低频大幅隔振器设计及实验

孙秀婷，孙英超，钱佳伟，徐鉴; Sun Xiuting; Sun Yingchao; Qian Jiawei; Xu Jian

引 en

低频大幅隔振器设计及实验^*

孙秀婷^1,2
机构：
1. 同济大学航空航天与力学学院,上海 200092
2. 同济大学民航航空器结构智能辅助适航重点实验室,上海 200092
×
，孙英超¹
机构：
1. 同济大学航空航天与力学学院,上海 200092
×
，钱佳伟¹
机构：
1. 同济大学航空航天与力学学院,上海 200092
×
，徐鉴¹
机构：
1. 同济大学航空航天与力学学院,上海 200092
×

1. 同济大学航空航天与力学学院,上海 200092；
2. 同济大学民航航空器结构智能辅助适航重点实验室,上海 200092；

Design and Experiment of a Vibration Isolator for Low Frequency and Large Amplitude Excitation^*

Sun Xiuting^1,2
Affiliation：
1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092 , China
2. Key Laboratory of AI-aided Airworthiness of Civil Aircraft Structures, Civil Aviation Administration, Tongji University, Shanghai 200092 , China
×
，Sun Yingchao¹
Affiliation：
1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092 , China
×
，Qian Jiawei¹
Affiliation：
1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092 , China
×
，Xu Jian¹
Affiliation：
1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092 , China
×

1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092 , China；
2. Key Laboratory of AI-aided Airworthiness of Civil Aircraft Structures, Civil Aviation Administration, Tongji University, Shanghai 200092 , China；

通讯作者:

徐鉴,E-mail:xujian@tongji.edu.cn

中图分类号:O328

文献标识码:A

文章编号:1672-6553-2024-22(2)-059-009

DOI:10.6052/1672-6553-2024-009

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出版信息

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目录contents

摘要 Abstract
关键词 Keywords
1 折纸隔振器建模
1.1 宽零刚度隔振器创新结构设计
1.2 宽零刚度隔振器模型
2 动力学分析
3 实验
4 结论
参考文献

摘要

为了突破传统隔振器刚度和承载能力之间的矛盾,需要隔振器具有高的静态刚度,低动态刚度的特性.如今的准零刚度隔振器技术可以实现低频微幅隔振,但是对于大幅振动,隔振效果并不明显甚至失效,因此突破宽幅隔振成为隔振领域亟待解决的问题.为此,我们利用多稳态折纸通过并联装配的方式,构造具有宽幅零刚度区间的折纸型隔振器,以解决传统隔振器振动抑制幅值较低的问题.本文建立了宽零刚度隔振器模型,提出宽幅零刚度的设计方法,并通过动力学分析分析了模型的隔振效果.最后搭建试验样机,验证了理论的正确性.这种设计打破了传统准零刚度隔振器单点准零的设计准则,能够在一个大幅范围内保证稳定性,同时实现零刚度,极大拓宽了隔振器的适用范围.这种设计理念能够被用在新隔振材料设计和航空、船舶等大幅低频动态环境中.

Abstract

Vibration isolators with high-static-low-dynamic-stiffness (HSLDS) characteristics are required in order to break through the contradiction between the stiffness and the load bearing capacity of the traditional vibration isolator. Nowadays, quasi-zero-stiffness vibration isolator technology can realize low-frequency vibration isolation under a small amplitude, but for large amplitude vibration, the vibration isolation effect is weakened or even ineffective. Therefore, wide-range amplitude vibration isolation has become a problem to be solved in the field of vibration isolation. In order to solve the problem of small vibration suppression amplitude of traditional vibration isolators, a parallel-assembly origami vibration isolator with wide zero stiffness range is proposed. The dynamic model of the origami vibration isolator with wide zero stiffness range is established, and design methodology for wide zero stiffness range is proposed. Based on the dynamic model, the vibration isolation effectiveness is analyzed. Finally, the correctness of the dynamic analysis is verified experimentally. This new design breaks through the design criterion of the traditional quasi-zero stiffness isolator that zero stiffness is only achieved at a specific point. Stability can be guaranteed over a large range, while achieving zero stiffness, which greatly broadens the application range of vibration isolators. This design concept can be used in the design of new vibration isolation materials and in large low-frequency dynamic environments such as aerospace and ships.

关键词

宽范围零刚度；高静低动系统；非线性隔振；低频激励

Keywords

wide range zero stiffness ； high-static-low-dynamic-stiffness systems ； nonlinear vibration isolation ； low frequency excitation

引言
振动与人类生活和工业发展密切相关.生活中不良的振动会影响人们的舒适度，工业中不可避免的振动则会对工程器械带来损耗和危害.通过观察发现，在实际工程中，振动大都有低频大振幅振动的特点，低频必定伴随着大幅度的振动.因此，隔振器的隔振频带如何向低频拓展、隔振幅值如何拓宽成为了当今学者主要的研究目标.线性隔振器存在刚度和承载能力之间的设计瓶颈，无法实现低频隔振.学者们设计了具有高静低动特性的准零刚度隔振器^[1].通过引入负刚度元件后有静高承载能力，在振动时因为负刚度的存在有低的动态刚度.突破了承载和刚度的设计瓶颈，将隔振频率引入低频区域.
通过引入两个斜弹簧提供非线性负刚度，与垂直正刚度弹簧组成三弹簧式准零刚度结构，其设计准则通常基于线性刚度为零，由非线性刚度提供承载能力，由此实现高静低动特性^[2-6].除了三弹簧式QZS，基于正负刚度并联隔振原理，Xu等人^[7]通过引入磁铁提供负刚度与正刚度弹簧组合构造准零刚度隔振器.Sun等人^[8]利用磁结构构造准零刚度连续隔振结构.Dong等人^[9]构造了磁负刚度弹簧高静-低动刚度隔振器，并进行了隔振仿真实验.磁负刚度结构也经常用于构造QZS^[10-14].随着仿生学的发展和折纸结构^[15-18]的研究，这两种新设计也逐渐被用于QZS的设计当中^[19-21].Sun等人^[22]对剪刀型隔振结构进行研究，并通过改变结构层数，连杆结构参数实现了结构的刚度可调.Han等人^[23]以Miura-Origami为灵感将其等效成四连杆加水平弹簧结构，通过添加垂直正刚度弹簧设计了一种具有准零刚度的非线性隔振器.Ishida等人^[24]基于kresling折纸结构，用等效水平杆、纵向杆、对角杆组装了一个折纸胞体，研究发现在其压缩过程中具有变刚度的特性，因此作者加入了一个线性正刚度弹簧与之平衡，使结构在压缩过程中某个位置附近，正负刚度互相抵消，实现小范围准零刚度.Liu等人^[25]提出了一种具有准零刚度（QZS）特性的新型弹性折纸结构，以提供有效的低频隔振性能.Zeng等人^[26]提出了一种具有几何非线性关系特征的新型折纸结构，并将其应用于新型准零刚度（QZS）隔振器的设计中.综上所述大部分准零刚度隔振器其设计准则都是单点设计，一旦振动增加，非线性系统的振动特性依赖于振动状态导致零动态刚度被破坏.因此以大幅振动隔振为需求，学者们提出了高阶设计准则和渐进准零刚度设计.为了拓宽准零刚度的范围，学者们提出了滚子式准零刚度隔振器，通过增加凸轮接触结构，其恢复力通过滚子产生与运动方向相同的竖向分力实现负刚度效应，使刚度成为随结构参数变化的分段函数，在滚子保持接触时都能实现动态刚度为零的目的.提高了有效隔振的范围.Ye等人^[27]设计了多凸轮滚子准零刚度结构，解决了单凸轮不连续的问题.Li等人^[28]基于凸轮的负刚度机制提出了非圆凸轮准零刚度隔振器.Wang等人^[29]对滚子进行了进一步设计，将其改造成可设计的曲面，在大范围的位移时能够保持准零刚度.但是凸轮结构存在摩擦和稳定性的问题，同时其准零设计准则仍然是平衡点处的单点设计.2022年，Yan等人^[30，31]将磁场、三弹簧、凸轮滚子系统进行异构融合设计，提出了渐进准零刚度特性隔振器，打破了准零刚度特性依赖负刚度元件的设计机理，动态零刚度位移区域得到拓宽.
受此启发，结合折纸结构多稳态特性，本文采用多稳态折纸并联的方法，设计宽幅零刚度隔振器.另一方面，折纸结构在工艺上具有体积小、质量轻，自身可连续大幅折叠等优点，可以有效避免机械式存在的摩擦和质量大等问题，并且系统的稳定性能够被保证.文章第一章通过Miura-Qri内嵌和外凸两个构型并联的方式构造线性负刚度段，与线性正刚度弹簧并联建立了宽零刚度折纸隔振器模型，阐述了宽零刚度构造原理，并推导了结构的本构关系.第二章建立了动力学模型，定义位移传递率，对结构的隔振能力进行了理论分析.最后搭建试验样机，验证了理论结果的正确性.
1 折纸隔振器建模
1.1 宽零刚度隔振器创新结构设计
如图1（a）所示，Miura-Qri结构由A、B两个折纸单元连接而成，单个折纸胞一共有12条弹性折痕，其中a_A、a_B和b分别是A和B单元折痕和公共折痕的长度.结构只有一个自由度，有内嵌和外凸两种折叠构型.为保证折叠运动过程中A、B单元保持连接，折纸单元参数和折叠角需要满足如下关系：

a_{A} c o s γ_{A} = a_{B} c o s γ_{B}, θ_{B} = a r c c o s (c o s θ_{A} \frac{\tan γ_{A}}{\tan γ_{B}})

(1)

同时折纸胞的折叠运动可以用两个相邻面的二面角 $\partial_{j s}$ 描述，二面角 $\partial_{j s}$ （j=A，B; s=1，2，3，4）与折叠角θ_j之间的关系为^[32]

\begin{matrix} \partial_{j 1} = \partial_{j 3} = π - 2 θ_{j}, s i n \frac{\partial_{j 2}}{2} = \frac{\cos θ_{j}}{\sqrt{1 - {s i n}^{2} θ_{j} {s i n}^{2} γ_{j}}} \\ \partial_{j 4} = 2 π - \partial_{j 3} \end{matrix}

(2)

图1（a）Miura-Qri结构单元，（b）Miura-Qri结构，（c）Miura-Qri结构两种稳定构型
Fig.1 (a) Miura-Qri structural unit, (b) Miura-Qri structure, (c) two stable configurations of Miura-Qri structure
定义A、B单元折痕的单位长度扭簧刚度为k_A、k_B，公共折痕的单位长度扭转弹簧刚度为k_C。得到12条折痕a_js（j=A，B，s=1，2，3，4）、b 的扭转弹簧刚度K_js（j=A，B，s=1，2，3，4）为K_A1=K_A3=k_Ab，K_A2=K_A4=k_Aa_A，K_B1=K_B3=k_Bb，K_B2=K_B4=k_Ba_B，K_C=k_Cb.
由12条弹性折痕产生的折纸胞的总势能为

\begin{matrix} V = \frac{1}{2} [\sum_{s = 1}^{4} K_{A s} {(\partial_{A s} - \partial_{A s 0})}^{2} + \\ \sum_{s = 1}^{4} K_{B s} {(\partial_{B s} - \partial_{B s 0})}^{2} + 4 K_{C} {(\partial_{C} - \partial_{C 0})}^{2}] \end{matrix}

(3)

其中 $\partial_{A s 0}$ 、 $\partial_{B s 0}$ 和 $\partial_{C 0}$ 为各个折痕二面角的初始角度.
单胞中心顶点之间的距离即胞体长度h满足h=a_Bsinθ_Bsinγ_B-a_Asinθ_Asinγ_A.如图1（c）所示以初始折叠角θ_A0为起始点，此时h=h₀，可以得到运动坐标y关于折叠角的函数y=h-h₀.通过势能对位移y求导可以得到结构的力与位移方程.

F = \frac{d V}{d y} = \frac{d V}{d θ_{A}} {(\frac{d y}{d θ_{A}})}^{- 1}

(4)

选择结构的可调节参数为：A、B折纸单元的结构单元角度γ_A、γ_B和结构初始状态角θ_A0（图中虚线圆圈所示）.当折痕处有弯曲刚度存在时，结构能够表现出双稳态的力学特性^[19].具体结构参数的影响如图2所示.
图2（a）（b）表明，随着B单元角的降低，即结构的初始单元角度差的增大，结构从一个稳态越向另一个稳态所需要突破的能量壁垒就越大，体现在力位移曲线上就是所需的力更大，这样会导致恢复力的对称性更差.另一方面初始位置会影响结构是否出现双稳态效果，以及双稳态情况下结构两个平衡位置之间的距离.综上，Miura-Qri结构其恢复力有很强的不对称性和非线性.如果直接使用Miura-Qri构造大范围零刚度带，很难找到与之匹配的非线性不对称正刚度.因此本文将两个相同Miura-Qri结构以结构对称的形式并联，即首—首相接或者尾—尾相接的方式连接，构造一个拥有近似线性，同时对称的恢复力结构.再通过与线性正刚度结构匹配即可形成较大范围的零刚度区域.具体并联步骤及设计原理如图3所示.
图2 Miura-Qri结构势能.（a）θ_A0=60°，γ_B=75°，γ_B=70°和γ_B=60°，θ_A0=45°，θ_A0=40°；Miura-Qri结构力与位移曲线，（b）θ_A0=60°，γ_B=75°，γ_B=70°和γ_B=60°，θ_A0=45°，θ_A0=40°
Fig.2 Miura-Qri structural potential energy when (a) θ_A0=60°, γ_B=75°, γ_B=70°, and when γ_B=60°, θ_A0=45°, θ_A0=40°; Miura-Qri structural resilience when (b) θ_A0=60°, γ_B=75°, γ_B=70°, and when γ_B=60°, θ_A0=45°, θ_A0=40°
图3 并联设计原理
Fig.3 Parallel connection design principle
1.2 宽零刚度隔振器模型
尾-尾并联折纸结构模型如图4（a）所示，记为一个折纸对，取单个折纸胞的p为首端、q为尾端，结构只有沿折纸可伸缩方向一个自由度.胞体1的首端和胞体2的首端通过连杆固接在基座上，胞体1的尾端和胞体2的尾端通过连杆与集中固定连接.胞体1的胞长h₁=p₁q₁，胞体2的胞长h₂=p₂q₂.同样以无应力状态为起始点（y=0，h₁=h₁₀，h₂=h₂₀）.
折纸对系统的总势能为两个折纸胞势能之和 $V = \sum_{i = 1}^{2} V_{i} （ i = 1，2 ）$ .其中

\begin{matrix} V_{i} = \frac{1}{2} [\sum_{s = 1}^{4} K_{A s}^{i} {(\partial_{A s}^{i} - \partial_{A s 0}^{i})}^{2} + \\ \sum_{s = 1}^{4} K_{B s}^{i} {(\partial_{B s}^{i} - \partial_{B s 0}^{i})}^{2} + 4 K_{C}^{i} {(\partial_{C}^{i} - \partial_{C 0}^{i})}^{2}] \end{matrix}

(5)

由式h=a_Bsinθ_Bsinγ_B-a_Asinθ_Asinγ_A和h₁=h₁₀+y、h₂=h₂₀-y得到y与θ¹_A、θ²_A的关系
$y = a_{B}^{1} s i n \{\arccos [c o s (θ_{A}^{1}) \frac{\tan (γ_{A}^{1})}{\tan (γ_{B}^{1})}]\} s i n (γ_{B}^{1}) -$

\begin{matrix} a_{A}^{1} s i n (θ_{A}^{1}) s i n (γ_{A}^{1}) - h_{10} = a_{A}^{2} s i n (θ_{A}^{2}) s i n (γ_{A}^{2}) + \\ h_{20} - a_{B}^{2} s i n \{\arccos [c o s (θ_{A}^{2}) \frac{\tan (γ_{A}^{2})}{\tan (γ_{B}^{2})}]\} s i n (γ_{B}^{2}) \end{matrix}

(6)

通过势能对位移y求导可以得到结构的力-位移与刚度-位移方程.

F = \frac{d V_{1}}{d θ_{A}^{1}} (\frac{d y}{d θ_{A}^{1}}) - 1 + \frac{d V_{2}}{d θ_{A}^{2}} (\frac{d y}{d θ_{A}^{2}}) - 1

(7)

K = \frac{d F}{d θ_{A}^{1}} (\frac{d y}{d θ_{A}^{1}}) - 1 + \frac{d F}{d θ_{A}^{2}} (\frac{d y}{d θ_{A}^{2}}) - 1

(8)

为了构造对称线性恢复力，选用同构型的两个Miura-Qri结构以尾—尾相接的方式并联.胞体具体结构参数如表格1所示.并联结构势能以及恢复力和刚度曲线如图所示，由图4（c）可知，并联之后，结构仍具有变刚度，多稳态的性质.y=y₁、y=y₃为稳定平衡位置，y=y₂为不稳定平衡位置.由于同构型的对称性，结构的恢复力关于非稳定平衡点具有良好的对称性，但是并非完全对称，不完全对称是因为单个折纸胞初始状态对结构势能的影响.图中k_min（22.5，0.089）为最大负刚度点，为了避免宽零刚度隔振器出现负刚度，选取的并联正刚度弹簧刚度k_n≥|k_min|，设置线性弹簧预拉，以保证零刚度点位于平衡位置.并联结构和结构的力与位移曲线如图4（d）和图4（e）所示.根据以上的宽零刚度设计方法，从图5（a）的恢复力曲线可以看到，宽幅零刚度的位移边界达到[-0.2，0.2]，远大于传统准零刚度单点设计的幅值范围.换算为有量纲下的零刚度位移边界，有效零刚度范围在[-7.62，7.62]mm范围内.
图4（a）折纸对结构；（b）折纸对结构势能；（c）力与位移曲线;（d）宽零刚度隔振器结构；（e）力与位移曲线
Fig.4 (a) Model of Ori-couple structure; (b) Potential energy of Ori-couple structure; (c) Force displacement curve of Ori-couple structure (d) Model of wide-range zero stiffness isolator; (e) Force displacement curve of wide-range zero stiffness isolator
图5 无量纲力拟合与误差
Fig.5 Dimensionless restoring force fitting and error
表1 结构参数
Table1 Structure parameters
为了研究系统的隔振性能，将力与位移曲线进行五阶多项式拟合，由于并联结构的近似零刚度段较长，以平衡位置为中心，选择三种范围的数据进行多项式拟合，以并联之后平衡位置为零点，选取新坐标 $Z = y - y_{k_{m i n}}$ ，设力的形式为

F = P_{1} Z + P_{2} Z^{2} + P_{3} Z^{3} + P_{4} Z^{4} + P_{5} Z^{5}

(9)

将力无量纲化得到

f = p_{1} z + p_{2} z^{2} + p_{3} z^{3} + p_{4} z^{4} + p_{5} z^{5}

(10)

其中 $f = F / (k_{n} b) ， p_{i} = P_{i} b^{i - 1} / k_{n}$ .
无量纲拟合结果和拟合误差如图5（b）所示，拟合误差图像表明，小范围和大范围的拟合误差较大.选择中范围数据点拟合结果作为恢复力函数进行分析，拟合函数为f=0.003z+0.049z²+0.51z³-2.32z⁴+5.12z⁵.
2 动力学分析
为了研究折纸型宽零刚度隔振器的隔振性能，本章节通过建立动力学模型，定义位移传递率，使用高阶谐波平衡法求解非线性动力学方程，对隔振器的隔振性能进行了分析.假设系统受到周期激励，响应大小为z_b=z₀cos（wt）.利用牛顿法得到隔振器轴向动力学方程：

\begin{matrix} M \ddot{Z} + C \dot{Z} + k L (p_{1} z + p_{2} z^{2} + p_{3} z^{3} + p_{4} z^{4} + \\ p_{5} z^{5}) = - M Z_{0} ω^{2} c o s (ω t) \end{matrix}

(11)

式中M为被隔振物体集中质量，Z=Z_p-Z₀为集中质量对于基座的相对位移，Z_p、Z₀分别为集中质量和基座的绝对位移.将方程进行无量纲化得到

\begin{matrix} \ddot{z} + 2 ξ \dot{z} + p_{1} z + p_{2} z^{2} + p_{3} z^{3} + p_{4} z^{4} + \\ p_{5} z^{5} = - z_{0} Ω^{2} c o s (Ω τ) \\ ω_{n} = \sqrt{\frac{k}{M}}, τ = ω_{n} t, Ω = \frac{ω}{ω_{n}}, ξ = \frac{C}{2 M ω_{n}}, z_{0} = \frac{Z_{0}}{L} \end{matrix}

(12)

采用高阶谐波平衡法对式子进行求解，由于系统力的不对称性，设解的形式为z=A₀+Acos（Ωτ+φ），A₀为响应偏移量，A为振幅.将解带入方程（12），忽略高阶项，平衡谐波项，得到三组关于a₀、a、φ的代数方程组.

T_{1} (A_{0}, A_{1}) = z_{0} Ω^{2} c o s (φ)

(13)

T_{2} (A_{0}, A_{1}) = z_{0} Ω^{2} s i n (φ)

(14)

T_{3} (A_{0}, A_{1}) = 0

(15)

系统的位移传递率可以通过响应与激励的幅值比来定义，给定阻尼系数和频率求解得到位移传递率.

\begin{matrix} T = \frac{|z_{p}|}{|z_{b}|} = \frac{|z + z_{b}|}{|z_{b}|} \\ = \frac{\sqrt{a^{2} + z_{0}^{2} + 2 a z_{0} c o s φ}}{z_{0}} \end{matrix}

(16)

图6（a）显示了阻尼系数为0.06时不同激励幅值下的传递率曲线，随着激励幅值的增大，样机的隔振率降低，激励幅值可达到0.15（5.7mm）.图6（b）显示了不同阻尼对结构传递率的影响，由图可知，增大阻尼可以有效降低共振峰值，但是阻尼过大在高频区域的隔振率也会增大，因此实际工程中并非阻尼越大越好.
图6（a）阻尼系数ξ=0.06时，不同激励幅值下的位移传递率；（b）激励幅值z₀=0.1时，不同阻尼系数对传递率的影响；（c）当z₀=0.035，ξ=0.06时两种宽零刚度隔振器传递率比较
Fig.6 Displacement transfer rate under different excitation amplitudes when damping coefficient ξ=0.06; (b) When the excitation amplitude z₀=0.1, the influence of different damping coefficients on the transmission rate; (c) Comparison of transmission rates between two types of wide zero stiffness isolators when z₀=0.035, ξ=0.06
为了验证两个折纸胞并联，零刚度范围更大，可隔振幅值更大.我们设置了对照组，即在不加入线性正弹簧时，通过调节结构参数实现折纸对结构的准零刚度，即θ¹_A0=0°，θ²_A0=0°.如图6（c）所示，展示了在阻尼系数为0.035，激励幅值为0.06情况下，两种隔振器的传递率曲线，图像表明，在小阻尼，小激励幅值的情况下，由于双胞并联之后恢复力的对称性，加入线性正刚度弹簧后双胞并联的隔振效果要优于不加入弹簧并联的效果，验证了宽零刚度的有效性.综上所述，通过将两个折纸并联的方式构造对称恢复力，再与线性正刚度并联实现宽幅零刚度，可以有效拓宽隔振幅值.下一章节将通过实验验证理论的结果.
3 实验
在本节我们制作了一个试验样机对隔振器的隔振性能进行验证.如图7（a）所示为宽零刚度隔振器样机，包括外部框架（基座），两个Miura-Qri胞体、连杆和线性弹簧组成.折纸胞使用0.1mm厚的钢片通过塑料薄膜链接而成，使用预压弹簧钢片实现初始无应力状态的调整.线性弹簧原长23.19mm，预拉1mm.各部件的连接如图7（b）所示，使用连杆将两个折纸胞尾—尾相连并固定在框架上，两个胞体与集中质量连接，集中质量通过连杆与滑轨连接保证两个折纸胞和集中质量处于同一水平线上，再在矩形板和框架之间接入线性正刚度弹簧，最后将框架固定在激振台上，完成装配工作.图7（c）展示了装配实验效果图，1、2为结构未并联线性弹簧时，系统呈现双稳态效果，集中质量处于两个稳态平衡位置，3为结构并联线性弹簧后，系统呈现单稳态.隔振测试系统如图7（d）所示，使用信号发生器产生正弦谐波信号，通过功率放大器驱动激振台，并带动隔振样机产生振动.与此同时使用两个激光摄像头分别对准激振台和集中质量，实时记录位移时间数据，并将数据传输给电脑进行进一步的数据处理.
图7（a）宽零刚度隔离器模型；（b）隔振性能测试系统原理图；（c）并行单稳态物理模型；（d）隔振性能测试系统实验装置图；（e）宽零刚度隔振器在周期激励下的位移传递率；（f）频率为4Hz时不同激励幅值情况下的位移传递率
Fig.7 (a) Physical image of wide-range zero stiffness isolator; (b) Schematic diagram of vibration isolation performance testing system; (c) Parallel monostable physical model; (d) Experimental setup diagram of the vibration isolation performance test system; (e) Displacement transmission rate of wide-range zero stiffness isolator under periodic excitation; (f) Displacement transmission rate under different excitation amplitudes at a frequency of 4Hz
设置位移激励幅值z₀=5mm，集中质量为M=500g，在频率范围为0~10Hz之间对系统施加正弦激励振动，并记录系统的稳态响应结果.图7（e）为理论和实验的位移传递率图像，当频率为2.5Hz时，结构出现共振现象.图像表明，在激励发生大幅值振动时，隔振结构能够有效地降低振动的位移幅值，并随着激励频率的增加，隔振效果逐渐加强.图7（f）展示了频率为4Hz时不同激励幅值情况下的位移传递率，当激励幅值大约大于5mm时，隔振器结构发生失稳现象.
4 结论
本文基于多稳态折纸结构建立了宽零刚度隔振器模型，阐述了宽幅零刚度的设计原理，并对宽幅零刚度进行了结构设计.通过动力学建模分析了结构在大幅值位移激励下的隔振性能.最后搭建试验样机，验证了折纸并联结构在实现宽幅零刚度中的有效性.结果表明，提出的宽零刚度结构可以有效隔离激励幅值较大的振动，同时能够保证结构的稳定性.
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基本信息

中图分类号: O328
文献标识码: A
DOI: 10.6052/1672-6553-2024-009
文章编号: 1672-6553-2024-22(2)-059-009

基金信息

国家自然科学基金资助项目(11932015, 12122208, 12372002,12372043)；
中央高校基本科研业务费专项资金；
National Natural Science Foundation of China (11932015, 12122208, 12372002,12372043)；
Fundamental Research Funds for Central Universities；

引用信息

稿件历史

收稿日期: 2023-12-13

参考文献

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低频大幅隔振器设计及实验^*

Design and Experiment of a Vibration Isolator for Low Frequency and Large Amplitude Excitation^*

摘要

Abstract

关键词

Keywords

1 折纸隔振器建模

1.1 宽零刚度隔振器创新结构设计

(1)

(2)

(3)

(4)

1.2 宽零刚度隔振器模型

(5)

(6)

(7)

(8)

(9)

(10)

2 动力学分析

(11)

(12)

(13)

(14)

(15)

(16)

3 实验

4 结论

参考文献

基本信息

基金信息

引用信息

稿件历史

参考文献

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低频大幅隔振器设计及实验*

Design and Experiment of a Vibration Isolator for Low Frequency and Large Amplitude Excitation*

摘要

Abstract

关键词

Keywords

1 折纸隔振器建模

1.1 宽零刚度隔振器创新结构设计

(1)

(2)

(3)

(4)

1.2 宽零刚度隔振器模型

(5)

(6)

(7)

(8)

(9)

(10)

2 动力学分析

(11)

(12)

(13)

(14)

(15)

(16)

3 实验

4 结论

参考文献

基本信息

基金信息

引用信息

稿件历史

参考文献

微信公众号二维码

手机版网站二维码

低频大幅隔振器设计及实验^*

Design and Experiment of a Vibration Isolator for Low Frequency and Large Amplitude Excitation^*