The force transmissibility of MDOF structures with a non-linear viscous damping device

In the present study, the concept of the Output Frequency Response Function (OFRF), recently proposed by the authors, is applied to theoretically investigate the force transmissibility of MDOF structures with a cubic non-linear viscous damping device. The results analytically show that the introduction of cubic non-linear damping can significantly reduce the transmissibility over all resonance regions for a Multiple Degree of Freedom (MDOF) structure and at the same time leave the transmissibility over the isolation region virtually unaffected. The analysis also indicates that a strong linear damping may shift the system resonances and compromise the beneficial effects of cubic non-linear viscous damping on the force transmissibility of MDOF structures. This suggests that a less significant linear damping together with a strong cubic non-linear damping can be used in MDOF structures to achieve a desired vibration isolation performance. This research work has a significant implication for the design of viscously damped MDOF structures for a wide range of practical applications.     

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.     

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.     

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.      

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。     

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.     

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。     

DYNAMIC CHARACTERISTICS OF VIBRATION ISOLATION SYSTEM WITH CUBIC STIFFNESS AND HYSTERESIS 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。     

惯容器对隔振系统动态性能影响研究

本文设计了一种滚珠丝杠惯容器及ISD隔振系统,通过实验研究了惯性轮的转动惯量对惯容值的影响;同时,分析了滚珠丝杠惯容器的机械动力学特性,推导了ISD隔振系统的振动传递率计算公式,探讨了惯容器对ISD隔振系统动态特性的影响。在电机被动、主动和混合隔振工况下,开展了弹簧阻尼系统和ISD隔振系统的振动性能对比实验,验证了惯容器对振动系统固有频率和减振效果的影响规律。研究结果表明,惯容器可降低振动系统的固有频率,使共振频率向低频移动,共振振幅降低;在共振频率附近,惯容器可抑制共振振幅,惯容值越高,抑制效果越明显;ISD隔振系统在低频的减振效果优于传统的弹簧阻尼系统;随着频率比的增加,ISD隔振系统的传递率趋于稳定值,惯容器会引起高频隔振性能降低。     

Analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems

This study is concerned with the analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems. Analytical algorithms are derived using the Ritz–Galerkin method to evaluate the transmissibility of SDOF displacement vibration isolation and force vibration isolation systems where a nonlinear viscous damper is used as an energy dissipating device. The results reveal that compared to linear dampers, nonlinear viscous dampers can more significantly improve the system vibration isolation performance in a wider frequency range. A procedure is then proposed based on the analysis results to facilitate the design of nonlinear viscous dampers for system vibration isolation purposes. These results have significant implications for the design of vibration isolation systems in many engineering applications.     

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.     

滞回摩擦型调谐惯质阻尼器结构隔震研究

本文研究一种新型非线性阻尼器——滞回摩擦型调谐惯质阻尼器(HFTID)在工程结构抗震控制中的应用。HFTID由调谐惯质阻尼器(TID)和滞回弹簧摩擦元件并联组成。首先通过谐波平衡方法推导了HFTID单自由度系统力与位移的传递率。然后对HFTID进行了最佳调谐参数优化,得到HFTID最优参数的近似表达式,比较了HFTID和TID振动控制系统的减振效果。结果表明,HFTID相比TID可以进一步降低振动控制系统的传递率。最后,以一栋多层隔震结构为例,将HFTID与TID的隔震效果进行了对比,结果表明,HFTID相比TID在降低地震响应峰值和均方根值方面具有更大优势,验证了HFTID在降低地震响应方面的有效性和实用性。HFTID在建筑和桥梁结构抗震、车辆悬挂系统和其他机械隔震问题上具有潜在的应用前景。     

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...     

Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

A novel vibration isolation device called the nonlinear energy sink(NES)with Ni Ti NOL-steel wire ropes(Ni Ti-ST) is applied to a whole-spacecraft system. The Ni Ti-ST is used to describe the damping of the NES, which is coupled with the modified Bouc-Wen model of hysteresis. The NES with Ni Ti-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET) to concentrate the energy locally on the nonlinear oscillator, and then dissipates it through damping in the NES with Ni Ti-ST.The generalized vibration transmissibility, obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with Ni Ti-ST based on the transmissibility of NOFRFs. Finally, the effects of vibration suppression by varying the parameters of Ni Ti-ST are analyzed from the perspective of energy absorption. The results indicate that NES with Ni Ti-ST can reduce excessive vibration of the whole-spacecraft system, without changing its natural frequency. Moreover, the NES with Ni Ti-ST can be directly used in practical engineering applications.     

Vibration isolation performance evaluation of the discrete whole-spacecraft vibration isolation platform for flexible spacecrafts

The method for evaluating the vibration isolation performance of discrete whole-spacecraft vibration isolation of flexible spacecrafts is studied in the paper. The dynamic model of the discrete whole-spacecraft system is built and model reduction is proposed. The analysis of vibration isolation method of vibration transmissibility from the isolator to satellite is discussed. Then, the evaluation method is studied from the perspective of simulation and experiment, and the results show the correctness of the theoretical analysis. The power flow evaluation method of discrete whole-spacecraft of the flexible spacecraft is introduced. By studying the power flow of the vibration isolation, we find that this method supplements inadequacies of the vibration transmissibility. At last, it is proposed that the vibration isolation performance should be evaluated by combining the vibration transmissibility at some key points of the satellite and the power flow of the vibration isolator.     

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.     

附加约束阻尼层对星箭系统动特性的影响分析

在星箭连接支架外表面附加约束阻尼层可抑制星箭对接界面的振动,从而降低卫星在发射过程中所承受的振动和噪声载荷.本文将有限元技术与矩阵特征值摄动分析方法相结合,就卫星支架局部修改(附加约束阻尼层)对星箭系统动态特性的影响进行了分析.以已有星箭系统结构的模态信息为基础,给出了支架部位附加约束阻尼层后星箭系统动态特性变化的定量计算方法,并证明了该减振技术能够不明显的改变原星箭系统的固有特性.     

长型浮置板轨道隔振系统理论分析(I)——弥散曲线及临界速度

浮置板轨道结构是近年来减振降噪效果最好的轨道结构形式.将整个轨道结构看作一个隔振黑匣子,钢轨与浮置板分别用欧拉梁来模拟,推导动力方程,用傅氏变换将其转换到频率-波数域中,求得系统的弥散方程,并给出轨道结构临界速度计算方法.定义了反映浮置板轨道结构参数的质量比例ξ_(m)、刚度比例ξ_(h)及阻尼比例ξ_(c)等三个系数.在给定实际中板上结构物理参数的条件下,深入讨论了三个比例系数对于系统弥散曲线以及临界速度的影响,进而为浮置板轨道共振频率及临界速度的初步设计提供建议.