Review on research progress of nonlinear vibration isolation and time-delayed suppression method
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摘要: 振动问题与人类日常生活和科技发展紧密相关. 振动不但会干扰人类的生活、影响人类健康, 也会造成建筑物、机械设备和精密仪器的无法正常使用甚至损坏. 于是, 在航空航天、汽车工程、船舶工程、大型结构及精密仪器加工等领域, 人们利用弹性元件或控制装置形成有效的振动隔离或消除装备, 有效的隔振能够提高人员和装备的安全性、稳定性、可控性和舒适性. 现代结构的大型化和复杂化发展, 对隔振和消振器的宽频抑振效果提出了新挑战. 然而, 基于线性理论的设计优化方法在分析和应用中出现了无法调和的矛盾, 即, 如果要拓宽隔振频带, 就必须降低隔振结构的刚度, 这导致结构承载能力下降. 本文对典型的非线性隔振器高静低动设计方法、动力学建模、动力学分析进行了详细的综述, 阐明不同机理下呈现的恢复力本构和准零刚度设计准则, 在面向航空航天、精密加工、汽车船舶等领域的不同需求时, 能够从动力学特征上进行选型; 另外, 关注到基于仿生和超结构的隔振和消振设计方法, 在非线性恢复力本构的力学机理解释和调控上产生了新的问题和挑战, 引发出变刚度、大变形动力学分析及其控制新方法、新策略和实验新技术的研究; 最后, 随着结构零部件向着轻质化和柔性化的方向发展, 运动部件末端的隔振效果受限于部件的柔性, 即使通过耦合多层准零刚度结构也难以实现被隔结构在空间上的快速定位, 关注到时滞控制的调幅调频机理, 本文对时滞抑振原理及设计方法进行讨论, 提供时滞抑制柔性低频振动成功案例, 为极端工况下的有效、简单、快速的主动隔振消振提供了可能性. 未来, 基于大数据时代的数据密集型研究范式, 非线性隔振和消振技术将面向复杂工况实现更精确、更智能的控制效果, 在精密仪器、航空航天等国家重大需求领域实现泛化应用.Abstract: Vibration problem is closely related to human daily life and the development of science and technology. Undersigned vibration would affect human health, also cause the failure of buildings, mechanical equipment and precision instruments. In the fields of aerospace, automotive engineering, marine engineering, large structure and precision instrument processing, elastic components or control devices are utilized to form effective vibration isolation environment. Effective vibration isolation can improve the safety, stability, controllability and comfort of human and equipment. However, the design method based on linear theory appears irreconcilable contradiction for applications. The stiffness of the vibration isolation structure reduces for wider band for vibration isolation, which results the decrease of loading capacity. In this paper, the high-static-low-dynamic design methods of nonlinear vibration isolators are reviewed in detail. Based on the dynamic modeling and analysis of nonlinearity induced by different mechanisms, the quasi-zero stiffness design criteria are presented, which provides the selection principle of the kind of isolator in aerospace, precision machining, automobile and ship. Then, attentions are paid on the design methods of bionics and metastructure for vibration suppression, which causes new problems and challenges in the explanation on mechanical bionic mechanism and regulation on the nonlinear restoring force constitutive. The studies on new methods, strategies and experimental techniques are introduced. Finally, faced to the development of light-weight and flexibility of structures, the vibration isolation effect is limited by the flexibility of parts. Even through coupling multi-layer quasi-zero-stiffness structures are assembled, it is difficult to realize the rapid positioning of the isolated structure in space. Considering the amplitude and frequency modulation by time delay, different design methods of vibration suppression with time delay are proposed. Successful cases of time-delayed suppression of flexible low-frequency vibration are given, which provides a possibility for effective, simple and rapid active vibration isolation and vibration elimination under extreme working conditions. In the future, based on the new analysis method according to data-driven, the nonlinear vibration isolation and suppression technology would realize more accurate and intelligent control effect in complex working conditions.
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图 2 几类三弹簧设计准零刚度隔振器原理图(Lee & Goverdovski 2012)
图 3 几类三弹簧设计准零刚度非线性隔振器的结构简图及拓展设计. (a)通过水平方向弹簧预压实现负刚度 (Kovacic et al. 2008), (b)水平方向弹簧串联连杆增大负刚度效果(Le & Ahn 2013), (c)屈曲梁实现负刚度 (Liu XT et al. 2013), (d)利用菱形机构实现负刚度(Sun & Jing 2015), (e)考虑串并联阻尼的三弹簧隔振器(Liu CR et al. 2020a), (f) 增加附加小球的三弹簧准零刚度隔振器(Liu CR et al. 2021a), (g)具有三弹簧设计二级隔振模型 (Lu et al. 2017), (h)三弹簧设计的径向扭转准零刚度隔振器(Miyasato et al. 2021)
图 4 三弹簧隔振器的高静低动特性应用. (a)三弹簧准零刚度隔振器作为桥梁支座(Bouna et al. 2020), (b)三弹簧隔振器作为汽车悬挂系统(Suman et al. 2021), (c)三弹簧隔振器作为转子系统弹性支座(Abbasi et al. 2021)
图 5 典型的复合型三弹簧准零刚度隔振器. (a) 嵌套型三弹簧准零刚度隔振器及其宽幅零刚度特性(Wang K et al. 2020), (b) 连杆嵌套三弹簧准零刚度隔振器及其宽幅零刚度特性(Yang T et al. 2021a), (c) 空间多组斜弹簧布置的准零刚度隔振器(徐道临 等 2014), (d)四弹簧准零刚度隔振器(Gatti 2020), (e)多组斜弹簧准零刚度隔振器(Zhao et al. 2020, 2021), (f)斜向连杆框架型负刚度隔振设备(张也 等 2018)
图 6 多连杆多弹簧单方向/多方向准零刚度隔振器.(a)负刚度的产生(彭献 等 1997), (b)装配水平和竖直两方向弹簧的菱形机构(陈然 2019), (c)剪刀型隔振平台(Sun XT et al. 2014a), (d)装配多组弹性元件的剪刀型隔振平台(Zhang & Zhang 2016), (e)菱形机构与竖向正刚度并联形成的准零刚度隔振平台(姚国 等 2020), (f)菱形机构并联竖向弹簧、阻尼器和控制器形成隔振平台(Wang Y et al. 2021), (g)连杆和弹簧串并联形成非线性隔振器(Gatti 2021), (h)利用菱形机构形成六自由度稳定平台(Wang X et al. 2020)
图 7 几类凸轮−滚子型的分段准零刚度隔振器. (a)凸轮滚子形成准零刚度隔振器(王毅 等 2015, 周加喜 等 2015, Zhou JX et al. 2015a), (b)融合连杆机构和凸轮滚子的准零刚度隔振器(Sun XT et al. 2018b), (c)串联气动弹簧的凸轮滚子分段准零刚度隔振器(Vo et al. 2021, Vo & Le 2022), (d)具有可设计接触曲面的凸轮滚子隔振器(Li M et al. 2020), (e)三弹簧链杆融合凸轮滚子的准零刚度隔振器(Zhang YL et al. 2021), (f)凸轮约束曲面的高阶准零刚度隔振设计方法(Wang & Wang, 2022), (g)不倒翁原理的滚轮隔振结构(Yan B et al. 2022b), (h)多个凸轮构成的变刚度隔振器及其阶梯式高静低动特性(Ye et al. 2020), (i)水平方向布置耗散元件的准零刚度隔振器(Donmez et al. 2020)
图 8 凸轮滚子扭转方向准零刚度隔振装置. (a)凸轮滚子设计的扭转隔振器(Zhou JX et al. 2015b), (b) 融合叉形结构和凸轮滚子两方向隔振平台(孙秀婷和富展展 2018), (c)凸轮滚子摆振−颠振两方向隔振平台(Ye et al. 2021)
图 9 利用磁效应实现非线性隔振器. (a) 通过磁场实现低频隔振器(Carrella et al. 2008), (b)电磁场设计准零刚度隔振器(Chen et al. 2021), (c)磁铁连杆串联设计的准零刚度隔振平台(Xu DL et al. 2013), (d)两对磁铁形成负刚度特性原理图(Wu W et al. 2014), (e)磁铁并联连续梁形成准零刚度隔振器(Sun XT et al. 2019a), (f)环形磁铁套筒装配形成准零刚度隔振器(Xie et al. 2022)
图 10 磁体负刚度多方向高静低动隔振平台. (a)应用于婴儿转运车的磁力准零刚度隔振平台(Wang Q et al. 2020), (b)利用磁力负刚度构建的Stewart隔振平台(Zheng et al. 2018), (c)应用于空间天线的电磁双稳态隔振器(Yan B et al. 2022a), (d)电磁弹簧与三弹簧准零刚度构型混合的隔振平台(Jiang et al. 2020)
图 11 仿动物单自由度非线性隔振器. (a)仿腿部构型的隔振元胞(Sun XT et al. 2018a), (b)仿青蛙腿部的隔振单元(Zeng et al. 2021), (c)仿猫腿构型的隔振器连杆仿生机理(Yan G et al. 2020a), (d)仿猫爪构型隔振器力学模型(Yan G et al. 2022c), (e)仿蟑螂身体和腿部的多连杆隔振器(Ling P et al. 2022), (f)仿脊椎的多层串联菱形连杆非线性隔振器(Jin GX et al. 2022).
图 12 仿禽类颈部的多层隔振器仿生机理及力学原理图. (a)仿一类鸟脖子的多层准零刚度隔振器(Deng TC et al. 2020), (b)仿脖子的多层隔振结构及标准单元结构图(Sun XT et al. 2021, Sun XT et al. 2022)
图 13 Miura折纸和Kresling折纸结构作为隔振器的结构设计和准零刚度机理. (a)Miura-Ori单胞结构及其恢复力本构(Sadeghi & Li SY 2017), (b) Miura-Ori等效多连杆结构机理及变刚度特性(Han HS et al. 2021), (c)Miura-Ori的等效空间桁架结构及准零刚度特性(Ye et al. 2022), (d) Miura-Ori串联形成管状射流折纸结构作为隔振器的原理和实验图(Sadeghi & Li SY 2019), (e) Tachi-Miura折纸串并联形成的隔振器(Liu SW et al. 2021), (f) Kresling折纸结构及其等效变形框架(Ishida et al. 2017a), (g)两级Kresling隔振结构(Li Z et al. 2020)
图 14 折纸超材料吸振隔振结构. (a)可调谐、可编程的Miura折纸结构的材料及其等效动力学系统(Phanisri et al. 2018), (b)用Kresling折纸结构实现变刚度的局部振子(Zhang MK et al. 2021), (c) Kresling折纸结构实现变刚度扭转振动的局部振子(Xu ZL et al. 2021)
图 15 基于折纸概念的柔性隔振器. (a) Z型折型柔性梁形成卫星动量轮多方向隔振结构(Yan G et al. 2020b), (b) 双稳屈曲梁隔振微结构(Dalela et al. 2022), (c)可编程隔振超材料单胞构造及堆叠(Zhang Q et al. 2021)
图 16 利用时滞的隔振器和隔振平台. (a)考虑时滞的主动LGQ控制的隔振结构 (Weng et al. 2011), (b)时滞反馈控制非线性隔振结构(Zhou JX et al. 2012, Li YL et al. 2011, 2013), (c)具有两层独立时滞隔振系统(Nia & Sipahi 2013), (d)两方向时滞控制隔振器均匀布置形成六自由度主动隔振平台(Sun & Kim 2012, 2013)
图 17 时滞反馈控制下的准零刚度隔振器的力学简图和幅频变化. (a)时滞线性反馈控制下的连杆弹簧准零刚度隔振器及时滞的抑振效果(Sun XT et al. 2014b), (b)时滞非线性反馈控制下的凸轮滚子准零刚度隔振器及不同控制策略和时滞下的幅频曲线的变化(Cheng et al. 2016), (c)时滞控制准零刚度隔振器在谐波和随机激励下的稳定性和共振幅值(Yang & Cao, 2017, 2018), (d)时滞线性反馈下的双层隔振器及幅值随时滞的变化(Zhang HP et al. 2020)
图 18 时滞反馈吸振器. (a)单自由度主系统的时滞吸振设计(Vyhlídal et al. 2019), (b)平面运动的主系统时滞吸振设计(Sika et al. 2021), (c)时滞反馈控制吸振器(Wang & Xu 2019), (d)时滞反馈控制非线性隔振系统(Wang F et al. 2021)
图 19 时滞反馈吸振器对多自由度线性/非线性主系统的吸振效果. (a)单个时滞吸振器的吸振机理和效果(Jenkins & Olgac 2019), (b)时滞吸振器形成吸−隔复合周期结构(Wang F et al. 2022), (c)多自由度非线性系统时滞吸振器结构图(Meng H et al. 2021a)
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