力学学报, 2019, 51(2): 354-363 DOI: 10.6052/0459-1879-18-266

工程振动非线性控制专题

基于混杂双稳定层合板的准零刚度隔振装置 1)

李昊2), 赵发刚, 周徐斌

上海卫星工程研究所,上海 200240

A QUASI-ZERO STIFFNESS VIBRATION ISOLATOR BASED ON HYBRID BISTABLE COMPOSITE LAMINATE 1)

Li Hao2), Zhao Fagang, Zhou Xubin

Shanghai Institute of Satellite Engineering, Shanghai 200240, China

收稿日期: 2018-08-10   接受日期: 2019-01-21   网络出版日期: 2019-03-18

基金资助: 国家自然科学基金资助项目.  51605299

Received: 2018-08-10   Accepted: 2019-01-21   Online: 2019-03-18

作者简介 About authors

2)李昊,工程师,主要研究方向:非线性隔振系统.E-mail:hithaoli@126.com

摘要

准零刚度隔振装置(quasi-zero stiffness,QZS)在其平衡位置处的刚度接近于零,能够有效地隔离加速度幅值较低的微振动.因此,准零刚度隔振装置在卫星等航天器结构的微振动抑制领域有较好的应用前景.准零刚度隔振装置通常由正刚度部件及负刚度部件并联而成.在众多准零刚度隔振装置概念中,负刚度部件通常需要多个弹性部件及特定约束边界形成负刚度特性,导致准零刚度隔振装置的整体质量及体积相对较大.然而,航天器结构对隔振装置的质量特性及安装空间提出较高要求,因此需开发新型准零刚度隔振装置,降低隔振装置的质量及体积以满足航天器结构的使用要求.本文提出了一种基于混杂双稳定复合材料层合板的准零刚度隔振装置.通过利用混杂双稳定复合材料层合板自身的负刚度特性,降低了准零刚度隔振装置的结构复杂程度.本文对提出的准零刚度隔振装置的力学原理进行说明,对其隔振效果进行了仿真分析,并进行了隔振效果验证试验.隔振试验表明,准零刚度隔振装置的振动传递率曲线不再具有峰值,其实际振动传递率低于具有相同正刚度的线性隔振系统.基于试验及仿真分析结果,本文对隔振装置隔振性能的影响因素进行了分析讨论.分析结果显示,隔震装置中线性弹簧刚度与双稳定层合板负刚度之间的差异以及微小装配误差将导致隔振装置的隔振效果出现降低.

关键词: 准零刚度 ; 隔振装置 ; 负刚度 ; 双稳定层合板

Abstract

A quasi-zero stiffness (QZS) vibration isolator has zero stiffness at its equilibrium position, and is efficient in isolating the low amplitude micro vibrations. Therefore, the QZS vibration isolators have excellent potential in applying on the micro vibration isolation of space structures, e.g. satellite structures. Normally, a QZS vibration isolator composes of a positive stiffness element and a negative stiffness element. In many concepts of QZS vibration isolators, the negative stiffness elements are inefficient in weight and volume, because they are normally combined by several components, and external restrains or forces are needed to stress certain components. As a result, the volume and weight of the QZS vibration isolators are unacceptable in some applications, such as space technology and aviation technology. In order to improve the weight and volume of QZS vibration isolators, in this study a novel QZS vibration isolator is put forward by applying the bistable composite laminates as negative stiffness element. The system of this QZS vibration isolator is greatly simplified because of the inherent negative stiffness of bistable laminates. The principle of this novel QZS vibration isolator is illustrated, and the performance of which is analyzed by finite element method. A prototype of the novel QZS vibration isolator is fabricated and is tested in experiment. Experimental results indicate that the acceleration transmission rate of the proposed QZS vibration isolator is much improved comparing with a linear spring isolator. Nevertheless, the tested results of the isolator are not as good as predicted via the finite element analysis. The in practice performance of the proposed QZS vibration isolator is analyzed and discussed. Finite element analysis illustrates that both manufacturing error and assembly error have significant negative influence on the practical performance of the proposed QZS vibration isolator, and the robustness of the isolator should be improved in the future work.

Keywords: quasi-zero stiffness ; vibration isolator ; negative stiffness ; bistable laminate

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本文引用格式

李昊, 赵发刚, 周徐斌. 基于混杂双稳定层合板的准零刚度隔振装置 1). 力学学报[J], 2019, 51(2): 354-363 DOI:10.6052/0459-1879-18-266

Li Hao, Zhao Fagang, Zhou Xubin. A QUASI-ZERO STIFFNESS VIBRATION ISOLATOR BASED ON HYBRID BISTABLE COMPOSITE LAMINATE 1). Chinese Journal of Theoretical and Applied Mechanics[J], 2019, 51(2): 354-363 DOI:10.6052/0459-1879-18-266

引 言

线性被动隔振装置具有结构简单,可靠性高的优点.然而,线性被动隔振装置只有在其固有频率远低于振动频率时才能有效工作.当振动的频率低于线性隔振装置固有频率的$\sqrt 2$倍时,线性隔振装置却将振动能量进一步放大.因此,线性隔振系统通常无法满足低频或超低频的隔振需求.为实现从低频到高频的全频段隔振,非线性隔振装置的概念得到广泛关注,并已应用于工程隔振领域[1-12].其中,准零刚度隔振装置由于具有高静刚度低动刚度的特性受到广泛关注.准零刚度隔振装置的高静刚度特性使其具有较大的静承载能力,而低动刚度特性使其对于低频及超低频振动具有较好的隔振效果[12-20].目前,准零刚度隔振装置已经应用于对振动环境有高要求的自然科学领域,如零重力环境模拟[21]及高精度仪器设备的微振动隔离等[22-23].准零刚度隔振装置通常由正刚度部件及负刚度部件并联而成.在过去几十年研究中,国内外学者提出多种形式的准零刚度隔振装置,代表性的几种准零刚度隔振装置原理见图1所示[16, 19].经过多年研究,多种形式的准零刚度隔振装置基本理论已有丰硕研究成果[9,12, 14-15, 17-18, 24].

图1

图1   不同形式准零刚度隔振装置示意图[16]

Fig.1   Sketch maps of representative QZS vibration isolators[16]


图1中所示的准零刚度隔振装置,其特点是需要对其负刚度部件施加特定的力及约束以实现负刚度特性,因此其负刚度部件难以小型化,导致准零刚度隔振装置的重量及体积通常较大.然而,在一些特殊的应用场景,如航天器结构中,其结构重量及体积通常被严格控制.因此,针对准零刚度隔振装置的小型化及轻量化需求,亟需开发新型负刚度部件.

本文提出了一种基于混杂双稳定复合材料层合板的新型准零刚度隔振装置.混杂双稳定复合材料层合板具有两种稳定构型及一种不稳定的中间状态,即马鞍形构型[25-27].当双稳定复合材料层合板在外在约束下处于马鞍形构型时,整体结构刚度为负.Lu等[11]利用双稳定复合材料层合板的负刚度特性提出了一种非线性隔振装置,但并没有对隔振装置中的正负刚度部件的刚度值进行匹配,隔振装置的固有频率在双稳定复合材料层合板作用下出现降低,但其振动传递率仍然存在明显峰值.与已有研究不同,本文利用双稳定复合材料层合板作为负刚度部件,通过对正负刚度元件的刚度进行匹配设计,实现了隔振装置的准零刚度特性,即隔振装置在平衡位置处的刚度等于零.由于具有准零刚度特性,本文所提出的隔振装置在微振动激励下,其振动传递率理论上将不再具有峰值,能够实现近全频段的高效隔振.本文对新型准零刚度隔振装置的原理进行分析研究,并利用有限元方法预测了其隔振效果;通过试验测试了准零刚度隔振装置的振动传递率,分析并讨论了制造误差及装配误差对其隔振效率影响.本文第1节给出了基于双稳定层合板的准零刚度隔振装置详细设计原理,第2节对准零刚度隔振装置的隔振效果进行了分析,第3节对准零刚度隔振器的隔振效果进行了试验研究,并分析讨论了制造误差及安装误差对其隔振效率的影响.

1 基于混杂双稳定层合板的准零刚度隔振装置设计

本文采用铺层为[0/Al/90]的混杂双稳定层合板构建准零刚度隔振装置.当[0/Al/90]的混杂非对称层合板的尺寸及铺层厚度满足一定条件时,在其内部残余热应力作用下,层合板具有两种稳定的圆柱形构型[28-31].正方形[0/Al/90]双稳定层合板的典型稳定构型见图2所示.将双稳定层合板中间点固定,并在其4个角点施加垂直方向的载荷,如图2所示,当施加的载荷超过一个临界值后,层合板将从一种稳定构型跳变为另一种稳定构型.混杂双稳定层合板在构型转变过程中的角点力-位移曲线及层合板的应变能曲线见图3所示.混杂双稳定层合板的应变能曲线具有两个局部势能井,验证了其双稳定特性;力位移曲线说明混杂双稳定层合板从一个势能井进入另一个势能井的过程中,显示出负刚度特性.

图2

图2   正方形双稳定层合板稳定构型示意图

Fig.2   Sketch maps of representative QZS vibration isolators


图3

图3   双稳定层合板的典型应变能及力-位移曲线

Fig.3   Classical strain energy curve and load-displacement curves of a bistable laminate


混杂双稳定层合板具有结构简单、质量轻及体积小的优点.基于混杂双稳定层合板的准零刚度隔振装置的原理见图4所示.混杂双稳定层合板与线性弹簧并联连接,层合板的四个角点通过连杆分别与隔振装置的输出端连接,层合板的中心点通过线性弹簧与隔振装置的输出端连接.当线性弹簧的刚度大于一个临界值时,混杂双稳定层合板在连杆及线性弹簧的约束下,处于两个稳定构型的中间状态,即具有负刚度的不稳定马鞍形构型.通过调整线性弹簧的刚度,使其等于混杂双稳定层合板的负刚度,则隔振装置在平衡位置时整体刚度为零.

图4

图4   基于混杂双稳定层合板的准零刚度隔振装置原理图

Fig.4   Principle of the quasi-stiffness vibration isolator based on bistable laminate


图4中的基本原理,基于混杂双稳定层合板的准零刚度隔振装置原理样机设计见图5所示.双稳定层合板通过四根连杆与隔振装置上平台连接,四根连杆的两端分别装有十字铰,使得连杆仅约束双稳定层合板角点的竖向位移,避免连杆对双稳定层合板角点转动自由度的约束.双稳定层合板的中心点通过螺杆与红色线性弹簧连接.为便于线性弹簧的预压紧及连接,将两个线性弹簧预压紧后装入与上平台固连的柱形空腔中,线性弹簧预压紧后避免了安装间隙对隔振装置准零刚度特性的影响.图5所示隔振装置中,正刚度部件的刚度为两个线性弹簧的正刚度之和.

图5

图5   基于混杂双稳定层合板的准零刚度隔振装置原理样机设计

Fig.5   Prototype design of the quasi-zero stiffness vibration isolator based on hybrid bistable composite laminate


2 隔振特性分析

采用商用有限元软件Abaqus建立了准零刚度隔振装置有限元模型.混杂双稳定层合板上下表面为单向碳纤维增强环氧树脂基复合材料,中间层为2A12铝合金.单向碳纤维增强复合材料 (CCF300/ 5428)参数为:$E_{11}=145$ GPa,$E_{22}=9.75$ GPa,${\rm G}_{12}=5.69$ GPa,$\nu _{12} = 0.312$,$\alpha _{11 }= 0.4\times 10^{-6}$°C-1,$\alpha _{22} =25\times 10^{-6}$°C-1,$t=0.125$ mm,固化温度$T= 140°C;铝合金2A12T4参数为:$E=70$ GPa,$\nu _{12} =0.3$,$\alpha _{11}=23.3\times 10^{-6}$°C-1.

准零刚度隔振器有限元模型见图6所示. 混杂双稳定层合板尺寸为80 mm×80 mm,铺层为[$0_{t = 0.25~{\rm mm}}/{\rm Al}_{t = 0.2~{\rm mm}}/90_{t = 0.25~{\rm mm}}$],层合板采用壳单元S4R(4节点减缩积分壳单元)建模;隔振装置上平台设置为刚体,层合板四个角点采用MPC-LINK约束与上平台连接,层合板中心点采用弹簧单元与上平台中心点连接.

图6

图6   准零刚度隔振装置有限元模型

Fig.6   Finite element model of QZS vibration isolator


约束上平台的位移,在双稳定层合板中心点施加垂直方向的位移载荷,隔振装置整体的力位移曲线预测结果见图7所示,其中线性弹簧刚度分别为13 kN/m,16 kN/m及20 kN/m.有限元分析结果显示,在混杂双稳定层合板的作用下,隔振装置整体为非线性结构,其整体刚度在平衡位置处达到最小值.当双稳定层合板的尺寸及铺层确定后,可通过调整线性弹簧的刚度实现隔振装置的准零刚度特性.理论上,当实现准零刚度特性时,线性弹簧的临界刚度值应等于混杂双稳定层合板的最小负刚度绝对值.

图7

图7   准零刚度隔振装置力位移曲线,其中混杂双稳定层合板的铺层为[$0_{ 0.25~{\rm mm}}/{\rm Al}_{ 0.2~{\rm mm}}/90_{ 0.25~{\rm mm}}$],k为线性弹簧的总刚度

Fig.7   Load-displacement curves of the vibration isolator, the lay-up of the bistable laminate is [$0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{ 0.25~{\rm mm}}$], k is the stiffness of linear spring


利用有限元模型可计算出复合材料铺层和铝合金铺层厚度对混杂双稳定层合板最小负刚度的影响规律.通过计算出不同铺层厚度情况下双稳定层合板的力-位移曲线,再通过求导计算其刚度,得到混杂双稳定层合板的最小负刚度.理想情况下,准零刚度隔振装置中线性弹簧的刚度等于混杂双稳定层合板最小负刚度的绝对值.准零刚度隔振装置中线性弹簧的刚度匹配值随混杂双稳定复合材料层合板复合材料铺层厚度及铝合金铺层厚度的变化规律见图8所示.有限元分析结果显示,随着双稳定复合材料层合板铺层厚度的变化,匹配的线性弹簧刚度呈非线性变化,并存在一个最大值.分析结果表明,准零刚度隔振器的静刚度特性可通过调整混杂双稳定复合材料层合板的厚度在较宽范围内变化.

图8

图8   准零刚度隔振装置中线性弹簧刚度随混杂双稳定复合材料层合板铺层厚度变化规律

Fig.8   Spring stiffnesses for the quasi-stiffness vibration isolators applying different bistable laminates


为验证基于混杂双稳定复合材料层合板的准零刚度隔振装置的隔振效果,利用有限元方法分析了隔振装置在不同频率下的振动传递率.有限元模型见图6所示,其中混杂双稳定复合材料层合板的尺寸及铺层为80 mm×80 mm,[$0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{0.25~{\rm mm}}$],其最小负刚度为$-16.295$ kN/m,线性弹簧刚度为16.295 kN/m. 采用有限元软件Abaqus的隐式动力学分析方法分析隔振装置模型在不同幅度简谐激励下的响应.分析中,在混杂双稳定层合板中线点输入竖直方向简谐激励,并输出模型顶部刚性平台的加速度曲线.计算过程中设置复合材料的质量阻尼系数为100.准零刚度隔振装置的振动传递率预测结果见图9所示,其中振动传递率为输出加速度最大值与激励加速度最大值的比值.计算结果显示,利用混杂双稳定复合材料层合板作为负刚度部件,准零刚度隔振装置的振动传递率在较低频率振动的激励下便迅速下降,并随着激励频率的增加稳定在较低值.分析结果说明图5中的准零刚度隔振装置无明显共振点,在从低频到高频范围内都能够有效地实现微振动隔离.图5中准零刚度隔振装置的隔振频率范围与线性弹簧的隔振频率范围对比见表1所示,准零刚度隔振装置的隔振频率范围明显大于刚度为16.295 kN/m线性弹簧的隔振频率范围.

表1   准零刚度隔振装置与线性弹簧隔振装置隔振频率范围对比

Table 1  Valid working frequency range of linear and QZS vibration isolators

Excitation acceleration and isolated mass10 mg 0.2 kg 30 mg 0.2 kg30 mg 0.6 kg
linear vibration isolator K = 16.295 kN/m> 64.3 Hz37.2 Hz
quasi-zero stiffness vibration isolator> 5.6 Hz >8.0 Hz> 6.8 Hz

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图9

图9   准零刚度隔振装置振动传递率预测结果(混杂双稳定复合材料层合板尺寸及铺层为80 mm×80 mm, [$0_{0.25~{\rm mm}}/{\rm Al}_{\rm 0.2~{\rm mm}}/90_{0.25~{\rm mm}}$]

Fig.9   Predicted acceleration transmission rates of a QZS vibration isolator, a 80 mm×80 mm, [$0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{0.25~{\rm mm}}$] bistable laminate is applied in the isolator


3 试验验证

为验证所设计的准零刚度隔振装置实际隔振效果,制备了一个隔振器原理样机,见图10所示.试验中,采用扫频试验测量准零刚度隔振装置在不同频率下的振动传递率.试验中,首先测量了隔振装置中混杂双稳定复合材料层合板的力位移曲线.将隔振装置中的线性弹簧拆除,并将层合板的中心点与力学试验机相连,通过力学试验机对层合板中心点施加位移载荷,并实时测量加载点的反力.混杂双稳定复合材料层合板的力-位移曲线测量结果见图11所示.测量结果显示,80 mm×80 mm,$[0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{0.25~{\rm mm}}]$双稳定层合板的最小负刚度值为$-19.18$kN/m,小于有限元模型的预测值.试验测量值与有限元预测值之间的差异导致原因可能包括:复合材料的材料性能参数误差、层合板固化过程中的固化温度控制误差以及铺层厚度的误差.为实现准零刚度特性,隔振装置中的线性弹簧的匹配刚度应为19.18 kN/m.实际试验中难以对线性弹簧刚度进行精确的控制,隔振装置中采用的线性弹簧实际刚度为24 kN/m.

图10

图10   基于混杂双稳定复合材料层合板的准零刚度隔振装置原理样机(混杂复合层合板尺寸及铺层分别为80 mm×80 mm,$[0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{0.25~{\rm mm}}]$

Fig.10   Prototype of a quasi-stiffness vibration isolator, the dimension and lay-up of the bistable laminate are 80 mm×80 mm,$[0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{0.25~{\rm mm}}]$


图11

图11   80 mm×80 mm,[$0_{0.25~{\rm mm}}/{\rm Al}_{\rm 0.2~{\rm mm}}/90_{\rm 0.25~{\rm mm}}$]混杂双稳定复合材料层合板的力-位移曲线

Fig.11   Measured load-displacement curve of the 80 mm×\\80 mm,[$0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{0.25~{\rm mm}}$] bistable laminate


准零刚度隔振装置振动传递率测量扫频试验设置见图12所示.试验中,采用振动台对隔振装置进行正弦激励,扫频速度为2 oct/min,振动台激励加速度峰值为30 mg并保持不变.为与准零刚度隔振装置进行对比,将隔振装置中的混杂双稳定层合板去除,仅利用其线性弹簧作为隔振部件,进行了二次扫频试验.扫频试验结果见图13. 所示准零刚度隔振装置的最大振动传递率为5 dB,而线性弹簧的在共振峰的最大振动传递率达到13.6 dB.准零刚度隔振装置的起始隔振频率为39 Hz,线性弹簧的起始隔振频率为44 Hz.试验结果显示,利用混杂双稳定层合板作为负刚度部件后,准零刚度隔振装置的隔振效果明显优于线性弹簧.

图12

图12   扫频试验设置

Fig.12   Sweeping frequency experiment settlement


图13

图13   线性弹簧与准零刚度隔振装置的扫频试验结果对比

Fig.13   Sweeping frequency experiment results of the linear spring and the QZS vibration isolator


4 分析讨论

试验中准零刚度隔振装置的实际隔振效果虽优于线性弹簧,但与有限元模型的分析结果(理想状态)相比有一定差距.本节对隔振装置隔振效果的两种影响因素进行分析,分别为线性弹簧的刚度误差及隔振装置的装配误差.试验中,线性弹簧的刚度为24 kN/m,大于理想状态下的刚度19.18 kN/m.为分析线性弹簧刚度误差的影响,在有限元模型中设置弹簧单元的刚度分别大于理想刚度5%及10%情况下隔振装置的振动传递率,分析结果见图14所示.分析结果显示,线性弹簧的刚度误差对隔振装置的振动传递率具有明显影响.当线性弹簧刚度大于理想刚度5%时,隔振装置的振动传递率便出现明显峰值,并且振动传递率的下降率出现降低的现象.当线性弹簧的刚度误差增大至10%后,隔振装置的振动传递率进一步上升,其隔振效果越接近于线性隔振系统.

图14

图14   线性弹簧刚度误差对准零刚度隔振装置影响分析结果(采用80 mm×80 mm, [$0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{0.25~{\rm mm}}$]混杂双稳定层合板,激励加速度峰值为30 mg,被隔质量为0.6 kg)

Fig.14   Predicted influence of spring stiffness error on the performance of QZS vibration isolator, the 80 mm×80 mm, [$0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{0.25~{\rm mm}}$] bistable laminate is applied in the isolator, the excitation acceleration magnitude is 30 mg, and the isolated mass is 0.6 kg


准零刚度隔振系统在平衡位置处的刚度为零.在试验中,为了消除平衡被隔质量重力的影响,需通过调整混杂双稳定层合板中心点与线性弹簧之间的距离,使得弹簧在被隔质量的重力压缩后,弹簧对混杂双稳定层合板中心点的竖向约束力恰好为零.试验中,实际上难以使得准零刚度隔振装置在静止状态下正好处于刚度为0的平衡位置.为分析装配误差对准零刚度隔振装置的影响,假设静止状态下装配误差平衡位置处弹簧的弹力与被隔物体的重力差值为0.02 N,有限元分析显示对应的装配误差为0.144 mm.装配误差的影响分析结果见图 15所示,在0.144 mm的装配误差影响下,准零刚度隔振装置的振动传递率出现明显提高.当同时考虑0.144 mm的装配误差及5%的弹簧刚度误差时,分析结果显示准零刚度隔振器的弹簧误差及装配误差对其隔振效果的不利影响会出现累加现象,振动传递率进一步上升,并且在11 Hz处出现了一个28 dB的峰值.考虑弹簧刚度误差及装配误差后准零刚度隔振装置的隔振性能统计见表2.

表2   考虑弹簧刚度误差及装配误差后准零刚度隔振装置的隔振性能

Table 2  Predicted major characteristics of QZS vibration isolator with spring stiffness error and assembly error

ErrorMaximum vibration transmission rateValid vibration isolating frequency range
0%15.08dB> 5.6 Hz
5 % error of spring stiffness19.97 dB> 13 Hz
10% error of spring stiffness26.16db> 21 Hz
0.144 mm assembly error(the preload of the linear spring is 0.02N smaller than the gravity of isolated mass)20.46 dB> 11 Hz
5 % error of spring stiffness plus 0.144 mm assembly error28.22 dB> 17 Hz

新窗口打开| 下载CSV


图15

图15   装配误差对准零刚度隔振装置影响分析结果(采用\\80 mm×80 mm, [$0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{0.25~{\rm mm}}$]混杂双稳定层合板,激励加速度峰值为30 mg,被隔质量为0.6 kg)

Fig.15   Predicted influence of assemble error on the performance of QZS vibration isolator, the 80 mm×80 mm, [$0_{0.25~{\rm mm}}/{\rm Al}_{0.2~{\rm mm}}/90_{0.25~{\rm mm}}$] bistable laminate is applied in the isolator, the excitation acceleration magnitude is 30 mg, and the isolated mass is 0.6 kg


有限元分析结果显示理想情况下基于混杂双稳定层合板的准零刚度隔振装置对低频至高频的微振动都具有很好的隔振效果.隔振试验显示,虽然准零刚度隔振装置样机的隔振效率优于线性弹簧隔振器,但远达不到理想状态下的设计目标.在实际制备过程中,线性弹簧的刚度误差及装配误差难以完全消除,因此仍需要进行深入的优化分析研究,以提升隔振装置的实际隔振效果.由于零刚度往往为理想情况下正负刚度部件刚度精确平衡的结果,其制备误差导致的隔振性能下降是各种形式准零刚度隔振装置所面临的共同难题..[7].混杂双稳定层合板作为负刚度部件,在结构简单的前提下,却同时具有多个优化参数,如层合板的铺层厚度、材料属性及材料方向等.通过多个参数的系统优化,实现其负刚度特性的优化设计,进而降低制造误差对准零刚度隔振装置隔振效果的不利影响.

5 结 论

本文研究了基于混杂双稳定层合板的准零刚度隔振装置.由于混杂双稳定层合在构型转变的过程中具有负刚度特性,准零刚度隔振装置利用混杂双稳定层合板作为负刚度部件,与线性弹簧并联后实现了准零刚度特性.有限元分析显示,所提出的准零刚度隔振装置,其振动传递率在小于10 Hz的较低频率时便迅速下降至较低值,实现了从低频到高频的近全频段高效隔振.准零刚度隔振装置样机的振动传递率试验显示,其振动传递率小于具有相同正刚度的线性弹簧,但总体隔振效果与有限元分析结果相比不够理想.为分析隔振效果降低原因,利用有限元模型分析了样机制造过程中的误差对其隔振效果的影响,包括线性弹簧刚度误差及装配误差.有限元分析结果显示,线性弹簧的刚度误差及装备误差对隔振装置的隔振效果具有可叠加的不利影响.在弹簧刚度误差及装配误差影响下,隔振装置的振动传递率将出现峰值,并且有效隔振频率范围将减小.本文所提出的准零刚度隔振装置,通过利用混杂双稳定复合材料层合板作为负刚度部件,具有结构简单、重量轻及设计自由度大的优势,未来需通过对混杂双稳定复合材料层合板的负刚度特性进一步优化,以降低弹簧刚度误差及装配误差对其隔振效果的不利影响.

The authors have declared that no competing interests exist.
作者已声明无竞争性利益关系。

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Chinese Journal of Theoretical and Applied Mechanics, 2017,49(3):550-564(in Chinese))

DOI      URL    

工程中航空航天、船舶与海洋结构物及其上装备和精密仪器易受极端环境干扰和破坏,使得非线性隔振理论在近十年来迅猛发展;针对日益严峻的隔振和抗冲击等要求,工程师和科学家们已发展出各种不同的非线性隔振系统,包括主动、半主动、被动和复合隔振.利用非线性改善的被动隔振兼具传统被动隔振的鲁棒性和主动隔振的高效性成为振动控制领域的先进技术.本文主要综述了非线性隔振理论和应用的近十年进展,包括非线性隔振设计、建模、分析、仿真和实验.在隔振系统的构建中,既考虑了刚度非线性又考虑了阻尼非线性;动力学响应的研究中,既有确定性分析又有随机分析.首先提出了适用于非线性隔振系统改进的评价方式;其次综述了高静态低动态刚度隔振及其加强形式非线性阻尼加强和双层非线性隔振,混沌反控制技术、内共振影响、非线性能量阱应用等振动机制利用型隔振和非线性隔振功能材料.最后,对非线性隔振研究发展的热点和关键性问题进行了分析和展望.

Lu Z, Ynag T, J.Brennan M , et al.

Experimental investigation of a two-stage nonlinear vibration isolation system with high-static-low-dynamic stiffness

Journal of Applied Mechanics, 2017,84(021001):1-9

[本文引用: 1]

Zhang C, Ji C .

Shock isolation performance of a novel quasi-zero stiffness displacement restrictor

//Proc. 24th International Congress on Sound and Vibration, London, 7.23-7.27, 2017: 1-8

[本文引用: 3]

Alabuzhev P, Gritchin A, Kim L. Vibration Protecting and Mesauring System With Quasi-Zero Stiffness. New York: Hemisphere Publishing Co., 1989

Carrella A, Brennan MJ, Waters TP .

Optimization of a quasi-zero-stiffness isolator

Journal of Mechanical Science and Technology, 2007,21(6):946-949

DOI      URL     [本文引用: 1]

The frequency range over which a mount can isolate a mass from a vibrating base (or vice versa) is often limited by the mount stiffness required to support the weight of the mass. This compromise can be made more favourable by employing non-linear mounts with a softening spring characteristic such that small excursions about the static equilibrium position result in small dynamic spring forces and a correspondingly low natural frequency. This paper concerns the force-displacement characteristic of a so-called quasi-zero-stiffness (QZS) mechanism which is characterised by an appreciable static stiffness but very small (theoretically zero) dynamic stiffness.The mechanism studied comprises a vertical spring acting in parallel with two further springs which, when inclined at an appropriate angle to the vertical, produce a cancelling negative stiffness effect. Analysis of the system shows that a QZS characteristic can be obtained if the system parameters (angle of inclination and ratio of spring stiffnesses) are opportunely chosen. By introducing the additional criterion that the displacement of the system be largest without exceeding a desired (low) value of stiffness an optimal set of parameter values is derived. Under sufficiently large displacements the stiffness of the QZS mechanism can eventually exceed that of the simple mass-spring system and criteria for this detrimental scenario to arise are presented.

Robertson WS, Kidner MRF, Cazzolato BS .

Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation

Journal of Sound and Vibration, 2009,326(1-2):88-103

[本文引用: 1]

Niu F, Meng L, Wu W , et al.

Recent advances in quasi-zero-stiffness vibration isolation systems

Applied Mechanics and Materials, 2013, 397-400:295-303

DOI      URL     [本文引用: 3]

The quasi-zero-stiffness vibration isolation system has witnessed significant development due to the pressing demands for low frequency and ultra-low frequency vibration isolation. In this study, the isolation theory and the characteristic of the quasi-zero-stiffness vibration isolation system are illustrated. Based on its implementation mechanics, a comprehensive assessment of recent advances of the quasi-zero-stiffness vibration isolation system is presented. The future research directions are finally prospected.

Sun X, Xu J, Jing XJ , et al.

Beneficial performance of a quasi-zero-stiffness vibration isolator with time-delayed active control

International Journal of Mechanical Sciences, 2014,82:32-40

DOI      URL     [本文引用: 1]

61The model of quasi-zero-stiffness vibration isolator with active control is established.61Existence and stability of equilibria of the system are analyzed for engineering application.61Time delay induces beneficial on isolation for impact load and force excitation.61Time delay has significant effect on vibration isolation in the resonant region for base excitation.

Wang Y, Li S, Cheng C .

Investigation on a quasi-zero-stiffness vibration isolator under random excitation

Journal of Theoretical and Applied Mechianics, 2016,54(2):621-632

[本文引用: 1]

李东海, 赵寿根, 何玉金 .

正负刚度并联准零刚度隔振器的静态特性研究

强度与环境, 2017,44(6):31-36

DOI      URL     [本文引用: 1]

研究了一种准零刚度隔振器,这种隔振器由一对斜置弹簧和一个竖直弹簧组成。由斜置弹簧产生负刚度特性,与垂直弹簧产生的正刚度相互并联,从而产生准零刚度特性。本文研究了该准零刚度隔振器的力-位移特性和刚度-位移特性。通过理论推导,研究了该隔振器产生准零刚度特性的机理,从而获得了准零刚度隔振器的几何构型,在此基础上分析了准零刚度隔振器的静态稳定性。最后该隔振器的力-位移特性和刚度-位移特性的多项式表达,从而可以降低分析难度且具有足够的精度。为准零刚度隔振器的静力学设计奠定基础。

( Li Donghai, Zhao Shougen, He Yujin .

Study on static characteristic of a quasi-zero-stiffness vibration isolator of positive and negative stiffness in parallel

Structure & Environment Engineering, 2017,44(6):31-36 (in Chinese))

DOI      URL     [本文引用: 1]

研究了一种准零刚度隔振器,这种隔振器由一对斜置弹簧和一个竖直弹簧组成。由斜置弹簧产生负刚度特性,与垂直弹簧产生的正刚度相互并联,从而产生准零刚度特性。本文研究了该准零刚度隔振器的力-位移特性和刚度-位移特性。通过理论推导,研究了该隔振器产生准零刚度特性的机理,从而获得了准零刚度隔振器的几何构型,在此基础上分析了准零刚度隔振器的静态稳定性。最后该隔振器的力-位移特性和刚度-位移特性的多项式表达,从而可以降低分析难度且具有足够的精度。为准零刚度隔振器的静力学设计奠定基础。

孙秀婷, 富展展 .

一类新型多方向准零刚度隔振平台

力学季刊, 2018,39(2):249-257

URL     [本文引用: 1]

本文提出了一种新的多自由度非线性隔振平台.利用一组预压的三角机构和曲面边界同时实现了竖直-旋转多自由度上的负刚度特性,结合正刚度原件,实现竖直-旋转多自由度准零刚度特性.首先,文章基于平面问题建立竖直-旋转两自由度隔振平台的力学模型,确定结构参数与非线性刚度之间的关系.可以看到,通过设计预压弹性元件的结构参数可以同时实现两自由度的准零刚度特性.然后,利用谐波平衡法建立振动响应与频率之间的关系,确定有效的振动带隙的宽度,由此确定结构参数的最优取值.本文提出的隔振平台可以用于大型装备的隔振,也适用于微振动的工况,还可以作为教学的演示实验.

( Sun Xiuting, Fu Zhanzhan .

A novel multi-direction quasi-zero-stiffness vibration isolation platform

Chinese Quarterly of Mechanics, 2018,39(2):249-257(in Chinese))

URL     [本文引用: 1]

本文提出了一种新的多自由度非线性隔振平台.利用一组预压的三角机构和曲面边界同时实现了竖直-旋转多自由度上的负刚度特性,结合正刚度原件,实现竖直-旋转多自由度准零刚度特性.首先,文章基于平面问题建立竖直-旋转两自由度隔振平台的力学模型,确定结构参数与非线性刚度之间的关系.可以看到,通过设计预压弹性元件的结构参数可以同时实现两自由度的准零刚度特性.然后,利用谐波平衡法建立振动响应与频率之间的关系,确定有效的振动带隙的宽度,由此确定结构参数的最优取值.本文提出的隔振平台可以用于大型装备的隔振,也适用于微振动的工况,还可以作为教学的演示实验.

Denoyer K, Johnson C .

Recent achievements in vibration isolation systems for space launch and on-orbit applications

//Proc. 52nd International Astronautical Congress, Toulouse, France, 2001

[本文引用: 1]

Dankowski.

State of the art vibration isolation of large coordinate measuring machine with an adverse environment

//Proc. 2nd Euspen International Conference, Turin, Italy, 2001

[本文引用: 1]

Winterflood J . High performance vibration isolation for gravitational wave detection. University of Western Australia, 2001

[本文引用: 1]

朱光楠 . 基于准零刚度特性的变压器抗震设计与隔振研究.[硕士论文]. 哈尔滨: 哈尔滨工业大学, 2017

[本文引用: 1]

( Zhu Guangnan . Anti-seismic and vibration isolation study on a nonlinear system with quasi-zero stiffness. [Master Thesis]. Harbin: Harbin Institute of Technology, 2017 (in Chinese))

[本文引用: 1]

Dai F, Li H, Du S .

Cured shape and snap-through of bistable twisting hybrid [0/90/metal] T laminates

Composites Science and Technology, 2013,86(1):76-81

DOI      URL     [本文引用: 1]

This paper presents a bistable twisting CFRP-metal hybrid laminate which has an external isotropic metallic layer. Different from the pure unsymmetric CFRP laminate and the hybrid unsymmetric laminate with an inner metallic layer, the laminate presented can be transformed from one negative curvature to another negative curvature instead of from one negative curvature to another positive curvature. Their room temperature shapes can be a unique paraboloid shape, a twisted cylindrical shape, or a twisted cylindrical shape that can be snapped through to another twisted cylindrical shape. The cured shape of the hybrid laminate is studied using analytical, finite element and experimental techniques. The investigation is focused on the hybrid laminate with lay-up of [0/90/metal] T, and shows that the principal direction of cured curvature is 45deg. The predicted cured shape and the snap-through loads agree well with experimental results. [All rights reserved Elsevier].

Shaw A, Neild S, Wagg D , et al.

A nonlinear spring mechanism incorporating a bistable composite plate for vibration isolation

Journal of Sound and Vibration, 2013,332(24):6265-6275

DOI      URL    

The High Static Low Dynamic Stiffness (HSLDS) concept is a design strategy for a nonlinear anti-vibration mount that seeks to increase isolation by lowering the natural frequency of the mount whilst maintaining the same static load bearing capacity. It has previously been proposed that an HSLDS mount could be implemented by connecting linear springs in parallel with the transverse flexure of a composite bistable plate — a plate that has two stable shapes between which it may snap. Using a bistable plate in this way will lead to lightweight and efficient designs of HSLDS mounts. This paper experimentally demonstrates the feasibility of this idea. Firstly, the quasi-static force–displacement curve of a mounted bistable plate is determined experimentally. Then the dynamic response of a nonlinear mass–spring system incorporating this plate is measured. Excellent agreement is obtained when compared to theoretical predictions based on the measured force–displacement curve, and the system shows a greater isolation region and a lower peak response to base excitation than the equivalent linear system.

Hyer MW .

The room-temperature shapes of four-layer unsymmetric cross-ply laminates

Journal of Composite Materials, 1982,16(4):318

DOI      URL     [本文引用: 1]

A previous approximate theory for predicting the room-temperature shapes of unsymmetric laminates is examined in light of the assumptions regarding the inplane strains. The previous theory, which was a geometrically nonlinear extension of classical lamination theory, was felt to be restrictive and this paper develops a new theory in which these restrictions are relaxed. It is shown that despite the previous concern, there is little difference between the previous theory and this theory. This paper presents numerical results for the inplane residual strains of unsymmetric laminates which have cooled from curing into a cylindrical room-temperature shape. It is shown that the residual strains are compressive and practically independent of spatial location on the laminate. In another facet of the paper, the room-temperature shapes of all four-layer unsymmetric cross-ply laminates are predicted. There are only four unique stacking arrangements for this category of laminates and it is shown that their shapes are a strong function of their stacking arrangement. Keywords: Composite materials, Unsymmetric laminates, Thermal stresses, Thermal buckling, Residual stresses, Cross-ply laminates.

戴福洪, 张博明, 杜善义 .

非对称复合材料薄层板固化变形及其应用

哈尔滨工业大学学报, 2008,40(1):58-60

DOI      URL     [本文引用: 1]

阐述了Rayleigh-Litz法与有限元方法在非对称复合材料薄层板固化变形预报中的应用及特点.讨论了化学收缩作用、固化周期、铺层厚度比、长宽比等对非对称复合材料层板固化变形的影响.指出了非对称复合材料薄层板固化后多稳定构型分析中有待解决的几个问题,并对其在自适应结构上的应用提出了设想.

( Dai Fuhong, Zhang Boming, Du Shanyi .

Cured deformation and application of unsymmetric composite thin laminates

Journal of Harbin Institute of Technology, 2008,40(1):58-60 (in Chinese))

DOI      URL     [本文引用: 1]

阐述了Rayleigh-Litz法与有限元方法在非对称复合材料薄层板固化变形预报中的应用及特点.讨论了化学收缩作用、固化周期、铺层厚度比、长宽比等对非对称复合材料层板固化变形的影响.指出了非对称复合材料薄层板固化后多稳定构型分析中有待解决的几个问题,并对其在自适应结构上的应用提出了设想.

Arrieta AF, Neild SA, Wagg DJ .

On the cross-well dynamics of a bi-stable composite plate

Journal of Sound and Vibration, 2011,330(14):3424-3441

DOI      URL    

Multi-stable composites are a novel type of composites capable of adopting multiple statically stable configurations. Due to the multi-stability property this type of composite material has been considered for several applications, particularly for morphing structures. The change of shape between stable states is achieved by a nonlinear mechanism known as snap-through. Most of the research done on these composites has focused on predicting the configuration after manufacture, its static characteristics and static actuation strategies to induce snap-through. However, these structures will operate subject to dynamic loads. Yet, very little work has been carried out to examine the dynamic behaviour of bi-stable composites. This paper focuses on the study of the cross-well dynamics of a bi-stable composite plate. A simple model previously derived for the dynamics confined to a single stable state is extended to include cross-well dynamics. The rich dynamics are experimentally investigated, focusing on cross-well oscillations and the key dynamic features of snap-through. Numerical simulations are obtained and compared to the experimental results showing good agreement. In particular, experimentally observed characteristics suggesting chaotic oscillations for cross-well dynamics are captured well by the proposed model. The results herein could be used for implementing control strategies for both configuration morphing and undesired snap-through suppression of bi-stable composites.

Moore M, Ziaei-Rad S, Firouzian-Nejad A .

Temperature-curvature relationships in asymmetric angle ply laminates by considering the effects of resin layers and temperature dependency of material properties

Journal of Composite Materials, 2014,48(9):1071-1089

DOI      URL    

Not Available

李昊 . 双稳定复合材料层板的构型分析及其动力学特性研究. [博士论文]. 哈尔滨: 哈尔滨工业大学, 2015

[本文引用: 1]

( Li Hao . Configuration analysis and dynamics research of bistable composite laminates. [PhD Thesis]. Harbin: Harbin Institute of Technology, 2015 (in Chinese))

[本文引用: 1]

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