A quasi-zero-stiffness isolator with a shear-thinning viscous damper

Quasi-zero-stiffness(QZS) vibration isolators have been widely studied,because they show excellent high static and low dynamic stiffnesses and can effectively solve low-frequency and ultralow-frequency vibration. However, traditional QZS(T-QZS)vibration isolators usually adopt linear damping, owing to which achieving good isolation performance at both low and high frequencies is difficult. T-QZS isolators exhibit hardening stiffness characteristics, and their vibration isolation performance is e...     

Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine

Human motion induced vibration has very low frequency, ranging from 2 Hz to 5 Hz. Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the high load capacity. In this paper, inspired by the human spine, we propose a novel bionic human spine inspired quasi-zero stiffness (QZS) vibration isolator which consists of a cascaded multi-stage negative stiffness structure. The force and stiffness characteristics are investigated first, the dynamic model is established by Newton’s second law, and the isolation performance is analyzed by the harmonic balance method (HBM). Numerical results show that the bionic isolator can obtain better low-frequency isolation performance by increasing the number of negative structure stages, and reducing the damping values and external force values can obtain better low-frequency isolation performance. In comparison with the linear structure and existing traditional QZS isolator, the bionic spine isolator has better vibration isolation performance in low-frequency regions. It paves the way for the design of bionic ultra-low-frequency isolators and shows potential in many engineering applications.

     

Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping

A geometric nonlinear damping is proposed and applied to a quasi-zero stiffness (QZS) vibration isolator with the purpose of improving the performance of low-frequency vibration isolation. The force, stiffness and damping characteristics of the system are presented first. The steady-state solutions of the QZS system are obtained based on the averaging method for both force and base excitations and further verified by numerical simulation. The force and displacement transmissibility of the QZS vibration isolator are then analysed. The results indicate that increasing the nonlinear damping can effectively suppress the force transmissibility in resonant region with the isolation performance in higher frequencies unaffected. In addition, the application of the nonlinear damping in the QZS vibration isolator can essentially eliminate the unbounded response for the base excitation. Finally, the equivalent damping ratio is defined and discussed from the viewpoint of vibration control.     

Modeling,analysis, and simulation of X-shape quasi-zero-stiffness-roller vibration isolators

Existing quasi-zero stiffness (QZS) isolators are reviewed. In terms of their advantages, a novel X-shape QZS isolator combined with the cam-roller-spring mechanism (CRSM) is proposed. Different from the existing X-shape isolators, oblique springs are used to enhance the negative stiffness of the system. Meanwhile, the CRSM is used to eliminate the gravity of the loading mass, while the X-shape structure leaves its static position. The existing QZS isolators are demonstrated and classified according to their nonlinearity mechanisms and classical shapes. It is shown that the oblique spring can realize negative stiffness based on the simplest mechanism. The X-shape has a strong capacity of loading mass, while the CRSM can achieve a designed restoring force at any position. The proposed isolator combines all these advantages together. Based on the harmonic balance method (HBM) and the simulation, the displacement transmissibilities of the proposed isolator, the X-shape isolators just with oblique springs, and the X-shape isolators in the traditional form are studied. The results show that the proposed isolator has the lowest beginning isolation frequency and the smallest maximum displacement transmissibility. However, it still has some disadvantages similar to the existing QZS isolators. This means that its parameters should be designed carefully so as to avoid becoming a bistable system, in which there are two potential wells in the potential energy curve and thus the isolation performance will be worsened.

     

A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms

Vibration isolation is one of the most efficient approaches to protecting host structures from harmful vibrations, especially in aerospace, mechanical, and architectural engineering, etc. Traditional linear vibration isolation is hard to meet the requirements of the loading capacity and isolation band simultaneously, which limits further engineering application, especially in the low-frequency range. In recent twenty years, the nonlinear vibration isolation technology has been widely investigated to broaden the vibration isolation band by exploiting beneficial nonlinearities. One of the most widely studied objects is the “three-spring” configured quasi-zero-stiffness (QZS) vibration isolator, which can realize the negative stiffness and high-static-low-dynamic stiffness (HSLDS) characteristics. The nonlinear vibration isolation with QZS can overcome the drawbacks of the linear one to achieve a better broadband vibration isolation performance. Due to the characteristics of fast response, strong stroke, nonlinearities, easy control, and low-cost, the nonlinear vibration with electromagnetic mechanisms has attracted attention. In this review, we focus on the basic theory, design methodology, nonlinear damping mechanism, and active control of electromagnetic QZS vibration isolators. Furthermore, we provide perspectives for further studies with electromagnetic devices to realize high-efficiency vibration isolation.

     

A high-static–low-dynamic-stiffness vibration isolator with the auxiliary system

High-static–low-dynamic-stiffness (HSLDS) vibration isolators seek to widen the frequency range of isolation by decreasing the dynamic stiffness so as to reduce the natural frequency, while maintaining the same static displacement as equivalent linear isolators. However, in many cases especially under light damping or large excitations, the peak transmissibility is very large and the hardening nonlinearity causes the transmissibility curve to bend to the right seriously or in other words causes the jump phenomenon, resulting in a greatly reduced isolation region. In this paper, an auxiliary system is added to the HSLDS isolator to overcome these disadvantages, with the static displacement of the isolation object remaining unchanged. Coefficient-varying harmonic balance method is proposed in this paper to find the dynamic response and most importantly analyze the stability of the steady-state response. The isolation performance of the HSLDS-AS isolator, which is evaluated by displacement transmissibility, is compared with that of the equivalent HSLDS isolator. The effects of system parameters on the isolation performance are investigated. It is shown that the auxiliary system can lower the peak transmissibility and eliminate the jump phenomenon, resulting in a wide isolation region, and the HSLDS-AS isolator has strong designability with many parameters tunable.     

基于混杂双稳定层合板的准零刚度隔振装置

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.      

Reducing force transmissibility in multiple degrees of freedom structures through anti-symmetric nonlinear viscous damping

In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom (MDOF) structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force transmissibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.     

Performance analysis of a nonlinear inerter-based vibration isolator with inerter embedded in a linkage mechanism

This study presents an inerter-based nonlinear vibration isolator with geometrical nonlinearity created by configuring an inerter in a diamond-shaped linkage mechanism. The isolation performance of the proposed nonlinear isolator subjected to force or base-motion excitations is investigated. Both analytical and alternating frequency-time harmonic balance methods as well as numerical integration method are used to obtain the dynamic response. Beneficial performance of the nonlinear isolator is demonstrated by various performance indices including the force and displacement transmissibility as well as power flow variables. It is found that the use of the nonlinear inerter in the isolator can shift and bend the peaks of the transmissibility and time-averaged power flow to the low-frequency range, creating a larger frequency band of effective vibration isolation. It is also shown that the inertance-to-mass ratio and the initial distance of the nonlinear inerter can be effectively tailored to achieve reduced transmissibility and power transmission at interested frequencies. Anti-resonant peaks appear at specific frequency, creating near-zero energy transmission and significantly reducing vibration transmission to a base structure on which the proposed isolator is mounted.

     

Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators

The purpose of this study is to explore the advantages and characteristics of nonlinear butyl rubber (type IIR) isolators in vibratory shear by comparison with linear isolators. It is known that the mechanical properties of viscoelastic materials exhibit significant frequency and temperature dependence, and in some cases, nonlinear dynamic behavior as well. Nonlinear characteristics in shear deformation are reflected in mechanical properties such as stiffness and damping. Furthermore, even when the excitation amplitude is small the response amplitude may often be large enough that nonlinearities cannot be ignored. The treatment involves developing phenomenological models of the effective storage modulus and effective loss factor of a rubber isolator material as a function of excitation amplitude. The transmissibility of a nonlinear viscoelastic isolator is compared with that of a linear isolator using an equivalent linear damping coefficient. Forced resonance vibration and impedance tests are used to characterize nonlinear parameters and to measure the normalized transmissibility. It is found that as the excitation amplitude of the nonlinear viscoelastic isolator increases, the response amplitude decreases and the transmissibility is improved over that of the linear isolator for excitation frequency that exceeds a particular value governed by the temperature and excitation amplitude. The method of multiple scales and numerical simulations are used to predict the response characteristics of the isolator based on the phenomenological modeling under different values of system parameters.     

含机械调频式动力吸振器的准零刚度隔振系统隔振性能分析

基于动力吸振器原理,在单自由度准零刚度隔振器基础上耦合可调频动力吸振器构成两自由度隔振系统。首先,对动力吸振器工作原理进行理论分析并提出其力学模型;其次,通过静力学分析,推导出系统满足零刚度条件时,各参数间的关系并分析其对系统刚度特性的影响;然后,建立两自由度隔振系统非线性动力学方程,利用谐波平衡法进行幅频响应解析分析,得到力传递率表达式;最后,数值分析动力吸振器阻尼、刚度、质量、激励力幅值和弹簧片有效长度对力传递率的影响规律,并与单自由度准零刚度隔振系统及两自由度线性隔振系统对比分析。结果表明：通过选择适当的动力吸振器参数不仅可以减小系统的起始隔振频率,增宽隔振频带,且还能加快系统力传递率在特定频段内的衰减速率,改善系统的低频隔振性能,实现激励频率的可适应性。     

带非线性弹簧的两自由度准零刚度隔振系统力传递率特性

基于多自由度系统中的反共振特性,分别在传统线性隔振系统的上、下两层引入非线性倾斜弹簧负刚度机构,构成两自由度准零刚度隔振器。通过静态特性分析,推导出系统满足零刚度条件时,各参数之间的关系,分析了力学参数及结构参数对系统刚度特性的影响。建立两自由度准零刚度隔振系统的非线性动力学方程,利用平均法求解,推导出力传递率表达式,结合数值分析方法,探讨系统在不同的上、下层隔振器阻尼比、竖直刚度比及质量比情况下的力传递率特性,并与单自由度准零刚度隔振系统及线性斜弹簧两自由度准零刚度隔振系统进行对比研究。结果表明：当结构参数 （即：倾斜弹簧处于静平衡位置的长度与倾斜弹簧原长的比值）较小且倾斜弹簧为软化弹簧时,可在平衡位置附近获得较小的系统刚度及较大的低刚度区间;通过选择适当的上、下层隔振器阻尼比、竖直刚度比与质量比,可减小系统的起始隔振频率,增宽隔振频带,加快系统力传递率在特定频段内的衰减速率,改善系统的低频隔振性能。     

Effects of anti-symmetric nonlinear viscous damping on the force transmissibility of multi-degree of freedom structures

In the present study, the concept of the output frequency response function is applied to theoretically investigate the force transmissibility of multi-degree of freedom (MDOF) structures with a nonlinear anti-symmetric viscous damping. The results reveal that an anti-symmetric nonlinear viscous damping can significantly reduce the transmissibility over all resonance regions for MDOF structures while it has almost no effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to overcome the dilemma in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant region but increases the transmissibility over non-resonant regions.     

An improved quasi-zero stiffness vibration isolation system utilizing dry friction damping

Nonlinear Dynamics - Quasi-zero stiffness (QZS) isolators, a nonlinear vibration isolation technique, enhance the isolation performance, by lowering the natural frequencies of an isolation system...     

Study of the effects of cubic nonlinear damping on vibration isolations using Harmonic Balance Method

In the present study, Harmonic Balance Method (HBM) is applied to investigate the performance of passive vibration isolators with cubic nonlinear damping. The results reveal that introducing either cubic nonlinear damping or linear damping could significantly reduce both the displacement transmissibility and the force transmissibility of the isolators over the resonance region. However, at the non-resonance region where frequency is lower than the resonant frequency, both the linear damping and the cubic nonlinear damping have almost no effect on the isolators. At the non-resonance region with higher frequency, increasing the linear damping has almost no effects on the displacement transmissibility but could raise the force transmissibility. In addition, the influence of the cubic nonlinear damping on the isolators is dependent on the type of the disturbing force. If the strength of the disturbing force is constant and independent of the excitation frequency, then the effect of cubic nonlinear damping on both the force and displacement transmissibility would be negligible. But, when the strength of the disturbing force is dependent of the excitation frequency, increasing the cubic nonlinear damping could slightly reduce the relative displacement transmissibility and increase the absolute displacement transmissibility but could significantly increase the force transmissibility. These conclusions are of significant importance in the analysis and design of nonlinear passive vibration isolators.     

几何非线性摩擦阻尼隔振系统动力学行为研究

非线性隔振系统由于具有较线性系统更优的隔振性能,因此在工程中应用广泛.本文通过配置与被隔振对象的运动方向相垂直的库伦摩擦阻尼器,构建了几何非线性摩擦阻尼模型.由于引入了几何非线性,因此其摩擦力与位移正相关,这与传统与位移无关摩擦力模型有显著不同.首先,建立了具有几何非线性摩擦阻尼的数学模型以及隔振系统的受迫振动方程;然后,使用谐波平衡法求解了动力学方程,并使用数值仿真方法验证了谐波平衡法求解的准确性;最后,研究了几何非线性摩擦阻尼隔振器的绝对位移传递率和相对位移传递率.研究结果表明,在库伦摩擦阻尼选择适当,非线性摩擦阻尼系统可以在保持高频振动衰减效果的前提下,显著降低系统共振峰,其性能优于传统的恒定摩擦阻尼隔振模型.同时,几何非线性摩擦阻尼系统能够避免传统摩擦阻尼系统中的“锁定”现象,从传递率角度来说,不利于共振峰控制;但从激励环境改变引发隔振系统失效的角度来看,几何非线性摩擦阻尼系统可以拓宽系统对激励幅值的适应范围,避免隔振系统失效.本文的研究结果对此类隔振系统的设计和摩擦阻尼参数的选择具有通用的指导意义.      

一类新型多方向准零刚度隔振平台

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．     

Low-frequency multi-direction vibration isolation via a new arrangement of the X-shaped linkage mechanism

Nonlinear Dynamics - Most existing quasi-zero stiffness (QZS) isolators with excellent vibration isolation performance in the low-frequency range are designed to attenuate vibration transmission...     

Study on the force transmissibility of vibration isolators with geometric nonlinear damping

By a special layout of the damper in a vibration isolation system, the velocity-nth power damping of the damper can be transformed into the velocity-displacement dependent damping in the moving direction due to geometric nonlinearity. This study is mainly concerned with the mechanism of this geometric nonlinear damping and tries to find some guidelines for designing isolators with high performance, regardless of the isolator is passive or active. The model used in this study is an unconstrained two-degree-of-freedom isolation system, which is suitable for investigating vibration isolation in space vehicles. The motion equation is solved by the averaging method to obtain the amplitude–frequency equation. The influence of damping coefficients on the force transmissibility is analyzed. Results show that this kind of damping has some advantages in improving isolation performance at both the resonance and higher frequencies. Meanwhile, it can also degrade the isolation performance if unreasonable parameters are chosen.     

含立方刚度和滞回的隔振系统动力学特性分析 1)

包含立方刚度和Bouc-Wen 型滞回的隔振系统具有复杂的非线性动力学特性。系统无阻尼响应模型可基于无滞回恢复力建立,利用谐波平衡法和泰勒展开求得近似解析解。系统有阻尼响应模型可利用解析/数值联合方法求解,该方法基于谐波平衡法和Levenberg-Marquardt 迭代算法,对于滞回产生的多值非光滑函数项,先计算时域响应再通过快速傅里叶变换求解谐波项系数。上述方法在含水平绞制梁的非线性隔振系统分析中得到有效应用。分析表明,在Bouc-Wen 型滞回和立方刚度的综合影响下,隔振系统呈现渐软–渐硬特性,滞回阻尼和线性阻尼都可以有效抑制共振,但前者高频隔振效果优于后者。