准零刚度隔振结构设计与应用

王强; 周加喜; 王凯; 覃宇; 高靖航; 谭栋国

doi:10.6052/1000-0992-26-028

准零刚度隔振结构设计与应用

doi: 10.6052/1000-0992-26-028 cstr: 32046.14.1000-0992-26-028

王强^{1, 2},
周加喜^2, ,,
王凯^2, ,,
覃宇²,
高靖航³,
谭栋国⁴

1.
湖南工商大学智能工程与智能制造学院, 长沙 410205
2.
湖南大学机械与运载工程学院, 长沙 410082
3.
奥克兰大学机械与机电工程系, 奥克兰 1010
4.
湖南科技大学土木工程学院, 湘潭 411201

基金项目: 本文得到了国家自然科学基金 (12402011, 12472010, 12622202, U2468213)、湖南省自然科学基金 (2026JJ60007) 及湖南省教育厅优秀青年基金 (25B0568) 的联合资助. 同时, 衷心感谢燕山大学文桂林教授在研究过程中给予的宝贵指导与建议.

详细信息

作者简介:
王强 (第一作者), 湖南工商大学校聘副教授、硕士生导师, 主要从事非线性动力学与低频振动控制研究. 主持国家自然科学基金青年科学基金项目、中国博士后科学基金面上项目、湖南省自然科学基金及湖南省教育厅优秀青年项目等多项科研课题, 在 MSSP、IJMS、Nonlinear Dynamics、Nano Energy 等国际期刊发表论文20余篇, 其中2篇入选ESI高被引论文

周加喜 (通讯作者), 湖南大学教授、博导, 国家高层次青年人才, 湖南省科技创新领军人才.研究方向为减振理论及应用, 主持国家自然科学基金以及企业合作课题30余项, 发表学术论文140余篇, 授权国家专利30余项, 入选爱思唯尔中国高被引学者, 获湖南省自然科学奖一等奖 (第一完成人)、陕西省科学技术奖一等奖、中国振动工程学会科学技术奖二等奖、电力建设科技进步奖二等奖, 兼任中国力学学会理事、《振动工程学报》编委、《动力学与控制学报》编委

王凯 (通讯作者), 王凯, 湖南大学副教授、博导, 国家高层次青年人才, 入选“香江学者”计划, International Journal of Dynamics and Control副主编. 研究方向为非线性动力学与控制, 主持国家自然科学基金 (面上/青B/青C) 以及企业合作课题10项, 发表学术论文90余篇, 授权国家专利10项, 获中国振动工程学会科学技术奖二等奖 (第一完成人)、湖南省自然科学奖一等奖, 任Applied Mathematics and Mechanics (English Edition)、Sustainability以及动力学与控制学报等期刊编委或青年编委

通讯作者:
jxizhou@hnu.edu.cn

wangkai@hnu.edu.cn

中图分类号: U24
计量
- 文章访问数: 18
- HTML全文浏览量: 5
- PDF下载量: 0
- 被引次数: 0
出版历程
- 收稿日期: 2026-07-13
- 录用日期: 2026-09-07
- 网络出版日期: 2026-09-12

Design and Application of Quasi-Zero-Stiffness Vibration Isolation Structures

WANG Qiang^{1, 2},
ZHOU Jiaxi^{2
, ,},
WANG Kai^{2
, ,},
QIN Yu²,
GAO Jinghang³,
TAN Dongguo⁴

1.
School of Intelligent Engineering and Intelligent Manufacturing, Hunan University of Technology and Business, Changsha 410205, China
2.
College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
3.
Department of Mechanical and Mechatronics Engineering, The University of Auckland, Auckland 1010 New Zealand
4.
School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, China

More Information

Corresponding author: jxizhou@hnu.edu.cn; wangkai@hnu.edu.cn

摘要

摘要: 振动诱发的结构疲劳、动态失稳与功能退化严重影响装备的服役可靠性, 因此实施有效的隔振措施至关重要. 然而, 传统线性隔振结构受制于低静刚度与承载能力之间固有矛盾, 难以实现有效的低频振动隔离. 近年来, 准零刚度隔振结构因其能保持高静刚度的同时显著降低动刚度, 从而将隔振频率拓展至低频甚至超低频, 而受到广泛关注. 本文以典型准零刚度隔振结构的实现方式为切入点, 系统综述了斜弹簧式、连杆−弹簧式、凸轮−滚子式、屈曲梁/板/环式、永磁铁式、折纸式以及仿生式等多种准零刚度隔振结构的设计方法. 在此基础上, 进一步梳理了多层准零刚度隔振结构与多向准零刚度隔振结构的研究进展, 并总结了准零刚度隔振结构在交通运输、机械传动、医疗器械、土木工程及输流管道等领域的典型应用. 面对工业装备向高端化、精密化持续演进的趋势, 本文最后结合拓扑优化、数据驱动建模、主动控制及振动能量俘获等新兴研究方向, 对准零刚度隔振技术的未来发展进行了展望, 以期为该领域的深入研究提供参考.
- 准零刚度 /
- 低频隔振 /
- 非线性振动 /
- 多层隔振 /
- 多向隔振
Abstract: Vibration-induced structural fatigue, dynamic instability, and functional degradation can significantly reduce the service reliability of engineering equipment, making effective vibration isolation essential. However, conventional linear vibration isolation structures are limited by the inherent trade-off between low static stiffness and load-bearing capacity, which restricts their performance at low frequencies. Quasi-zero-stiffness (QZS) vibration isolation structures have therefore attracted increasing attention because they combine high static stiffness with low dynamic stiffness, enabling vibration isolation at low and even ultra-low frequencies. This paper reviews typical QZS designs, including oblique-spring, linkage–spring, cam–roller, buckled beam/plate/ring, permanent-magnet, origami-inspired, and bio-inspired configurations. Recent developments in multilayer and multidirectional QZS vibration isolation structures are also summarized, together with representative applications in transportation, mechanical transmission, medical equipment, civil engineering, and fluid-conveying pipelines. Finally, future research directions are discussed, including topology optimization, data-driven modelling, active control, and vibration energy harvesting. This review aims to provide a useful reference for further development of QZS vibration isolation technology.
- quasi-zero stiffness /
- low-frequency vibration isolation /
- nonlinear vibration /
- multi-layer vibration isolation /
- multi-directional vibration isolation

HTML全文

图 1 线性与准零刚度隔振性能对比. (a)线性隔振系统, (b)准零刚度隔振系统, (c)回复力与位移, (d)刚度与位移, (e)传递率

下载: 全尺寸图片幻灯片

图 2 准零刚度隔振结构的实现方式. (a)静力学特性, (b)不同类型隔振结构

下载: 全尺寸图片幻灯片

图 3 不同振动形式动力学模型.(a)直线振动, (b)扭转振动

下载: 全尺寸图片幻灯片

图 4 斜弹簧准零刚度隔振结构. (a)三弹簧准零刚度结构(Carrella et al. 2007), (b)五弹簧准零刚度结构(Xu et al. 2014), (c)含两对斜弹簧的准零刚度结构(Zhao et al. 2021), (d)双侧阻尼多弹簧准零刚度结构(Hao et al. 2016), (e)半主动多弹簧准零刚度结构(Wen et al. 2021), (f)利用侧向弹簧刚度调控的半主动准零刚度结构(Ran et al. 2024)

下载: 全尺寸图片幻灯片

图 5 斜连杆−弹簧准零刚度隔振结构. (a)经典杆簧式准零刚度结构(Zhang et al. 2004), (b)连杆−弹簧式准零刚度结构(Wang et al. 2018 ), (c)滑杆−弹簧式准零刚度结构(Liu et al. 2020), (d)引入非线性惯容器连杆−弹簧式准零刚度结构(Liu et al. 2021), (e) X形混合杠杆式准零刚度结构(Liu et al. 2015), (f)非对称结构X形准零刚度结构(Liu et al. 2024)

下载: 全尺寸图片幻灯片

图 6 凸轮−滚子准零刚度隔振结构. (a)凸轮−滚子准零刚度结构(Zhou et al. 2015), (b)轮廓可设计凸轮−滚子准零刚度结构(Yao et al. 2020), (c)抛物线型凸轮−滚子准零刚度结构(Zuo et al. 2024), (d)弹簧−连杆与凸轮−滚子混合式准零刚度结构(Sun et al. 2025), (e)自适应凸轮−滚子混合式准零刚度结构(Ye et al. 2020), (f)具有时滞立方位移反馈的凸轮−滚子准零刚度结构(Cheng et al. 2016)

下载: 全尺寸图片幻灯片

图 7 屈曲梁/板/环式准零刚度隔振结构. (a)欧拉屈曲梁式准零刚度结构(Huang et al. 2014), (b)滑动屈曲梁式准零刚度结构(Huang et al. 2014), (c)余弦梁与半圆拱并联式准零刚度结构(Dalela et al. 2022), (d)屈曲失稳与弯曲变形式准零刚度结构(Liang et al. 2024), (e)整体式柔性曲梁准零刚度结构(Hou et al. 2024), (f)拓扑优化式准零刚度结构(Xu et al. 2024)

下载: 全尺寸图片幻灯片

图 8 磁力准零刚度隔振结构. (a)磁环式准零刚度结构(Xu et al. 2013), (b)多磁块式准零刚度结构(Wu et al. 2014), (c)长方体磁铁阵列准零刚度结构(Wu et al. 2022), (d)高阶稳定特征的磁力型准零刚度结构(Liu et al. 2024), (e)杠杆式磁力准零刚度结构(Yan et al. 2022), (f)可调磁力式准零刚度结构(Liang et al. 2024)

下载: 全尺寸图片幻灯片

图 9 仿生准零刚度隔振结构. (a)受鸟腿启发的X形准零刚度结构(Wang et al. 2019), (b)考虑非对称结构的X形准零刚度结构(Wu et al. 2015), (c)受鸟腿启发的大行程准零刚度结构(Sun et al. 2018), (d)仿蛙腿结构准零刚度结构(Zeng et al. 2021), (e) 仿多边形骨架准零刚度结构(Yan et al. 2020), (f) 仿生M形准零刚度结构(蓝春波 et al. 2025), (g)仿蟑螂结构的准零刚度结构(Ling et al. 2022), (h)仿海马外骨骼准零刚度结构(王尚文 et al. 2026)

下载: 全尺寸图片幻灯片

图 10 折纸准零刚度隔振结构.(a) Kresling圆柱折纸结构准零刚度结构(Ishida et al. 2017), (b) Fluidic origami蜂窝结构准零刚度结构(Sadeghi et al. 2019), (c) Miura-origami tube构型准零刚度结构(Han et al. 2021), (d) Tachi-Miura折纸构型准零刚度结构(Liu et al. 2021), (e) Miura-origami构型准零刚度结构(Han et al. 2024), (f)基于桁架−弹簧的Miura-origami构型准零刚度结构(Ye et al. 2022)

下载: 全尺寸图片幻灯片

图 11 单层扭转准零刚度隔振结构. (a)凸轮滚子扭转准零刚度结构(Zhou et al. 2015), (b)磁力扭转准零刚度结构(Zheng et al. 2018), (c) 基于连杆−弹簧扭转准零刚度结构(王晓杰 et al. 2018), (d)斜弹簧式扭转准零刚度结构(Kim et al. 2015), (e)柔性杆元件和电磁元件扭转准零刚度结构(Xu et al. 2024), (f)基于张拉一体化准零刚度结构(Sun et al. 2025), (g) 双拉伸弹簧式扭转准零刚度结构(Noh et al. 2025), (h)基于曲梁几何设计的扭转准零刚度结构(Hu et al. 2026)

下载: 全尺寸图片幻灯片

图 12 单层与双层准零刚度隔振机构对比. (a)单层与双层准零刚度隔振系统的力学模型; (b)单层与双层准零刚度隔振结构的传递率.

下载: 全尺寸图片幻灯片

图 13 多层准零刚度隔振结构. (a)双层准零刚度隔振结构经典动力学模型(Gatti et al. 2010), (b)屈曲结构的双层准零刚度结构(Lu et al. 2017), (c) 凸轮滚子结构双层准零刚度结构(Lu et al. 2017), (d)基于X形结构的多层准零刚度结构(Sun et al. 2016), (e) 特定几何构形的曲线梁准零刚度结构(Zhang et al. 2021), (f)基于柔性结构单元多层准零刚度结构 (Zhou et al. 2024)

下载: 全尺寸图片幻灯片

图 14 多向准零刚度隔振结构. (a)面内多向准零刚度结构(Liu et al. 2021), (b)基于剪式连杆−弹簧的多向准零刚度结构(Sun et al. 2015), (c) 基于X形连杆结构的准零刚度结构(Chai et al. 2022), (d)多向悬浮式准零刚度结构(Qi et al. 2025), (e)磁力式六自由度准零刚度结构(Zhou et al. 2017), (f)可调磁力式准零刚度结构(Hao et al. 2022)

下载: 全尺寸图片幻灯片

图 15 准零刚度隔振结构的典型应用

下载: 全尺寸图片幻灯片

图 16 准零刚度隔振结构的挑战和展望

下载: 全尺寸图片幻灯片

表 1 准零刚度隔振系统核心术语与释义

术语名称	定义	隔振系统中的特点
准零刚度 (quasi-zero stiffness, QZS)	系统在静平衡位置附近总刚度趋近于零 (通常取非负值以保证稳定性) 的一种非线性刚度特性.	能在保证足够静承载力的前提下显著降低系统固有频率, 从而大幅拓宽低频隔振频带, 是实现低频/超低频隔振的核心机制.
高静低动刚度 (high-static-low-dynamic stiffness, HSLDS)	系统同时具备“静态时高刚度”和“动态时低刚度”两种特性. 静态高刚度用于支撑重载、抵抗静变形; 动态低刚度用于降低固有频率.	解决了传统线性隔振系统“承载能力”与“低频隔振效果”之间的矛盾, 常作为准零刚度隔振系统的等效力学特性描述, 在工程隔振设计中应用广泛.
负刚度 (negative stiffness)	力−位移曲线的斜率为负值, 即系统偏离平衡位置时, 其所受恢复力的方向与位移方向相同 (而非相反), 使系统处于不稳定状态.	单独存在时系统会失稳, 但与正刚度并联后, 能相互抵消正刚度, 从而合成极低的总刚度 (QZS). 它是实现高静低动刚度的关键调控机制
传递率 (transmissibility, 通常用T表示)	指系统在稳态受迫振动下, 响应幅值 (传递出去的力或位移/加速度) 与激励幅值 (输入的扰动力或基础运动幅值) 的无量纲比值.	它是评判隔振效果好坏的最直接指标. 当 T<1 时, 表示系统起到了隔振作用 (传递力小于扰动力); 当T=1 时对应的频率即为起始隔振频率; 当 T>1 时, 系统反而放大了振动 (共振区).
起始隔振频率 (starting frequency of vibration isolation)	隔振系统传递率T=1 时所对应的激励频率. 当激励频率高于该频率时, 系统进入有效隔振区 (T<1 ). 起始频率越低, 系统的低频隔振性能越优.	该频率越低, 代表系统的低频隔振能力越强. 在准零刚度隔振系统中, 由于固有频率被压至极低, 起始隔振频率也相应向低频端大幅移动.
共振频率 (resonance frequency)	指系统幅频响应曲线中振幅达到峰值时所对应的激励频率. 对于准零刚度隔振系统, 由于其刚度随振幅变化呈现非线性特征, 共振频率不再是固定值, 而是随激励幅值的变化而发生偏移.	隔振设计的核心目标之一是避免或有效抑制该频率处的振动. 实际工程中需确保工作频率远离共振频率, 并通过阻尼或非线性刚度设计来抑制该频率处的剧烈振动.
共振峰值 (resonance peak amplitude)	系统在共振频率点处振动响应 (位移、速度或加速度) 的最大幅值.	峰值大小直接影响设备运行安全和结构疲劳寿命. 在准零刚度隔振系统中, 通常利用非线性刚度的“硬化”或“软化”效应, 或通过增加阻尼, 来降低或限制峰值, 从而有效抑制共振区的剧烈振动. 动超标.
传递率峰值 (peak transmissibility)	指在系统共振频率附近, 传递率−频率曲线上所达到的最大值	峰值大小由系统的阻尼比和非线性刚度共同决定. 阻尼越大, 峰值越低 (抑制共振), 但高频隔振性能会变差 (传递率回升).
传递率下降率 (decreasing rate of transmissibility)	传递率随频率升高而下降的斜率或速度. 通常以 dB/octave (分贝/倍频程) 或 dB/decade (分贝/十倍频程) 为单位进行量化.	衡量隔振系统高频衰减能力的关键指标. 下降率越大, 意味着高频振动被衰减得越快, 隔振效果越好

下载: 导出CSV

表 2 不同类型准零刚度隔振结构对比

隔振结构类型	优点	局限性	参考文献
斜弹簧准零刚度机构	结构简单、便于制造、参数调节灵活、可靠性高以及理论体系相对成熟	准零刚度区间较窄; 变承载质量或大幅激励时隔振性能下降; 弹簧与导向杆之间的摩擦在低频激励时可能导致隔振失效	(2007, 2021, 2016, 2014)
连杆−弹簧准零刚度机构	运动副精度高、负刚度可设计性强、准零刚度区间大、易于与其他机构集成	传统构型存在狭小低刚度区域和刚度渐硬非线性恢复力, 难以承受高振幅激励; 铰链间隙与摩擦影响精度与寿命	(2014, 2016, 2015, 2016, 2021)
凸轮−滚子准零刚度机构	可设计任意刚度曲线、摩擦损耗低、运动精度高、微幅振动敏感性强、动态响应迅速以及使用寿命长	典型构型存在较大摩擦阻尼; 准零刚度范围受凸轮尺寸限制; 圆形凸轮只能在很小范围内实现低刚度	(2020, 2016, 2017)
屈曲梁/板/环式准零刚度结构	结构紧凑、无活动关节、易于微型化与集成	对加工精度异常敏感; 高度依赖正负刚度的精确参数匹配; 负载适应性差; 转折处应力集中, 存在过早疲劳破坏问题	(2018, 2013, 2020, 2021)
磁力准零刚度机构	无接触、无摩擦、响应速度快、刚度可电控调节、无机械疲劳、稳定性强	磁悬浮式结构存在大幅失稳风险; 强非线性导致系统易诱发突跳现象; 热稳定性问题	(2022, 2009, 2013, 2018, 2020, 2019)
仿生准零刚度机构	准零刚度区间大、结构轻量化、适应性强	结构复杂, 制造难度大; 部分构型承载力下降; 易出现刚度硬化和非线性跳跃导致系统失稳	(2021, 2015, 2018, 2018, 2019)
折纸准零刚度机构	可折叠、体积可变、刚度可调范围极大、形状可重构	准零刚度行程较短, 限制了在低频隔振领域的应用推广	(2017, 2021, 2021, 2024, 2025)

下载: 导出CSV

表 3 单层、多层与多向准零刚度隔振结构性能对比

比较维度	单层准零刚度隔振结构	多层准零刚度隔振结构	多向准零刚度隔振结构
核心目标	实现单向低频振动隔离, 结构简单、易于实现	提升高频衰减速率, 实现低频高效隔振	实现多自由度或多方向低频振动隔离, 适应复杂激励环境
典型构型	斜弹簧式、连杆−弹簧式、凸轮−滚子式、屈曲梁式、磁力式、仿生式、折纸式	双层/多层弹簧−质量系统、多层屈曲梁堆叠、多层磁力机构串联、多层X形结构	面内多向隔振器、三自由度解耦式、六自由度Stewart平台、Gough-Stewart构型
承载能力	由正刚度元件决定, 可通过弹簧刚度与几何参数设计调控, 可满足轻载至中载需求	由多层叠加结构共同承担, 分布式承载, 适用于重载工况	由空间对称布置的多个准零刚度单元共同支撑, 可实现大承载 (数百公斤至数吨)
隔振频带	起始隔振频率低 (可至0.1 ~ 5 Hz), 高频段传递率下降率约为40 dB/decade	起始隔振频率与与单层相当 (可低至0.1 ~ 5 Hz), 高频段传递率下降率可达80 dB/decade, 隔振效率显著提升	各方向均可实现低频隔振 (起始频率6 ~ 10 Hz), 自由度间耦合效应需通过构型设计解耦
适用场景	基础隔振场景: 精密仪器支撑、车辆座椅悬架、设备隔振安装等	对隔振效率要求较高的场景: 舰船浮筏、航天器敏感载荷、精密测量平台	多源振动耦合场景: 航天器整星隔振、车载设备多维隔振、船舶动力系统
工程实现难度	较低. 构型成熟、元件标准, 便于加工与装配	中等. 层间耦合参数匹配复杂, 需精密装配与调试	高. 需多向准零刚度匹配与空间布局优化, 对设计、加工及装配精度要求极为苛刻
主要局限性	有效隔振频带相对较窄; 变载荷适应性差; 部分构型准零刚度行程有限	自由度增加引入额外共振峰, 需通过阻尼抑制; 结构复杂度与成本增加; 设计参数增多	构型复杂、体积较大; 多自由度非线性耦合效应难以完全消除; 成本高昂

下载: 导出CSV

参考文献(203)

[1]	蓝春波, 贾洁, 汪洋, 等. 2025. 仿节肢动物肢体构型的M形低频隔振结构设计及其动力学机理. 物理学报, 74(13): 37-51 (Lan C B, Jia J, Wang Y, et al. 2025. Design and dynamic mechanism of M-shaped low-frequency isolation structure imitating limb configuration of arthropods. Acta Physica Sinica, 74(13): 37-51). doi: 10.7498/aps.74.20241203 Lan C B, Jia J, Wang Y, et al. 2025. Design and dynamic mechanism of M-shaped low-frequency isolation structure imitating limb configuration of arthropods. Acta Physica Sinica, 74(13): 37-51. doi: 10.7498/aps.74.20241203
[2]	马原卉, 凌鹏, 赵杰烽, 等. 2025. 电磁准零刚度隔振器的负载自适应滑模控制研究. 振动工程学报, 38(9): 2044-2051 (Ma Y B, Ling P, Zhao J F, et al. 2025. Load adaptive sliding mode control of electromagnetic quasi-zero-stiffness isolators. Journal of Vibration Engineering, 38(9): 2044-2051). doi: 10.16385/j.cnki.issn.1004-4523.202310068 Ma Y B, Ling P, Zhao J F, et al. 2025. Load adaptive sliding mode control of electromagnetic quasi-zero-stiffness isolators. Journal of Vibration Engineering, 38(9): 2044-2051. doi: 10.16385/j.cnki.issn.1004-4523.202310068
[3]	孙秀婷, 钱佳伟, 齐志凤, 等. 2023. 非线性隔振及时滞消振方法研究进展. 力学进展, 53(2): 308-356 (Sun X T, Qian J W, Qi Z F, et al. 2023. Review on research progress of nonlinear vibration isolation and time-delayed suppression method. Advances in Mechanics, 53(2): 308-356). doi: 10.6052/1000-0992-22-048 Sun X T, Qian J W, Qi Z F, et al. 2023. Review on research progress of nonlinear vibration isolation and time-delayed suppression method. Advances in Mechanics, 53(2): 308-356. doi: 10.6052/1000-0992-22-048
[4]	王尚文, 凌鹏, 马洪业, 等. 2026. 仿海马外骨骼六边形结构设计及其低频隔振特性. 机械工程学报, 62(3): 435-445 (Wang S W, Ling P, Ma H Y, et al. 2026. Design and low-frequency vibration isolation characteristics of seahorse exoskeleton hexagonal structures. Journal of Mechanical Engineering, 62(3): 435-445). doi: 10.3901/JME.260096 Wang S W, Ling P, Ma H Y, et al. 2026. Design and low-frequency vibration isolation characteristics of seahorse exoskeleton hexagonal structures. Journal of Mechanical Engineering, 62(3): 435-445. doi: 10.3901/JME.260096
[5]	王晓杰, 刘辉, 郦文平, 等. 2018. 准零刚度扭转隔振器振动传递特性研究. 机械工程学报, 54(21): 49-56 (Wang X J, Liu H, Lu W P, et al. 2018. Vibration transmission characteristics of a quasi-zero stiffness torsional isolator. Journal of Mechanical Engineering, 54(21): 49-56). doi: 10.3901/JME.2018.21.049 Wang X J, Liu H, Lu W P, et al. 2018. Vibration transmission characteristics of a quasi-zero stiffness torsional isolator. Journal of Mechanical Engineering, 54(21): 49-56. doi: 10.3901/JME.2018.21.049
[6]	肖国栋, 孙秀婷. 2024. 仿生隔振器设计方法研究进展. 动力学与控制学报, 22(2): 4-22 (Xiao G D, Sun X T. 2024. Advances in design methods for bio-inspired isolator. Journal of Dynamics and Control, 22(2): 4-22). doi: 10.6052/1672-6553-2023-056 Xiao G D, Sun X T. 2024. Advances in design methods for bio-inspired isolator. Journal of Dynamics and Control, 22(2): 4-22. doi: 10.6052/1672-6553-2023-056
[7]	徐鉴. 2015. 振动控制研究进展综述. 力学季刊, 36(4): 547-565 (Xu J. 2015. Advances of research on vibration control. Chinese Quarterly of Mechanics, 36(4): 547-565). doi: 10.15959/j.cnki.0254-0053.2015.04.001 Xu J. 2015. Advances of research on vibration control. Chinese Quarterly of Mechanics, 36(4): 547-565. doi: 10.15959/j.cnki.0254-0053.2015.04.001
[8]	张文明, 卢佳佳, 颜格. 2025. 准零刚度隔振设计方法研究进展. 振动、测试与诊断, 45(5): 855-868 + 1057 (Zhang W M, Lu J J, Yan G. 2025. Advances in design methods for quasi-zero stiffness vibration isolation. Journal of Vibration, Measurement & Diagnosis, 45(5): 855-868 + 1057). doi: 10.16450/j.cnki.issn.1004-6801.2025.05.001 Zhang W M, Lu J J, Yan G. 2025. Advances in design methods for quasi-zero stiffness vibration isolation. Journal of Vibration, Measurement & Diagnosis, 45(5): 855-868 + 1057. doi: 10.16450/j.cnki.issn.1004-6801.2025.05.001
[9]	郑宜生, 袁怀炳, 瞿叶高, 等. 2026. 薄壁超结构振动与噪声控制及其在航空领域的应用. 力学进展, 56(1): 51-122 (Zheng Y S, Yuan H B, Qu Y G, et al. 2026. Advances in thin-walled metastructures for vibration and noise control and their applications in aerospace engineering. Advances in Mechanics, 56(1): 51-122). doi: 10.6052/1000-0992-25-024 Zheng Y S, Yuan H B, Qu Y G, et al. 2026. Advances in thin-walled metastructures for vibration and noise control and their applications in aerospace engineering. Advances in Mechanics, 56(1): 51-122. doi: 10.6052/1000-0992-25-024
[10]	周一帆, 高瑞齐, 吴明凯, 等. 2025. 气−磁-金属复合的大承载三向准零刚度减振器设计. 机械工程学报, 61(5): 50-61. (Zhou Y F, Gao R Q, Wu M K, et al. 2025. Design of 3D quasi-zero stiffness vibration isolator with high payload capacity via combination of gas-magnetic-metal springs. Journal of Mechanical Engineering, 61(5): 50-61). doi: 10.3901/JME.2025.05.050 Zhou Y F, Gao R Q, Wu M K, et al. 2025. Design of 3D quasi-zero stiffness vibration isolator with high payload capacity via combination of gas-magnetic-metal springs. Journal of Mechanical Engineering, 61(5): 50-61. doi: 10.3901/JME.2025.05.050
[11]	Abbasi A, Khadem S E, Bab S, et al. 2016. Vibration control of a rotor supported by journal bearings and an asymmetric high-static low-dynamic stiffness suspension. Nonlinear Dynamics, 85(1): 525-545. doi: 10.1007/s11071-016-2704-6
[12]	Abbasi A, Khadem S E, Bab S. 2018. Vibration control of a continuous rotating shaft employing high-static low-dynamic stiffness isolators. Journal of Vibration and Control, 24(4): 760-783. doi: 10.1177/1077546316651559
[13]	Adams M L. 2009. Rotating machinery vibration: from analysis to troubleshooting. CRC Press. Adams M L. 2009. Rotating machinery vibration: from analysis to troubleshooting. CRC Press.
[14]	Bailey-Van Kuren M, Shukla A. 2005. System design for isolation of a neonatal transport unit using passive and semi-active control strategies. Journal of Sound and Vibration, 286(1-2): 382-394. doi: 10.1016/j.jsv.2004.11.005
[15]	Bouna H S, Nbendjo B R, Woafo P. 2020. Isolation performance of a quasi-zero stiffness isolator in vibration isolation of a multi-span continuous beam bridge under pier base vibrating excitation. Nonlinear Dynamics, 100(2): 1125. doi: 10.1007/s11071-020-05580-z
[16]	Bouna H S, Nbendjo B R N. 2023. Analysis of the performance of quasi-zero stiffness isolator on the reduction of vibration on a multi-span continuous beam bridge under moving mass. Journal of Vibration Engineering & Technologies, 11(8): 3999-4013. doi: 10.1007/s42417-022-00797-1
[17]	Cai D A, Zhang H, Wang X W. 2025. Design and validation of quasi-zero stiffness metamaterial core in composite sandwich structures. Composite Structures, 371: 119502. doi: 10.1016/j.compstruct.2025.119502
[18]	Cai J J, Zhuang Z W, Cai J Z, et al. 2026. A large-linear-stroke magnetic negative-stiffness mechanism for quasi-zero-stiffness vibration isolation. Mechanical Systems and Signal Processing, 256: 114496. doi: 10.1016/j.ymssp.2026.114496
[19]	Cao Q J, Wiercigroch M, Pavlovskaia E E, et al. 2006. Archetypal oscillator for smooth and discontinuous dynamics. Physical Review E, 74(4): 046218. doi: 10.1103/PhysRevE.74.046218
[20]	Cao H, Chang Y P, Zhou J X, et al. 2021. High-efficiency vibration isolation for a three-phase power transformer by a quasi-zero-stiffness isolator. Shock and Vibration, 2021(1): 5596064. doi: 10.1155/2021/5596064
[21]	Carrella A, Brennan M J, Waters T P. 2007. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 301(3-5): 678-689. doi: 10.1016/j.jsv.2006.10.011
[22]	Carrella A, Brennan M J, Waters T P, et al. 2008. On the design of a high-static-low-dynamic stiffness isolator using linear mechanical springs and magnets. Journal of Sound and Vibration, 315(3): 712-720. doi: 10.1016/j.jsv.2008.01.046
[23]	Carrella A, Brennan M J, Waters T P, et al. 2012. Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. International Journal of Mechanical Sciences, 55(1): 22-29. doi: 10.1016/j.ijmecsci.2011.11.012
[24]	Chai K, Lou J, Yang Q C, et al. 2017. Characteristic analysis of vibration isolation system based on high-static-low-dynamic stiffness. Journal of Vibroengineering, 19(6): 4120-4137. doi: 10.21595/jve.2017.18268
[25]	Chai Y Y, Jing X J, Guo Y Q. 2022. A compact X-shaped mechanism based 3-DOF anti-vibration unit with enhanced tunable QZS property. Mechanical Systems and Signal Processing, 168: 108651. doi: 10.1016/j.ymssp.2021.108651
[26]	Chai Z Y, Zhang Z, Xu K F, et al. 2025. An innovative nonlinear bionic X-shaped vibration isolator enhanced by quasi-zero stiffness characteristics: theory and experimental investigation. Applied Mathematics and Mechanics (English Edition), 46(8): 1475-1492. doi: 10.1007/s10483-025-3277-8
[27]	Chen R Z, Li X P, Yang Z M, et al. 2021. A variable positive-negative stiffness joint with low frequency vibration isolation performance. Measurement, 185: 110046. doi: 10.1016/j.measurement.2021.110046
[28]	Chen Y H, Niu M Q, Fan Y M, et al. 2025. Quasi-zero-stiffness vibration isolation via a double-layer compliant mechanism. International Journal of Mechanical Sciences, 304: 110670. doi: 10.1016/j.ijmecsci.2025.110670
[29]	Cheng C, Li S M, Wang Y, et al. 2016. On the analysis of a high-static-low-dynamic stiffness vibration isolator with time-delayed cubic displacement feedback. Journal of Sound and Vibration, 378: 76-91. doi: 10.1016/j.jsv.2016.05.029
[30]	Dai H H, Jing X J, Wang Y, et al. 2018. Post-capture vibration suppression of spacecraft via a bio-inspired isolation system. Mechanical Systems and Signal Processing, 105: 214-240. doi: 10.1016/j.ymssp.2017.12.015
[31]	Dalela S, Balaji P S, Jena D P. 2022. Design of a metastructure for vibration isolation with quasi-zero-stiffness characteristics using bistable curved beam. Nonlinear Dynamics, 108(3): 1931-1971. doi: 10.1007/s11071-022-07301-0
[32]	Davoodi E, Safarpour P, Pourgholi M, et al. 2022. A nonlinear seat suspension with high-static low-dynamic stiffness based on negative stiffness structure for helicopter. Journal of Vibration and Control, 28(19-20): 2879-2899. doi: 10.1177/10775463211022482
[33]	Den Hartog J P. 1985. Mechanical vibrations. Courier Corporation. Den Hartog J P. 1985. Mechanical vibrations. Courier Corporation.
[34]	Deng T C, Wen G L, Ding H, et al. 2020. A bio-inspired isolator based on characteristics of quasi-zero stiffness and bird multi-layer neck. Mechanical Systems and Signal Processing, 145: 106967. doi: 10.1016/j.ymssp.2020.106967
[35]	Deng T C, Ding H, Mao X Y, et al. 2026. Fatigue life extension of fluid-conveying pipes via quasi-zero stiffness constraints. Nonlinear Dynamics, 114(9): 636. doi: 10.1007/s11071-026-12512-w
[36]	Ding H, Chen L Q. 2019. Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dynamics, 95(3): 2367-2382. doi: 10.1007/s11071-018-4697-9
[37]	Ding H, Ji J C, Chen L Q. 2019. Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics. Mechanical Systems and Signal Processing, 121: 675-688. doi: 10.1016/j.ymssp.2018.11.057
[38]	Dong G X, Zhang X N, Xie S L, et al. 2017. Simulated and experimental studies on a high-static-low-dynamic stiffness isolator using magnetic negative stiffness spring. Mechanical Systems and Signal Processing, 86: 188-203. doi: 10.1016/j.ymssp.2016.09.040
[39]	Dong G X, Zhang Y H, Luo Y J, et al. 2018. Enhanced isolation performance of a high-static-low-dynamic stiffness isolator with geometric nonlinear damping. Nonlinear Dynamics, 93(4): 2339-2356. doi: 10.1007/s11071-018-4328-5
[40]	Dou J X, Li Z P, Cao Y B, et al. 2023. Magnet based bi-stable nonlinear energy sink for torsional vibration suppression of rotor system. Mechanical Systems and Signal Processing, 186: 109859. doi: 10.1016/j.ymssp.2022.109859
[41]	Fan H G, Yang L J, Tian Y C, et al. 2020. Design of metastructures with quasi-zero dynamic stiffness for vibration isolation. Composite Structures, 243: 112244. doi: 10.1016/j.compstruct.2020.112244
[42]	Feng X, Jing X J. 2019. Human body inspired vibration isolation: Beneficial nonlinear stiffness, nonlinear damping & nonlinear inertia. Mechanical Systems and Signal Processing, 117: 786-812. doi: 10.1016/j.ymssp.2018.08.040
[43]	Feng Y P, Wang Y L, Wu Q J, et al. 2026. Stiffness-inverting low-profile metamaterial pair for large-stroke quasi-zero-stiffness vibration isolation. International Journal of Mechanical Sciences, 312: 111225. doi: 10.1016/j.ijmecsci.2026.111225
[44]	Fulton F, Sorokin V S. 2023. Analysis of the effects of nonlinear damping on a multiple-degree-of-freedom quasi-zero-stiffness vibration isolator. Mechanics Research Communications, 130: 104121. doi: 10.1016/j.mechrescom.2023.104121
[45]	Gajendragadkar G, Boyd J A, Potter D W, et al. 2000. Mechanical vibration in neonatal transport: a randomized study of different mattresses. Journal of Perinatology, 20(5): 307-310.
[46]	Gatti G, Kovacic I, Brennan M J. 2010. On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator. Journal of Sound and Vibration, 329(10): 1823-1835. doi: 10.1016/j.jsv.2009.11.019
[47]	Gatti G. 2021. Optimizing elastic potential energy via geometric nonlinear stiffness. Communications in Nonlinear Science and Numerical Simulation, 103: 106035. doi: 10.1016/j.cnsns.2021.106035
[48]	Gu Y P, Ma Y H, Ren G X. 2017. Stability and vibration characteristics of a rotor-gas foil bearings system with high-static-low-dynamic-stiffness supports. Journal of Sound and Vibration, 397: 152-170. doi: 10.1016/j.jsv.2017.02.047
[49]	Guo S, Zhu J Q, Lin M H, et al. 2026. A multifunctional cylindrical quasi-zero stiffness metamaterial for energy absorption, impact attenuation, and vibration isolation. Thin-Walled Structures, 223: 114611. doi: 10.1016/j.tws.2026.114611
[50]	Han Y W, Cao Q J, Chen Y S, et al. 2012. A novel smooth and discontinuous oscillator with strong irrational nonlinearities. Science China Physics, Mechanics and Astronomy, 55: 1832-1843. doi: 10.1007/s11433-012-4880-9
[51]	Han H S, Sorokin V, Tang L H, et al. 2021. A nonlinear vibration isolator with quasi-zero-stiffness inspired by Miura-origami tube. Nonlinear Dynamics, 105(2): 1313-1325. doi: 10.1007/s11071-021-06650-6
[52]	Han H S, Sorokin V, Tang L H, et al. 2022. Lightweight origami isolators with deployable mechanism and quasi-zero-stiffness property. Aerospace Science and Technology, 121: 107319. doi: 10.1016/j.ast.2021.107319
[53]	Han W J, Lu Z Q, Niu M Q, et al. 2022. A high-static-low-dynamics stiffness vibration isolator via an elliptical ring. Mechanical Systems and Signal Processing, 162: 108061. doi: 10.1016/j.ymssp.2021.108061
[54]	Han H S, Wang W Q, Yu B H, et al. 2024. Integrated design of quasi-zero-stiffness vibration isolators based on bifurcation theory. Aerospace Science and Technology, 146: 108940. doi: 10.1016/j.ast.2024.108940
[55]	Hao Z F, Cao Q J, Wiercigroch M. 2016. Two-sided damping constraint control strategy for high-performance vibration isolation and end-stop impact protection. Nonlinear Dynamics, 86(4): 2129-2144. doi: 10.1007/s11071-016-2685-5
[56]	Hao R B, Lu Z Q, Ding H, et al. 2022. Orthogonal six-DOFs vibration isolation with tunable high-static-low-dynamic stiffness: Experiment and analysis. International Journal of Mechanical Sciences, 222: 107237. doi: 10.1016/j.ijmecsci.2022.107237
[57]	He F F, Du J T, Liu Y. 2025. The bio-inspired spider web dynamic vibration absorber applied to the transverse-torsional-axial vibration in rotor systems. Mechanical Systems and Signal Processing, 237: 112993. doi: 10.1016/j.ymssp.2025.112993
[58]	Hou S, Wei J Z. 2024. A quasi-zero stiffness mechanism with monolithic flexible beams for low-frequency vibration isolation. Mechanical Systems and Signal Processing, 210: 111154. doi: 10.1016/j.ymssp.2024.111154
[59]	Hu C Z, Wang Z Y, Tang L H, et al. 2026. Accelerated design of curved-beam-based torsional isolator with quasi-zero stiffness. Engineering Structures, 352: 122141. doi: 10.1016/j.engstruct.2026.122141
[60]	Hua X D, Wang S L, Zhang J C, et al. 2025. Miura-origami inspired quasi-zero stiffness low-frequency vibration isolator. International Journal of Mechanical Sciences, 295: 110283. doi: 10.1016/j.ijmecsci.2025.110283
[61]	Huang X C, Liu X T, Hua H X. 2014. On the characteristics of an ultra-low frequency nonlinear isolator using sliding beam as negative stiffness. Journal of Mechanical Science and Technology, 28(3): 813-822. doi: 10.1007/s12206-013-1205-5
[62]	Ibrahim R A. 2008. Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration, 314(3-5): 371-452. doi: 10.1016/j.jsv.2008.01.014
[63]	Ishida S, Suzuki K, Shimosaka H. 2017. Design and experimental analysis of origami-inspired vibration isolator with quasi-zero-stiffness characteristic. Journal of Vibration and Acoustics-Transactions of the ASME, 139(5): 051004.
[64]	Jeon H, Jeon Y, Baek S. 2026. Active equilibrium control of a rhombus QZS Isolator: A hybrid strategy for payload compensation and resonance elimination. Mechanical Systems and Signal Processing, 257: 114561. doi: 10.1016/j.ymssp.2026.114561
[65]	Jiang Y L, Song C, Ding C M, et al. 2020. Design of magnetic-air hybrid quasi-zero stiffness vibration isolation system. Journal of Sound and Vibration, 477: 115346. doi: 10.1016/j.jsv.2020.115346
[66]	Jiang G Q, Wang Y, Li F M, et al. 2021. An integrated nonlinear passive vibration control system and its vibration reduction properties. Journal of Sound and Vibration, 509: 116231. doi: 10.1016/j.jsv.2021.116231
[67]	Jiang X W, Xu X, Shi T L, et al. 2024. Nonlinear characteristic analysis of gas-interconnected quasi-zero stiffness pneumatic suspension system: A theoretical and experimental study. Chinese Journal of Mechanical Engineering, 37(1): 58. doi: 10.1186/s10033-024-01039-z
[68]	Jiang Y, Song C S, Jiang Y L, et al. 2026. Integrated design of a metastructure with high load-carrying capacity and wide quasi-zero stiffness range for vibration isolation. Smart Materials and Structures, 35(7): 075041. doi: 10.1088/1361-665X/ae8a26
[69]	Jin G X, Wang Z H, Yang T Z. 2022. Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine. Applied Mathematics and Mechanics (English Edition), 43(6): 813-824. doi: 10.1007/s10483-022-2852-5
[70]	Kim G W, Shin S C. 2015. Research on the torque transmissibility of the passive torsional vibration isolator in an automotive clutch damper. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 229(13): 1840-1847. doi: 10.1177/0954407015579296
[71]	Kim J, Jeon Y, Um S, et al. 2019. A novel passive quasi-zero stiffness isolator for ultra-precision measurement systems. International Journal of Precision Engineering and Manufacturing, 20(9): 1573-1580. doi: 10.1007/s12541-019-00149-2
[72]	Kovacic I, Brennan M J, Waters T P. 2008. A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. Journal of Sound and Vibration, 315(3): 700-711. doi: 10.1016/j.jsv.2007.12.019
[73]	Li M, Cheng W, Xie R L. 2021. A quasi-zero-stiffness vibration isolator using a cam mechanism with user-defined profile. International Journal of Mechanical Sciences, 189: 105938. doi: 10.1016/j.ijmecsci.2020.105938
[74]	Li X, Li P Y, Dong X M. 2024. Nonlinear passive magnetorheological damping characteristics of the scissor-like isolation platform. Archive of Applied Mechanics, 94(7): 1967-1994. doi: 10.1007/s00419-024-02624-3
[75]	Li Y L, Wu Z Y, Peng Y, et al. 2024. Full-band vibration isolation of multi-step quasi-zero stiffness systems. International Journal of Mechanical Sciences, 274: 109277. doi: 10.1016/j.ijmecsci.2024.109277
[76]	Liang K, Jing Y H, Zhang X P. 2024. Design of broad quasi-zero stiffness platform metamaterials for vibration isolation. International Journal of Mechanical Sciences, 281: 109691. doi: 10.1016/j.ijmecsci.2024.109691
[77]	Ling P, Miao L L, Zhang W M, et al. 2022. Cockroach-inspired structure for low-frequency vibration isolation. Mechanical Systems and Signal Processing, 171: 108955. doi: 10.1016/j.ymssp.2022.108955
[78]	Liu X T, Huang X C, Hua H X. 2013. On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. Journal of Sound and Vibration, 332(14): 3359-3376. doi: 10.1016/j.jsv.2012.10.037
[79]	Liu C C, Jing X J, Li F M. 2015. Vibration isolation using a hybrid lever-type isolation system with an X-shape supporting structure. International Journal of Mechanical Sciences, 98: 169-177. doi: 10.1016/j.ijmecsci.2015.04.012
[80]	Liu X T, Zhao Q, Zhang Z Y, et al. 2019. An experiment investigation on the effect of Coulomb friction on the displacement transmissibility of a quasi-zero stiffness isolator. Journal of Mechanical Science and Technology, 33(1): 121-127. doi: 10.1007/s12206-018-1212-7
[81]	Liu C R, Yu K P, Tang J. 2020. New insights into the damping characteristics of a typical quasi-zero-stiffness vibration isolator. International Journal of Non-Linear Mechanics, 124: 103511. doi: 10.1016/j.ijnonlinmec.2020.103511
[82]	Liu C R, Yu K P. 2020. Superharmonic resonance of the quasi-zero-stiffness vibration isolator and its effect on the isolation performance. Nonlinear Dynamics, 100(1): 95-117. doi: 10.1007/s11071-020-05509-6
[83]	Liu C R, Yu K P, Liao B P, et al. 2021. Enhanced vibration isolation performance of quasi-zero-stiffness isolator by introducing tunable nonlinear inerter. Communications in Nonlinear Science and Numerical Simulation, 95: 105654. doi: 10.1016/j.cnsns.2020.105654
[84]	Liu C R, Zhao R, Yu K P, et al. 2021. In-plane quasi-zero-stiffness vibration isolator using magnetic interaction and cables: Theoretical and experimental study. Applied Mathematical Modelling, 96: 497-522. doi: 10.1016/j.apm.2021.03.035
[85]	Liu S W, Peng G L, Jin K. 2021. Design and characteristics of a novel QZS vibration isolation system with origami-inspired corrector. Nonlinear Dynamics, 106(1): 255-277. doi: 10.1007/s11071-021-06821-5
[86]	Liu S W, Peng G L, Jin K. 2022. Towards accurate modeling of the Tachi-Miura origami in vibration isolation platform with geometric nonlinear stiffness and damping. Applied Mathematical Modelling, 103: 674-695. doi: 10.1016/j.apm.2021.11.012
[87]	Liu B Y, Gu L, Dong M M. 2024. Bifurcation and dynamic analysis of quasi-zero stiffness isolator with asymmetric stiffness and mismatched load based on X-shaped negative stiffness structure. Acta Mechanica, 235(6): 3447-3462. doi: 10.1007/s00707-024-03901-6
[88]	Liu C R, Wang Y W, Zhang W, et al. 2024. Nonlinear dynamics of a magnetic vibration isolator with higher-order stable quasi-zero-stiffness. Mechanical Systems and Signal Processing, 218: 111584. doi: 10.1016/j.ymssp.2024.111584
[89]	Liu Z Q, Lv Q F, Li D Y, et al. 2025. A straight-arch-straight beam tandem quasi-zero stiffness structure. International Journal of Mechanical Sciences, 286: 109818. doi: 10.1016/j.ijmecsci.2024.109818
[90]	Lu Z Q, Brennan M J, Yang T J, et al. 2013. An investigation of a two-stage nonlinear vibration isolation system. Journal of Sound and Vibration, 332(6): 1456-1464. doi: 10.1016/j.jsv.2012.11.019
[91]	Lu Z Q, Yang T J, Brennan M J, et al. 2017. Experimental Investigation of a Two-Stage Nonlinear Vibration Isolation System With High-Static-Low-Dynamic Stiffness. Journal of Applied Mechanics- Transactions of the ASME, 84(2): 021001. doi: 10.1115/1.4034989
[92]	Lu Z Q, Brennan M, Ding H, et al. 2019. High-static-low-dynamic-stiffness vibration isolation enhanced by damping nonlinearity. Science China Technological Sciences, 62(7): 1103-1110. doi: 10.1007/s11431-017-9281-9
[93]	Lu H J, Wang W, Wu K, et al. 2025. A study on quasi-zero stiffness metamaterial vibration isolators based on large deformation of curved beams governed by the nonlinear Euler-Bernoulli equation. Smart Materials and Structures, 34(7): 075010. doi: 10.1088/1361-665X/ade8c0
[94]	Meng Q Y, Wang S J, Chang Z Y, et al. 2026. A novel quasi-zero stiffness isolation platform for enhancing the effective operating range via a quasi-linear stiffness compensation mechanism. Mechanical Systems and Signal Processing, 249: 114029. doi: 10.1016/j.ymssp.2026.114029
[95]	Misseroni D, Pratapa P P, Liu K, et al. 2024. Origami engineering. Nature Reviews Methods Primers, 4(1): 40. doi: 10.1038/s43586-024-00313-7
[96]	Navazi H M, Hojjati M. 2017. Nonlinear vibrations and stability analysis of a rotor on high-static-low-dynamic-stiffness supports using method of multiple scales. Aerospace Science and Technology, 63: 259-265. doi: 10.1016/j.ast.2017.01.007
[97]	Nie X, Xiao Z M, Wan T, et al. 2026. Dynamic characteristics of quasi-zero stiffness system composed of air spring and multiple magnetic rings. Nonlinear Dynamics, 114(3): 187. doi: 10.1007/s11071-025-12051-w
[98]	Niu M Q, Chen L Q. 2022. Nonlinear vibration isolation via a compliant mechanism and wire ropes. Nonlinear Dynamics, 107(2): 1687-1702. doi: 10.1007/s11071-021-06588-9
[99]	Noh J, Andreu A, Kim P, et al. 2025. Torsional stiffness-softening effect of torque-dependent variation in moment arm length for torsional vibration isolation. Nonlinear Dynamics, 113(16): 21073-21093. doi: 10.1007/s11071-025-11265-2
[100]	Pan W H, Xie H Y, Ai P F, et al. 2025. A novel large linear stroke high-static-low-dynamic stiffness vibration isolator with high magnetic negative stiffness and compactness. Engineering Structures, 331: 120014. doi: 10.1016/j.engstruct.2025.120014
[101]	Pan H B, Yang H, Zhou J X, et al. 2026. Nonlinear viscoelastic isolation performance of a quasi-zero-stiffness flywheel isolator. Mechanical Systems and Signal Processing, 257: 114541. doi: 10.1016/j.ymssp.2026.114541
[102]	Prehn J, McEwen I, Jeffries L, et al. 2015. Decreasing sound and vibration during ground transport of infants with very low birth weight. Journal of Perinatology, 35(2): 110-114. doi: 10.1038/jp.2014.172
[103]	Pu H Y, Yuan S J, Peng Y, et al. 2019. Multi-layer electromagnetic spring with tunable negative stiffness for semi-active vibration isolation. Mechanical Systems and Signal Processing, 121: 942-960. doi: 10.1016/j.ymssp.2018.12.028
[104]	Pu H Y, Liu J, Wang M, et al. 2024. Bio-inspired quasi-zero stiffness vibration isolator with quasilinear negative stiffness in full stroke. Journal of Sound and Vibration, 574: 118240. doi: 10.1016/j.jsv.2024.118240
[105]	Qi W H, Yan G, Lu J J, et al. 2022. Magnetically modulated sliding structure for low frequency vibration isolation. Journal of Sound and Vibration, 526: 116819. doi: 10.1016/j.jsv.2022.116819
[106]	Qi W H, Liu F R, Lu J J, et al. 2024. Generative quasi-zero stiffness paradigm for vibration isolation by constraining the constant force with hardening boundaries. Journal of Sound and Vibration, 589: 118548. doi: 10.1016/j.jsv.2024.118548
[107]	Qi W H, Zhao T Y, Gao Q H, et al. 2025. A magnetically levitated platform with multi-directional quasi-zero stiffness for low-frequency vibration protection. Engineering Structures, 341: 120823. doi: 10.1016/j.engstruct.2025.120823
[108]	Ran L Y, Wang J L, Halim D, et al. 2024. A semi-active quasi-zero-stiffness vibration isolation system through controllable lateral spring stiffness. Nonlinear Dynamics, 112(16): 13751-13770. doi: 10.1007/s11071-024-09770-x
[109]	Robertson W S, Kidner M R F, Cazzolato B S, et al. 2009. Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation. Journal of Sound and Vibration, 326(1-2): 88-103. doi: 10.1016/j.jsv.2009.04.015
[110]	Saber H, Zippo A, Samani F S, et al. 2026. Enhancing bridge vibration control through optimized quasi-zero-stiffness supports under moving mass. Computer Modeling in Engineering & Sciences, 147(2): 18. doi: 10.32604/cmes.2026.079313
[111]	Sadeghi S, Li S Y. 2019. Fluidic origami cellular structure with asymmetric quasi-zero stiffness for low-frequency vibration isolation. Smart Materials and Structures, 28(6): 065006. doi: 10.1088/1361-665X/ab143c
[112]	Saeed N A, Hou L, Yi H M, et al. 2026. On a broadband vibration isolator with tunable stiffness: from quasi-zero-stiffness to zero-stiffness behavior. Applied Mathematics and Mechanics (English Edition), 47(2): 255-282. doi: 10.1007/s10483-026-3351-9
[113]	Sui G D, Zhou C Y, Wu W T, et al. 2026. Dual-function of isolation and energy harvesting via a spatial cam-induced multi-region quasi-zero-stiffness mechanism. Mechanical Systems and Signal Processing, 257: 114534. doi: 10.1016/j.ymssp.2026.114534
[114]	Suman S, Balaji P S, Selvakumar K, et al. 2021. Nonlinear vibration control device for a vehicle suspension using negative stiffness mechanism. Journal of Vibration Engineering & Technologies, 9(5): 957-966. doi: 10.1007/s42417-020-00275-6
[115]	Sun X T, Jing X J, Xu J, et al. 2014. Vibration isolation via a scissor-like structured platform. Journal of Sound and Vibration, 333(9): 2404-2420. doi: 10.1016/j.jsv.2013.12.025
[116]	Sun X T, Jing X J. 2015. Multi-direction vibration isolation with quasi-zero stiffness by employing geometrical nonlinearity. Mechanical Systems and Signal Processing, 62-63: 149-163.
[117]	Sun X T, Jing X J. 2016. A nonlinear vibration isolator achieving high-static-low-dynamic stiffness and tunable anti-resonance frequency band. Mechanical Systems and Signal Processing, 80: 166-188. doi: 10.1016/j.ymssp.2016.04.011
[118]	Sun X T, Jing X J. 2016. Analysis and design of a nonlinear stiffness and damping system with a scissor-like structure. Mechanical Systems and Signal Processing, 66-67: 723-742.
[119]	Sun X T, Shu Z, Jian X, et al. 2018. Dynamical Analysis and Realization of an Adaptive Isolator. Journal of Applied Mechanics- Transactions of the ASME, 85(1): 011002. doi: 10.1115/1.4038285
[120]	Sun X T, Xu J, Wang F, et al. 2018. A novel isolation structure with flexible joints for impact and ultralow-frequency excitations. International Journal of Mechanical Sciences, 146: 366-376. doi: 10.1016/j.ijmecsci.2018.08.009
[121]	Sun X T, Wang F, Xu J. 2019. Analysis, design and experiment of continuous isolation structure with Local Quasi-Zero-Stiffness property by magnetic interaction. International Journal of Non-Linear Mechanics, 116: 289-301. doi: 10.1016/j.ijnonlinmec.2019.07.008
[122]	Sun Y, Zhao J L, Wang M, et al. 2020. High-static-low-dynamic stiffness isolator with tunable electromagnetic mechanism. IEEE-ASME Transactions on Mechatronics, 25(1): 316-326. doi: 10.1109/TMECH.2019.2954910
[123]	Sun K, Tang J, Wu Z J, et al. 2024. Coupled nonlinear vibration characteristics of quasi-zero-stiffness Gough-Stewart isolation platform. Aerospace Science and Technology, 152: 109352. doi: 10.1016/j.ast.2024.109352
[124]	Sun X T, Xu J, Qi Z F. 2024. Mechanism properties of a bird-neck bionic rigid-flexible structure. Fundamental Research, 4(6): 1613-1624. doi: 10.1016/j.fmre.2022.06.023
[125]	Sun Z Y, Yue X H, Li A, et al. 2025. A tensegrity-based torsional vibration isolator with broad quasi-zero-stiffness region. Mechanical Systems and Signal Processing, 224: 112215. doi: 10.1016/j.ymssp.2024.112215
[126]	Tang B, Brennan M J. 2014. On the shock performance of a nonlinear vibration isolator with high-static-low-dynamic-stiffness. International Journal of Mechanical Sciences, 81: 207-214. doi: 10.1016/j.ijmecsci.2014.02.019
[127]	Tang H Z, Li J Y, Nie M, et al. 2026. A Semi-Active Quasi-Zero-Stiffness Vibration Isolator Integrating Electromagnetic Spring and Magnetorheological Damper Under Variable Load. Journal of Vibration Engineering & Technologies, 14(7): 449. doi: 10.1007/s42417-026-02666-7
[128]	Tian R L, Wang M H, Zhang Y S, et al. 2024. A concave X-shaped structure supported by variable pitch springs for low-frequency vibration isolation. Mechanical Systems and Signal Processing, 218: 111587. doi: 10.1016/j.ymssp.2024.111587
[129]	Tian F H, Ma H Y, Yan B. 2026. Broad-range continuous load adaptability with electromagnetic constant-force compensated stair-step quasi-zero-stiffness vibration isolators. Mechanical Systems and Signal Processing, 258: 114602. doi: 10.2139/ssrn.6466348
[130]	Tuo J Y, Deng Z X, Zhang H S, et al. 2018. A 3-axis torsion quasi-zero-stiffness-based sensor system for angular vibration measurement. Journal of Vibration and Control, 24(18): 4325-4336. doi: 10.1177/1077546317724016
[131]	Wang K, Zhou J X, Xu D L. 2017. Sensitivity analysis of parametric errors on the performance of a torsion quasi-zero-stiffness vibration isolator. International Journal of Mechanical Sciences, 134: 336-346. doi: 10.1016/j.ijmecsci.2017.10.026
[132]	Wang X L, Zhou J X, Xu D L, et al. 2017. Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness. Nonlinear Dynamics, 87(1): 633-646. doi: 10.1007/s11071-016-3065-x
[133]	Wang Y, Li S M, Neild S A, et al. 2017. Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness. Nonlinear Dynamics, 88(1): 635-654. doi: 10.1007/s11071-016-3266-3
[134]	Wang X J, Liu H, Chen Y Q, et al. 2018. Beneficial stiffness design of a high-static-low-dynamic-stiffness vibration isolator based on static and dynamic analysis. International Journal of Mechanical Sciences, 142: 235-244. doi: 10.1016/j.ijmecsci.2018.04.053
[135]	Wang Y, Li S M, Cheng C, et al. 2018. Adaptive control of a vehicle-seat-human coupled model using quasi-zero-stiffness vibration isolator as seat suspension. Journal of Mechanical Science and Technology, 32(7): 2973-2985. doi: 10.1007/s12206-018-0601-2
[136]	Wang Y, Jing X J, Guo Y Q. 2019. Nonlinear analysis of a bio-inspired vertically asymmetric isolation system under different structural constraints. Nonlinear Dynamics, 95(1): 445-464. doi: 10.1007/s11071-018-4575-5
[137]	Wang Y, Jing X J. 2019. Nonlinear stiffness and dynamical response characteristics of an asymmetric X-shaped structure. Mechanical Systems and Signal Processing, 125: 142-169. doi: 10.1016/j.ymssp.2018.03.045
[138]	Wang Q, Zhou J X, Xu D L, et al. 2020. Design and experimental investigation of ultra-low frequency vibration isolation during neonatal transport. Mechanical Systems and Signal Processing, 139: 106633. doi: 10.1016/j.ymssp.2020.106633
[139]	Wang J X, Yao G. 2024. A 3-DOF frog-inspired quasi-zero stiffness isolator and its vibration control performance. Aerospace Science and Technology, 149: 109163. doi: 10.1016/j.ast.2024.109163
[140]	Wang J X, Yao G. 2025. A multiple layer enhanced quasi-zero stiffness vibration isolator with magnetically modulated nonlinear stiffness. Aerospace Science and Technology, 161: 110113. doi: 10.1016/j.ast.2025.110113
[141]	Wang G X, Wu K H, Sun H, et al. 2026. Design of Multi-level Vibration Isolation Structures Based on Double Cosine Beam Quasi-zero Stiffness Metastructures. Journal of Vibration Engineering & Technologies, 14(6): 394. doi: 10.1007/s42417-026-02547-z
[142]	Wang S W, Ling P, Yan G, et al. 2026. Multi-stage quasi-zero stiffness vibration isolation with linear-to-torsion magnetic negative stiffness mechanism for variable load. Mechanical Systems and Signal Processing, 249: 114055. doi: 10.1016/j.ymssp.2026.114055
[143]	Wen G L, He J F, Liu J, et al. 2021. Design, analysis and semi-active control of a quasi-zero stiffness vibration isolation system with six oblique springs. Nonlinear Dynamics, 106(1): 309-321. doi: 10.1007/s11071-021-06835-z
[144]	Wu W J, Chen X D, Shan Y H. 2014. Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness. Journal of Sound and Vibration, 333(13): 2958-2970. doi: 10.1016/j.jsv.2014.02.009
[145]	Wu Z J, Jing X J, Bian J, et al. 2015. Vibration isolation by exploring bio-inspired structural nonlinearity. Bioinspiration & Biomimetics, 10(5): 056015. doi: 10.1088/1748-3190/10/5/056015
[146]	Wu Z J, Jing X J, Sun B, et al. 2016. A 6DOF passive vibration isolator using X-shape supporting structures. Journal of Sound and Vibration, 380: 90-111. doi: 10.1016/j.jsv.2016.06.004
[147]	Wu J L, Zeng L Z, Han B, et al. 2022. Analysis and design of a novel arrayed magnetic spring with high negative stiffness for low-frequency vibration isolation. International Journal of Mechanical Sciences, 216: 106980. doi: 10.1016/j.ijmecsci.2021.106980
[148]	Wu W T, Jiang T C, Sui G D, et al. 2025. Bioinspired frog adaptive-mass quasi-zero stiffness vibration isolator. International Journal of Mechanical Sciences, 301: 110509. doi: 10.1016/j.ijmecsci.2025.110509
[149]	Xiao L, Sun X, Cheng L, et al. 2024. A 3D-printed quasi-zero-stiffness isolator for low-frequency vibration isolation: Modelling and experiments. Journal of Sound and Vibration, 577: 118308. doi: 10.1016/j.jsv.2024.118308
[150]	Xu D L, Yu Q P, Zhou J X, et al. 2013. Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 332(14): 3377-3389. doi: 10.1016/j.jsv.2013.01.034
[151]	Xu D L, Zhang Y Y, Zhou J X, et al. 2014. On the analytical and experimental assessment of the performance of a quasi-zero-stiffness isolator. Journal of Vibration and Control, 20(15): 2314-2325. doi: 10.1177/1077546313484049
[152]	Xu J W, Jing J P. 2024. Nonlinear behavior of quasi-zero stiffness nonlinear torsional vibration isolator. Nonlinear Dynamics, 112(4): 2545-2568. doi: 10.1007/s11071-023-09176-1
[153]	Xu Y Q, Dong H W, Wang Y S. 2024. Topology optimization of programable quasi-zero-stiffness metastructures for low-frequency vibration isolation. International Journal of Mechanical Sciences, 280: 109557. doi: 10.1016/j.ijmecsci.2024.109557
[154]	Yan L X, Xuan S H, Gong X L. 2018. Shock isolation performance of a geometric anti-spring isolator. Journal of Sound and Vibration, 413: 120-143. doi: 10.1016/j.jsv.2017.10.024
[155]	Yan G, Wang S, Zou H X, et al. 2020. Bio-inspired polygonal skeleton structure for vibration isolation: Design, modelling, and experiment. Science China Technological Sciences, 63(12): 2617-2630. doi: 10.1007/s11431-020-1568-8
[156]	Yan G, Zou H X, Wang S, et al. 2021. Bio-Inspired Vibration Isolation: Methodology and Design. Applied Mechanics Reviews, 73(2): 020801. doi: 10.1115/1.4049946
[157]	Yan B, Yu N, Wang Z H, et al. 2022. Lever-type quasi-zero stiffness vibration isolator with magnetic spring. Journal of Sound and Vibration, 527: 116865. doi: 10.1016/j.jsv.2022.116865
[158]	Yan G, Qi W H, Lu J J, et al. 2024. Bio-inspired multi-joint-collaborative vibration isolation. Journal of Sound and Vibration, 568: 118089. doi: 10.1016/j.jsv.2023.118089
[159]	Yang T, Cao Q J, Hao Z F. 2021. A novel nonlinear mechanical oscillator and its application in vibration isolation and energy harvesting. Mechanical Systems and Signal Processing, 155: 107636. doi: 10.1016/j.ymssp.2021.107636
[160]	Yang S L, Fan W, Liu Y L, et al. 2025. A high-static-low-dynamic stiffness wire rope isolator with a magnetic negative stiffness device: Experiment, analytical method, and optimization. Engineering Structures, 328: 119682. doi: 10.1016/j.engstruct.2025.119682
[161]	Yang S K, Shi X X, Wang X Z, et al. 2026. Nonlinear coupling mechanism of quasi-zero-stiffness units in multi-level structures. Applied Mathematics and Mechanics (English Edition), 47(6): 1215-1240. doi: 10.1007/s10483-026-3392-6
[162]	Yao Y H, Li H G, Li Y, et al. 2020. Analytical and experimental investigation of a high-static-low-dynamic stiffness isolator with cam-roller-spring mechanism. International Journal of Mechanical Sciences, 186: 105888. doi: 10.1016/j.ijmecsci.2020.105888
[163]	Ye K, Ji J C, Brown T. 2020. Design of a quasi-zero stiffness isolation system for supporting different loads. Journal of Sound and Vibration, 471: 115198. doi: 10.1016/j.jsv.2020.115198
[164]	Ye K, Ji J C, Brown T. 2021. A novel integrated quasi-zero stiffness vibration isolator for coupled translational and rotational vibrations. Mechanical Systems and Signal Processing, 149: 107340. doi: 10.1016/j.ymssp.2020.107340
[165]	Ye K, Ji J C. 2022. An origami inspired quasi-zero stiffness vibration isolator using a novel truss-spring based stack Miura-ori structure. Mechanical Systems and Signal Processing, 165: 108383. doi: 10.1016/j.ymssp.2021.108383
[166]	Yin Y Q, Zeng F C, Yu Y, et al. 2025. Constant-Force kirigami for scalable, shiftable, stair-stepping and static load-bearing quasi-zero-stiffness metamaterials. Mechanical Systems and Signal Processing, 240: 113433. doi: 10.1016/j.ymssp.2025.113433
[167]	Yingli L, Daolin X. 2018. Force transmissibility of floating raft systems with quasi-zero-stiffness isolators. Journal of Vibration and Control, 24(16): 3608-3616. doi: 10.1177/1077546317708460
[168]	Yu C Y, Jiang Q B, Fu Q D, et al. 2023. The X-shaped structure with nonlinear positive stiffness compensation for low-frequency vibration isolation. International Journal of Mechanical Sciences, 259: 108598. doi: 10.1016/j.ijmecsci.2023.108598
[169]	Yu K F, Chen Y W, Yu C Y, et al. 2024. Origami-inspire quasi-zero stiffness structure for flexible low-frequency vibration isolation. International Journal of Mechanical Sciences, 276: 109377. doi: 10.1016/j.ijmecsci.2024.109377
[170]	Yu N, Tian F H, Ma H Y, et al. 2025. Tunable quasi-zero stiffness vibration isolators with electromagnetic damping for low-frequency vibration isolation enhancement. Mechanical Systems and Signal Processing, 237: 113082. doi: 10.1016/j.ymssp.2025.113082
[171]	Yuan J, Zhou Y L, Zhang Y, et al. 2025. A large-stroke and adjustable-load magnetic quasi-zero stiffness isolator. Mechanical Systems and Signal Processing, 239: 113326. doi: 10.1016/j.ymssp.2025.113326
[172]	Zeng R, Wen G L, Zhou J X, et al. 2021. Limb-inspired bionic quasi-zero stiffness vibration isolator. Acta Mechanica Sinica, 37(7): 1152-1167. doi: 10.1007/s10409-021-01070-6
[173]	Zhang J Z, Li D, Chen M J, et al. 2004. An ultra-low frequency parallel connection nonlinear isolator for precision instruments. Key Engineering Materials, 257: 231-238. doi: 10.4028/www.scientific.net/kem.257-258.231
[174]	Zhang W, Zhao J B. 2016. Analysis on nonlinear stiffness and vibration isolation performance of scissor-like structure with full types. Nonlinear Dynamics, 86(1): 17-36. doi: 10.1007/s11071-016-2869-z
[175]	Zhang F, Xu M L, Shao S B, et al. 2020. A new high-static-low-dynamic stiffness vibration isolator based on magnetic negative stiffness mechanism employing variable reluctance stress. Journal of Sound and Vibration, 476: 115322. doi: 10.1016/j.jsv.2020.115322
[176]	Zhang Q L, Xia S, Xu D L, et al. 2020. A torsion-translational vibration isolator with quasi-zero stiffness. Nonlinear Dynamics, 99(2): 1467-1488. doi: 10.1007/s11071-019-05369-9
[177]	Zhang Q, Guo D K, Hu G K. 2021. Tailored mechanical metamaterials with programmable quasi-zero-stiffness features for full-band vibration isolation. Advanced Functional Materials, 31(33): 2101428. doi: 10.1002/adfm.202101428
[178]	Zhang C, He J S, Zhou G Q, et al. 2023. Compliant quasi-zero-stiffness isolator for low-frequency torsional vibration isolation. Mechanism and Machine Theory, 181: 105213. doi: 10.1016/j.mechmachtheory.2022.105213
[179]	Zhang X L, Lu X H, Li C C, et al. 2024. Design of hyperbolic quasi-zero stiffness metastructures coupled with nonlinear stiffness for low-frequency vibration isolation. Engineering Structures, 312: 118262. doi: 10.1016/j.engstruct.2024.118262
[180]	Zhang H L, Wang S W, Liu X A, et al. 2026. Quasi-zero stiffness vibration isolator for turtle-like limbs: High bearing capacity design and low-frequency vibration isolation performance analysis. Journal of Vibration and Control. Online First: 10775463261460576.
[181]	Zhao F, Ji J C, Ye K, et al. 2021. An innovative quasi-zero stiffness isolator with three pairs of oblique springs. International Journal of Mechanical Sciences, 192: 106093. doi: 10.1016/j.ijmecsci.2020.106093
[182]	Zhao Z Q, Yin J F, Zhang X G, et al. 2026. Design of assembled quasi-zero-stiffness metastructures with nonlinear stiffness coupling. Engineering Structures, 366: 123336. doi: 10.1016/j.engstruct.2026.123336
[183]	Zheng Y S, Zhang X N, Luo Y J, et al. 2016. Design and experiment of a high-static-low-dynamic stiffness isolator using a negative stiffness magnetic spring. Journal of Sound and Vibration, 360: 31-52. doi: 10.1016/j.jsv.2015.09.019
[184]	Zheng Y S, Li Q P, Yan B, et al. 2018. A Stewart isolator with high-static-low-dynamic stiffness struts based on negative stiffness magnetic springs. Journal of Sound and Vibration, 422: 390-408. doi: 10.1016/j.jsv.2018.02.046
[185]	Zheng Y S, Zhang X N, Luo Y J, et al. 2018. Analytical study of a quasi-zero stiffness coupling using a torsion magnetic spring with negative stiffness. Mechanical Systems and Signal Processing, 100: 135-151. doi: 10.1016/j.ymssp.2017.07.028
[186]	Zhou N, Liu K. 2010. A tunable high-static-low-dynamic stiffness vibration isolator. Journal of Sound and Vibration, 329(9): 1254-1273. doi: 10.1016/j.jsv.2009.11.001
[187]	Zhou J X, Wang X L, Xu D L, et al. 2015. Nonlinear dynamic characteristics of a quasi-zero stiffness vibration isolator with cam-roller-spring mechanisms. Journal of Sound and Vibration, 346: 53-69. doi: 10.1016/j.jsv.2015.02.005
[188]	Zhou J X, Xu D L, Bishop S. 2015. A torsion quasi-zero stiffness vibration isolator. Journal of Sound and Vibration, 338: 121-133. doi: 10.1016/j.jsv.2014.10.027
[189]	Zhou J X, Wang K, Xu D L, et al. 2017. A six degrees-of-freedom vibration isolation platform supported by a hexapod of quasi-zero-stiffness struts. Journal of Vibration and Acoustics, 139(3): 034502. doi: 10.1115/1.4035715
[190]	Zhou J X, Wang K, Xu D L, et al. 2017. Local resonator with high-static-low-dynamic stiffness for lowering band gaps of flexural wave in beams. Journal of Applied Physics, 121(4): 044902. doi: 10.1063/1.4974299
[191]	Zhou J X, Xiao Q Y, Xu D L, et al. 2017. A novel quasi-zero-stiffness strut and its applications in six-degree-of-freedom vibration isolation platform. Journal of Sound and Vibration, 394: 59-74. doi: 10.1016/j.jsv.2017.01.021
[192]	Zhou J X, Wang K, Xu D L, et al. 2018. Vibration isolation in neonatal transport by using a quasi-zero-stiffness isolator. Journal of Vibration and Control, 24(15): 3278-3291. doi: 10.1177/1077546317703866
[193]	Zhou J X, Pan H B, Cai C Q, et al. 2021. Tunable ultralow frequency wave attenuations in one-dimensional quasi-zero-stiffness metamaterial. International Journal of Mechanics and Materials in Design, 17(2): 285-300. doi: 10.1007/s10999-020-09525-7
[194]	Zhou C Y, Sui G D, Chen Y F, et al. 2024. A nonlinear low frequency quasi zero stiffness vibration isolator using double-arc flexible beams. International Journal of Mechanical Sciences, 276: 109378. doi: 10.1016/j.ijmecsci.2024.109378
[195]	Zhou H D, Gao J J, Chen Y, et al. 2024. A quasi-zero-stiffness vibration isolator inspired by Kresling origami. Structures, 69: 107315. doi: 10.1016/j.istruc.2024.107315
[196]	Zhou J H, Zhou J X, Pan H B, et al. 2024. Multi-layer quasi-zero-stiffness meta-structure for high-efficiency vibration isolation at low frequency. Applied Mathematics and Mechanics (English Edition), 45(7): 1189-1208. doi: 10.1007/s10483-024-3157-6
[197]	Zhou Y, Tachi T, Cai J G, et al. 2024. Tunable stiffness design of curved-crease origami and extended quasi-zero stiffness vibration isolator. Smart Materials and Structures, 33(2): 025033. doi: 10.1088/1361-665X/ad1e8b
[198]	Zhou C Y, Sui G D, Shan X B, et al. 2026. A spatially mechanical-decoupled three-DOF quasi-zero-stiffness isolator integrating flexible curved beams. International Journal of Mechanical Sciences, 312: 111160. doi: 10.1016/j.ijmecsci.2026.111160
[199]	Zhu T, Cazzolato B, Robertson W S P, et al. 2015. Vibration isolation using six degree-of-freedom quasi-zero stiffness magnetic levitation. Journal of Sound and Vibration, 358: 48-73. doi: 10.1016/j.jsv.2015.07.013
[200]	Zhu G N, Liu J Y, Cao Q J, et al. 2020. A two degree of freedom stable quasi-zero stiffness prototype and its applications in aseismic engineering. Science China Technological Sciences, 63(3): 496-505. doi: 10.1007/s11431-018-9524-2
[201]	Zhu Q B, Chai K, Lou J. 2026. Enhancing the near-linear working region of quasi-zero stiffness vibration isolators using a tri-rectangular-magnet configuration. Journal of Vibration and Control: 10775463261472765.
[202]	Zou W, Cheng C, Ma R, et al. 2021. Performance analysis of a quasi-zero stiffness vibration isolation system with scissor-like structures. Archive of Applied Mechanics, 91(1): 117-133. doi: 10.1007/s00419-020-01757-5
[203]	Zuo S, Wang D Y, Zhang Y S, et al. 2024. An innovative design of parabolic cam-roller quasi-zero-stiffness isolators for ultralow frequency vibration isolation. Nonlinear Dynamics, 112(21): 18717-18744. doi: 10.1007/s11071-024-10011-4