赵雷雷 , 于曰伟 , 周长城 , 等 . 特种车辆驾驶室减振器节流阀片开度及阻尼特性研究 [J ] . 兵工学报 , 2018 , 39 ( 4 ): 645 - 654 . DOI: 10.3969/j.issn.1000-1093.2018.04.003 http://doi.org/10.3969/j.issn.1000-1093.2018.04.003 特种车辆驾驶室减振器的阻尼特性是由阀系参数决定的，准确地求解节流阀片在阀口位置的变形是通过仿真准确获取减振器阻尼特性的关键。以特种车辆驾驶室减振器为研究对象，建立其节流阀片在区间线性均布压力下的力学模型及变形解析式，并进行了正确性验证。分析阀片开度随阀系结构参数变化的规律，在此基础上建立驾驶室减振器阻尼分段特性仿真模型，并通过仿真实例与试验进行了对比验证。结果表明，不同速度下阻尼力仿真结果与试验结果相对偏差均在6.19%以内，说明所建立的驾驶室减振器阻尼分段特性仿真模型可较为真实地复现减振器的动态阻尼特性。

ZHAO L L , YU Y W , ZHOU C C , et al . Throttle slice opening size and damping characteristics of cab damper for special vehicles [J ] . Acta Armanentarii , 2018 , 39 ( 4 ): 645 - 654 . (in Chinese)

房凌晖 , 郑翔玉 , 蔡宏图 , 等 . 坦克装甲车辆防护技术发展研究 [J ] . 四川兵工学报 , 2014 , 35 ( 3 ): 23 - 26 .

FANG L H , ZHENG X Y , CAI H T , et al . Development of tank and armored vehicle protection technology [J ] . Si Chuan Ordnance Journal , 2014 , 35 ( 3 ): 23 - 26 . (in Chinese)

HARRIS C M , PIERSOL A G . Harris’ shock and vibration handbook [M ] . 6th ed. New York, NY, US : McGraw Hill , 2010 .

PLATUS D L . Negative-stiffness-mechanism vibration isolation systems [J ] . Physica A: Statistical Mechanics and its Applications , 1992 , 161 : 44 - 54 .

ROBERTSON W S , KIDNER M R F , CAZZOLATO B S , et al . Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation [J ] . Journal of Sound and Vibration , 2009 , 326 ( 1/2 ): 88 - 103 . DOI: 10.1016/j.jsv.2009.04.015 http://doi.org/10.1016/j.jsv.2009.04.015 https://linkinghub.elsevier.com/retrieve/pii/S0022460X09003423 https://linkinghub.elsevier.com/retrieve/pii/S0022460X09003423

刘兴天 , 孙靖雅 , 肖锋 , 等 . 准零刚度微振动隔振器的原理和性能研究 [J ] . 振动与冲击 , 2013 , 32 ( 21 ): 69 - 73 .

LIU X T , SUN J Y , XIAO F , et al . Principle and performance of a quasi-zero stiffness isolator for micro-vibration isolation [J ] . Journal of Vibration and Shock , 2013 , 32 ( 21 ): 69 - 73 . (in Chinese)

刘琪 , 李占龙 , 王建梅 , 等 . 准零刚度低频隔振技术的研究进展 [J ] . 机械强度 , 2020 , 42 ( 4 ): 13 - 22 .

LIU Q , LI Z L , WANG J M , et al . Research progress on quasi-zero stiffness low-frequency vibration isolation technology [J ] . Journal of Mechanical Strength , 2020 , 42 ( 4 ): 13 - 22 . (in Chinese)

张建卓 , 李旦 , 董申 , 等 . 精密仪器用超低频非线性并联隔振系统研究 [J ] . 中国机械工程 , 2004 , 15 ( 1 ): 69 - 71 .

ZHANG J Z , LI D , DONG S , et al . Study on ultra-low frequency parallel connection isolator used for precision instruments [J ] . China Mechanical Engineering , 2004 , 15 ( 1 ): 69 - 71 . (in Chinese)

胡光军 , 周生通 , 李鸿光 . 一种非线性隔振器的静力分析与实验研究 [J ] . 噪声与振动控制 , 2011 , 31 ( 6 ): 69 - 71 . DOI: 10.3969/j.issn.1006-1355-2011.06.015 http://doi.org/10.3969/j.issn.1006-1355-2011.06.015 研究一种变刚度非线性隔振器，使该隔振器具有高静刚度低刚度的效果。根据水平铰支梁受水平力弯曲理论、刚度并联理论，分析斜薄壁梁在竖直方向力的作用下的力位移以及刚度位移特性，得到斜薄壁梁结构在竖直力作用下具有负刚度特性。通过与弹簧（正刚度）结构并联，理论结合实验验证一种并联结构隔振器样机，得到该样机具有高静刚度－小静变形，低动刚度－力的变化率很小。

HU G J , ZHOU S T , LI H G . Static analysis and experiment of a nonlinear vibration isolator [J ] . Noise and Vibration Control , 2011 , 31 ( 6 ): 69 - 71 . (in Chinese)

路纯红 , 白鸿柏 , 杨建春 , 等 . 超低频非线性隔振系统的研究 [J ] . 噪声与振动控制 , 2010 , 30 ( 4 ): 10 - 12 . DOI: 10.3969/j.issn.1006-1355.2010.04.003 http://doi.org/10.3969/j.issn.1006-1355.2010.04.003 通过分析正负刚度并联隔振机理，提出了一种新型超低频被动隔振系统。该系统采用负刚度机构与正刚度弹簧并联，具有高的支撑刚度和极低的运动刚度，且系统刚度呈现非线性，解决了传统被动隔振系统存在的超低频隔振难题。通过对该系统力学特性进行分析，给出了系统刚度表达式及在平衡位置处的零刚度条件，为新型超低频非线性隔振器的设计提供了理论指导。

LU C H , BAI H B , YANG J C , et al . Research on ultra-low frequency nonlinear vibration isolation system [J ] . Noise and Vibration Control , 2010 , 30 ( 4 ): 10 - 12 . (in Chinese)

王晓杰 , 刘辉 , 郦文平 , 等 . 准零刚度扭转隔振器振动传递特性研究 [J ] . 机械工程学报 , 2018 , 54 ( 21 ): 49 - 56 . DOI: 10.3901/JME.2018.21.049 http://doi.org/10.3901/JME.2018.21.049 针对一种应用连杆弹簧负刚度结构所设计的正负刚度并联扭转隔振器，通过分析其设计参数，得到了其在静平衡位置达到准零刚度的条件。针对所述系统，建立二自由度非线性动力学微分方程，应用谐波平衡法求解了准零刚度隔振器的振动响应。考虑激励幅值、系统阻尼和转动惯量等因素，从扭转振动力矩传递和扭转振动功率流传递两个角度分析了准零刚度隔振系统的非线性振动传递特性。结果表明，此隔振系统具有良好的低频隔振效果，且表现为振动传递的硬特性；从功率流角度的分析还表明，系统的瞬时传递功率流峰值与输入功率流和耗散功率流的变化趋势保持一致。在低于共振区域的低频区间内，隔振系统前后两端的转动惯量对系统振动具有较大影响。最后，对扭转隔振器的振动隔离特性进行了试验验证，试验结果表明，隔振器具有良好的低频振动隔离特性。

WANG X J , LIU H , LI W P , et al . Vibration transmission characteristics of a quasi-zero stiffness torsional isolator [J ] . Journal of Mechanical Engineering , 2018 , 54 ( 21 ): 49 - 56 . (in Chinese) DOI: 10.3901/JME.2018.21.049 http://doi.org/10.3901/JME.2018.21.049 A torsional isolator with negative stiffness structures is proposed and the quasi-zero stiffness characteristic is got by analyzing the design parameters of this isolation system. The two-degree freedoms dynamic model is built and the harmonic balance method is employed to solve for the dynamic response of the system. Considering the influence of amplitude, damping, and rotational inertia of the isolation system, the torque transmission and vibration power flow characteristics are investigated to examine the performance of this nonlinear isolator. The results show that this torsional isolator has good low-frequency isolation performance and hardening stiffness nonlinearity. From the analysis of the power flow behavior, the results show that there has a good correlation between input power flow, dissipated power flow and instantaneous transmitted power flow. Rotational inertia has great influence to the vibration performance of system in the low frequency away from the peak frequency regions. Finally, the vibration isolation characteristics of the torsional vibration isolator are tested. The experiment results show that the isolator has good isolation characteristics of low frequency vibration.

KOVACIC I , M. BRENNA J , WATERS T P . A study of a nonlinear vibration isolator with a qusia-zero stiffness characteristic [J ] . Journal of Sound and Vibration , 2008 , 315 ( 3 ): 700 - 711 . DOI: 10.1016/j.jsv.2007.12.019 http://doi.org/10.1016/j.jsv.2007.12.019 https://linkinghub.elsevier.com/retrieve/pii/S0022460X07009960 https://linkinghub.elsevier.com/retrieve/pii/S0022460X07009960

CARRELLA A , BRENNA M J , KOVACIC I , et al . On the force transmissibility of a vibration isolator with quasi-zero-stiffness [J ] . Journal of Sound and Vibration , 2009 , 322 ( 4/5 ): 707 - 717 . DOI: 10.1016/j.jsv.2008.11.034 http://doi.org/10.1016/j.jsv.2008.11.034 https://linkinghub.elsevier.com/retrieve/pii/S0022460X08009437 https://linkinghub.elsevier.com/retrieve/pii/S0022460X08009437

VALEEV A , ZOTOV A , KHARISOV S . Designing of compact low frequency vibration isolator with quasi-zero stiffness [J ] . Journal of low frequency noise vibration and active control , 2015 , 34 ( 4 ): 459 - 473 . DOI: 10.1260/0263-0923.34.4.459 http://doi.org/10.1260/0263-0923.34.4.459 http://journals.sagepub.com/doi/10.1260/0263-0923.34.4.459 http://journals.sagepub.com/doi/10.1260/0263-0923.34.4.459 This article considers the design of a compact isolator with quasi-zero stiffness. It has high vibration control properties at low weight and dimensions. Also the developed vibration isolator with quasi-zero stiffness can protect against low-frequency vibration. The vibration isolator is of a passive type, made from a single elastic material, which will be compact and convenient in manufacturing. An analytical study of the vibration isolation, its manufacturing and experimental static study are presented. The natural frequency of the developed vibration isolator with quasi-zero stiffness is less than 1 Hz.

任旭东 . 空气弹簧准零刚度隔振器的特性分析及应用研究 [D ] . 北京 : 军事医学科学院 , 2017 .

REN X D . Characteristics analysis and application study of the quasi-zero stiffness isolator using air spring [D ] . Beijing : Academy of Military Medical Sciences , 2017 . (in Chinese)

徐道临 , 张月英 , 周加喜 , 等 . 一种准零刚度隔振器的特性分析与实验研究 [J ] . 振动与冲击 , 2014 , 33 ( 11 ): 208 - 213 .

XU D L , ZHANG Y Y , ZHOU J X , et al . Characteristic analysis and experimental investigation for a vibration isolator with quasi-zero stiffness [J ] . Journal of Vibration and Shock , 2014 , 33 ( 11 ): 208 - 213 . (in Chinese)

蓝双 , 杨晓翔 . 新型准零刚度系统的设计、分析与仿真 [J ] . 机械强度 , 2018 , 40 ( 3 ): 515 - 521 . DOI: 10.16579/j.issn.1001.9669.2018.03.002 http://doi.org/10.16579/j.issn.1001.9669.2018.03.002 采用拉伸弹簧组成的负刚度机构与正刚度线性弹簧并联，设计出一种新型的拉伸式准零刚度隔振系统，可用于隔离低频或超低频振动。建立该系统的静力学模型，得到系统具有准零刚度特性时所需满足的条件；与一种压缩式隔振系统的力-位移曲线进行对比；分析垂向弹簧的调节对系统的影响；建立该系统在简谐位移激励下的非线性动力学方程，利用谐波平衡法求得系统的近似响应；与压缩式隔振系统的位移传递率曲线进行对比；探索系统各主要参数对响应的影响；建立Adams动力学模型，通过仿真结果来证明静力学模型的正确性，并模拟基座激励振动，证明了拉伸式准零刚度系统在低频或超低频隔振中的性能远优于线性系统。

LAN S , YANG X X . Design, analysis and simulation of a novel quasi-zero stiffness vibration isolation system [J ] . Journal of Mechanical Strength , 2018 , 40 ( 3 ): 515 - 521 . (in Chinese) DOI: 10.16579/j.issn.1001.9669.2018.03.002 http://doi.org/10.16579/j.issn.1001.9669.2018.03.002 Combining a negative stiffness mechanism composed of tension spring with a linear positive stiffness spring in parallel, a novel quasi-zero stiffness vibration isolation systemwas designed which can be used to isolate low or ultra-low vibration. The static model of the system was established and the condition of quasi-zero stiffness characteristics was obtained. The fore-displacement curves of the tension-type isolator and a compression-type isolator were compared. The effect of adjustment of vertical spring in the system was analyzed. The dynamic equation was established when the system was excited by a harmonic amplitude on the displacement and the equation was solved by using Harmonic Balance method. The displacement transmissibility curves of the tension-type and the compression-type isolators were also compared. The effect of the main parameters on response of the system was explored. ADAMS model was established and the static model was proved to be correct. The vibration simulation results prove that the quasi-zero stiffness system has greater advantage than linear system in low or ultra-low vibration isolation.

杜宁 , 胡明勇 , 毕勇 , 等 . 一种车载设备的低频水平减振方法 [J ] . 振动与冲击 , 2017 , 36 ( 7 ): 184 - 190 .

DU N , HU M Y , BI Y , et al . A low frequency horizontal vibration reduction method for a vehicle-borne photoelectric instrument [J ] . Journal of Vibration and Shock , 2017 , 36 ( 7 ): 184 - 190 . (in Chinese)

LIU Y Q , XU L L , SONG C F . Dynamic characteristics of a quasi-zero stiffness vibration isolator with nonlinear stiffness and damping [J ] . Archive of Applied Mechanics , 2019 , 89 : 1743 - 1759 . DOI: 10.1007/s00419-019-01541-0 http://doi.org/10.1007/s00419-019-01541-0

张春辉 , 曾泽璀 , 张磊 , 等 . 预紧式准零刚度隔冲器的隔冲性能研究 [J ] . 振动工程学报 , 2019 , 32 ( 5 ): 767 - 777 .

ZHANG C H , ZENG Z C , ZHANG L , et al . Research on the shock isolation performance of preload quasi-zerostiffness isolator [J ] . Journal of Vibration Engineering , 2019 , 32 ( 5 ): 767 - 777 . (in Chinese)

DONG G X , ZHANG X N , LUO Y J , et al . Analytical study of the low frequency multi-direction isolator with high-static-low-dynamic stiffness struts and spatial pendulum [J ] . Mechanical Systems and Signal Processing , 2018 , 110 : 521 - 539 . DOI: 10.1016/j.ymssp.2018.03.041 http://doi.org/10.1016/j.ymssp.2018.03.041 https://linkinghub.elsevier.com/retrieve/pii/S0888327018301602 https://linkinghub.elsevier.com/retrieve/pii/S0888327018301602

柴凯 , 杨庆超 , 朱石坚 , 等 . 矩形永磁铁的磁力计算及其应用 [J ] . 噪声与振动控制 , 2016 , 36 ( 6 ): 51 - 55 , 66. DOI: 10.3969/j.issn.1006-1335.2016.06.010 http://doi.org/10.3969/j.issn.1006-1335.2016.06.010 负刚度结构可用于系统的低频隔振，依据等效磁荷法建立矩形永磁铁的磁力和刚度解析模型，得到实现负刚度的最优磁铁布置和充磁方向，并设计三磁体型准零刚度隔振系统。仿真结果表明，矩形磁铁磁力和刚度计算模型准确，三磁体型准零刚度隔振器在不影响载荷性能的前提下具有优越的低频隔振性能。

CHAI K , YANG Q C , ZHU S J , et al . Magnetic force calculation of rectangular permanent magnets and its application [J ] . Noise and Vibration Control , 2016 , 36 ( 6 ): 51 - 55 , 66. (in Chinese) DOI: 10.3969/j.issn.1006-1335.2016.06.010 http://doi.org/10.3969/j.issn.1006-1335.2016.06.010 Negative stiffness mechanism can be used to isolate the low frequency vibration of the system. In this paper, an analytical expression of the force and stiffness was derived by using the equivalent magnetic charge method. Meanwhile, the optimal arrangement and magnetization of the rectangular permanent magnets were obtained to accomplish the negative stiffness. Finally, the trimagnets quasi-zero-stiffness vibration isolation was designed. The simulation results proved that the correctness of the theoretical analysis and the excellent low frequency vibration isolation performance was achieved without affecting the load ability.

王迎春 , 柴凯 , 刘树勇 , 等 . 永磁体型高静低动刚度隔振器试验研究 [J ] . 噪声与振动控制 , 2019 , 39 ( 5 ): 223 - 230 .

WANG Y C , CHAI K , LIU S Y , et al . Experimental study on the permanent magnets vibration isolators with high-static and low-dynamic stiffness [J ] . Noise and Vibration Control , 2019 , 39 ( 5 ): 223 - 230 . (in Chinese)

柴凯 , 杨庆超 , 朱石坚 , 等 . 双环永磁铁型准零刚度隔振器的设计和分析 [J/OL ] . 解放军理工大学学报(自然科学版) , 2017 (2017-04-11). http://kns.cnki.net/kcms/detail/32.1430.N.20170411.1118.004.html. http://kns.cnki.net/kcms/detail/32.1430.N.20170411.1118.004.html http://kns.cnki.net/kcms/detail/32.1430.N.20170411.1118.004.html

CHAI K , YANG Q C , ZHU S J , et al . Design and analysis of quasi-zero stiffness vibration isolator with bi-annular-shaped permanent magnet [J/OL ] . Journal of PLA University of Science and Technology(Natural Science Edition) , 2017 (2017-04-11). http://kns.cnki.net/kcms/detail/32.1430.N.20170411.1118.004.html. http://kns.cnki.net/kcms/detail/32.1430.N.20170411.1118.004.html http://kns.cnki.net/kcms/detail/32.1430.N.20170411.1118.004.html (in Chinese)

李爽 , 楼京俊 , 杨庆超 , 等 . 双环永磁体型高静低动刚度隔振器设计、建模与试验研究 [J ] . 振动工程学报 , 2019 , 32 ( 4 ): 675 - 684 .

LI S , LOU J J , YANG Q C , et al . Design and experiment of a vibration isolator using double-ring permanent magnets springs with negative stiffness [J ] . Journal of Vibration Engineering , 2019 , 32 ( 4 ): 675 - 684 . (in Chinese)

KIM J , JEON Y , UM S , et al . A Novel passive quasi-zero stiffness isolator for ultra-precision measurement systems [J ] . International Journal of Precision Engineering and Manufacturing , 2019 , 20 ( 9 ): 1573 - 1580 . DOI: 10.1007/s12541-019-00149-2 http://doi.org/10.1007/s12541-019-00149-2

王瑶 , 李占龙 , 刘琪 , 等 . 非接触多磁环负刚度机构非线性刚度行为特性研究 [J ] . 振动与冲击 , 2021 , 40 ( 15 ): 41 - 47 .

WANG Y , LI Z L , LIU Q , et al . Nonlinear stiffness behavior of non-contact multi-magnetic ring negative stiffness mechanism [J ] . Journal of Vibration and Shock , 2021 , 40 ( 15 ): 41 - 47 . (in Chinese)

彭远生 , 代洪华 , 张皓 , 等 . 仿生抗冲击Stewart隔振平台的动力学与控制 [J ] . 西北工业大学学报 , 2021 , 39 ( 2 ): 258 - 266 .

PENG Y S , DAI H H , ZHANG H , et al . Dynamics and control of a bio-inspired Stewart platform [J ] . Journal of Northwestern Polytechnical University , 2021 , 39 ( 2 ): 258 - 266 . (in Chinese) DOI: 10.1051/jnwpu/20213920258 http://doi.org/10.1051/jnwpu/20213920258 https://www.jnwpu.org/10.1051/jnwpu/20213920258 https://www.jnwpu.org/10.1051/jnwpu/20213920258 Collision and strong impacts take place in mission of the on orbit capture of non-cooperative spacecraft. So, it is necessary to design a vibration isolation system with efficient vibration isolation performance. A Stewart vibration isolation platform based on the bio-inspired isolation system is proposed in this paper. The characteristics of the novel bio-inspired Stewart platform realizes the vibration isolation protection of the serving spacecraft during the capture mission. The dynamic model of the vibration isolation platform is established by Lagrange's equations. The fidelity of the established dynamic model is verified via a comparison of the theoretical simulation and the ADAMS simulation. Comparisons between the presently proposed vibration isolation platform and the traditional spring-mass-damper type Stewart vibration isolation platform demonstrates the advantages of the present platform. The effects of system parameters on the isolation performance of the present platform are thoroughly investigated. The feedback linearization control method is used to control the present platform which overcomes the drift motion that occurs in the passive isolation case. The results show that the novel bio-inspired Stewart platform has excellent vibration isolation performance, which provides a promising way for the vibration isolation of the non-orbit capture mission.

张春辉 , 汪玉 , 温肇东 , 等 . 被动式Stewart隔冲平台的刚度特性 [J ] . 振动、测试与诊断 , 2015 , 35 ( 2 ): 289 - 294 , 399.

ZHANG C H , WANG Y , WEN Z D , et al . Research on stiffness characteristics of a passive stewart shock isolation platform [J ] . Journal of Vibration, Measurement &Diagnosis , 2015 , 35 ( 2 ): 289 - 294 , 399. (in Chinese)