliang，WANG Zhongyang，CHEN Zidong，et al. Vibration suppression and absorption using permanent magnet stiffness-varying mechanism[J]. Journal of Mechanical Engineering，2017，53(9)：66-72.
[94] HUANG X. Exploiting multi-stiffness combination inspired absorbers for simultaneous energy harvesting and vibration mitigation[J]. Applied Energy，2024，364：123124.
[95] SHUI X，WANG S. Investigation on a mechanical vibration absorber with tunable piecewise-linear stiffness[J]. Mechanical Systems and Signal Processing，2018，100：330-343.
[96] YANG Y，XIE R，LIU Q. Design of a passive damper with tunable stiffness and its application in thin-walled part milling[J]. The International Journal of Advanced Manufacturing Technology，2016，89(9-12)：2713-2720.
[97] 杨毅青，谢日成，徐东东. 旋转变刚度阻尼器抑制薄壁零件铣削颤振[J]. 振动与冲击，2018，37(2)：72-75.YANG Yiqing，XIE Richeng，XU Dongdong. Rotary variable stiffness damper for suppressing chatter in milling of thin-walled parts[J]. Journal of Vibration and Shock，2018，37(2)：72-75.
[98] MA W，YANG Y，YU J，et al. Improving processing stability of thin-walled casing workpieces by sucker- mounted tmd：Optimization，design，and implementation[J]. Mechanical Systems and Signal Processing，2024，216：111512.
[99] GUO X，ZHU Y，QU Y，et al. Design and experiment of an adaptive dynamic vibration absorber with smart leaf springs[J]. Applied Mathematics and Mechanics，2022，43(10)：1485-1502.
[100] 马强，狄杰建，赵全亮，等. 一种自调频动力吸振器及其吸振特性研究[J]. 应用力学学报，2014，31(4)：626-630.MA Qiang，DI Jiejian，ZHAO Quanliang，et al. Research on a dynamic vibration absorber with tunable resonant frequency and its damping effect[J]. Chinese Journal of Applied Mechanics，2014，31(4)：626-630.
[101] CHRISTIE M D，SUN S，DENG L，et al. A variable resonance magnetorheological-fluid-based pendulum tuned mass damper for seismic vibration suppression[J]. Mechanical Systems and Signal Processing，2018，116：530-544.
[102] 刘强，刘献礼，吴石，等. 变质量动力吸振器减振镗杆减振性能研究[J]. 哈尔滨理工大学学报，2018，23(5)：25-29.LIU Qiang，LIU Xianli，WU Shi，et al. Research on vibration reduction performance of boring bars with variable mass dynamic vibration absorbers[J]. Journal of Harbin University of Science and Technology，2018，23(5)：25-29.
[103] MEGAHED S M，EL-RAZIK A KH A. Vibration control of two degrees of freedom system using variable inertia vibration absorbers：Modeling and simulation[J]. Journal of Sound and Vibration，2010，329(23)：4841-4865.
[104] WU S T，CHEN Y R，WANG S S. Two-degree- of-freedom rotational-pendulum vibration absorbers[J]. Journal of Sound and Vibration，2010，330(6)：1052-1064.
[105] CHOWDHURY S，BANERJEE A，ADHIKARI S. The optimal design of dynamic systems with negative stiffness inertial amplifier tuned mass dampers[J]. Applied Mathematical Modelling，2022，114：694-721.
[106] ROBERSON R E. Synthesis of a nonlinear dynamic vibration absorber[J]. Journal of the Franklin Institute，1952，254(3)：205-220.
[107] VAKAKIS A F，GENDELMAN O V，BERGMAN L A，et al. Nonlinear targeted energy transfer in mechanical and structural systems[M]. Netherlands：Springer Science & Business Media，2009.
[108] GOURDON E，ALEXANDER N A，TAYLOR C A，et al. Nonlinear energy pumping under transient forcing with strongly nonlinear coupling：Theoretical and experimental results[J]. Journal of Sound and Vibration，2006，300(3-5)：522-551.
[109] SAVADKOOHI A T，VAURIGAUD B，LAMARQUE C H，et al. Targeted energy transfer with parallel nonlinear energy sinks，part ii：Theory and experiments[J]. Nonlinear Dynamics，2011，67(1)：37-46.
[110] GENG X F，DING H，MAO X Y，et al. Nonlinear energy sink with limited vibration amplitude[J]. Mechanical Systems and Signal Processing，2021，156：107625.
[111] 陈依林，杜敬涛，崔海健，等. 不同类型水平弹簧组合刚度非线性吸振器的性能分析及稳定性研究[J]. 力学学报，2023，55(1)：192-202.CHEN Yilin，DU Jingtao，CUI Haijian，et al. Performance analysis and stability study of different types of nonlinear vibration absorbers with combined stiffness of horizontal springs[J]. Chinese Journal of Theoretical and Applied Mechanics，2023，55(1)：192-202.
[112] AL-SHUDEIFAT M A. Highly efficient nonlinear energy sink[J]. Nonlinear Dynamics，2014，76(4)：1905-1920.
[113] ZENG Y，DING H，JI J C，et al. A tristable nonlinear energy sink to suppress strong excitation vibration[J]. Mechanical Systems and Signal Processing，2023，202：110694.
[114] WANG M，NAGARAJAIAH S，CHEN L. Adaptive passive negative stiffness and damping for retrofit of existing tall buildings with tuned mass damper：TMD-NSD[J]. Journal of Structural Engineering，2022，148(11)：04022180.
[115] REZAEI M，TALEBITOOTI R，LIAO W H. Exploiting bi-stable magneto-piezoelastic absorber for simultaneous energy harvesting and vibration mitigation[J]. International Journal of Mechanical Sciences，2021，207：106618.
[116] YAO H，CAO Y，DING Z，et al. Using grounded nonlinear energy sinks to suppress lateral vibration in rotor systems[J]. Mechanical Systems and Signal Processing，2019，124：237-253.
[117] MA W，YU J，YANG Y. Design and application of double-parallelograms-based tuned mass damper for low-frequency vibration absorption[J]. Journal of Vibration and Acoustics，2022，144(5)：051005.
[118] XIONG X，WANG Y，LI J，et al. Internal resonance analysis of bio-inspired x-shaped structure with nonlinear vibration absorber[J]. Mechanical Systems and Signal Processing，2022，185：109809.
[119] ZOU D，LIU G，RAO Z，et al. A device capable of customizing nonlinear forces for vibration energy harvesting，vibration isolation，and nonlinear energy sink[J]. Mechanical Systems and Signal Processing，2020，147：107101.
[120] WANG Z，DU Y，LI T，et al. A flute-inspired broadband piezoelectric vibration energy harvesting device with mechanical intelligent design[J]. Applied Energy，2021，303：117577.
[121] MÜLLER F，BECK M W，KRACK M. Experimental validation of a model for a self-adaptive beam-slider system[J]. Mechanical Systems and Signal Processing，2023，182：109551.
[122] LAN C B，CHEN Z N，HU G B，et al. Achieve frequency-self-tracking energy harvesting using a passively adaptive cantilever beam[J]. Mechanical Systems and Signal Processing，2021，156：107672.
[123] LEE D G，SHIN J C，KIM H S，et al. Autonomous resonance-tuning mechanism for environmental adaptive energy harvesting[J]. Advanced Science，2023，10：2205179.
[124] 翁俊，任可欣，于浚峰，等. 直升机桅杆上装设备动力吸振研究[J]. 电子机械工程，2024，40(4)：42-46，51. WENG Jun，REN Kexin，YU Junfeng，et al. Research on dynamic vibration absorption of helicopter mast electronic equipment[J]. Electro-Mechanical Engineering，2024，40(4)：42-46，51.
[125] HU H，HUANG R，QIN H，et al. Complex dynamics and targeted energy transfer of double-beam nonlinear energy sink with magnetic interactions[J]. Mechanical Systems and Signal Processing，2025，236：112942.
[126] WANG Z J，ZANG J，ZHANG Z，et al. Broadband vibration control in irregularly perforated composite hexagonal-prism frame via NiTi-ST-based nonlinear absorbers：Modeling，analysis，and experiments[J]. Mechanical Systems and Signal Processing，2025，237：112962.