Nonlinear Stiffness of a Magneto-Rheological Damper

The last decade has witnessed an important role of magneto-rheological dampers in the semi-active vibration control on the basis of empirical models. Those models established by fitting experimental data, however, do not offer any explicit expressions for the stiffness and the damping of magneto-rheological dampers. Hence, it is not easy for engineers to get any intuitive information about the effects of stiffness and damping of a magneto-rheological damper on the dynamic performance of a controlled system. To manifest the nonlinear properties of a magneto-rheological damper, this paper presents the hysteretic phenomena and the additional nonlinear stiffness of a typical magneto-rheological damper in terms of equivalent linear stiffness and equivalent linear damping. Then, it gives a brief discussion about the effect of nonlinear stiffness on the vibration control through the numerical simulations and an experiment for the semi-active suspension of a quarter car model with a magneto-rheological damper installed. Both numerical simulations and experimental results show that the additional nonlinear stiffness in the magneto-rheological damper is remarkable, and should be taken into consideration in the design of vibration control.     

Non-linear parametric modelling of a high-speed rail hydraulic yaw damper with series clearance and stiffness

At high operational speeds, the train system becomes very sensitive to parameter variations of components. Therefore, it is imperative to incorporate more accurate component models in the vehicle dynamics studies. This study addresses a more subtle and comprehensive non-linear parametric model of a high-speed rail hydraulic yaw damper. A new concept of a hydraulic yaw damper model is suggested, in which the small mounting clearance, the series stiffness, and the viscous damping are built in. The series stiffness is the tandem result of the dynamic oil stiffness, the rubber attachment stiffness, and the mounting seat stiffness. A dynamic oil property model is established and coupled to the entire modelling process, in which the density, the dynamic viscosity, the volumetric elastic modulus, and the stiffness of the oil are all changeable in terms of the instantaneous working pressure, the oil temperature, and the entrapped air ratio of the oil. The dynamic flow loss and the valve system dynamics are also incorporated. Experiments validated that the established non-linear parametric model is accurate and robust in predicting the damping characteristics within an extremely wide speed range. The validated damper model was then successfully applied to a thorough parameter sensitivity analysis and damping nature prediction under practical, in-service conditions. The established damper model couples all the main influential factors that are not or are insufficiently considered in normal-speed problems; thus, it will be more accurate and appropriate for furthering high-speed problem studies.     

考虑结点耗能的导管架平台的动力响应分析

为了降低导管架平台的动力响应，可在导管架平台的连接结点之间加入能量耗散材料。本文以将管接点和能量耗散材料理想化为由转动弹簧和转动阻尼器并联组成的等效单元，结合有限元和动力刚度法推导了其刚度、质量和阻尼矩阵。采用复模态分析和虚拟激励法分析了三维导管架平台的动力特性和随机地震响应，讨论了刚度系数和转动阻尼系数对动力特性和减震效果的影响。算例结果表明，适当选择转动阻尼系数可显著增加结构模态阻尼比和降低结构地震响应。此单元可方便地与通用的结构有限元程序配合，对三维平台结构进行动力分析。     

考虑人体耦合作用的结构竖向隔振研究

结构在环境振动或地震作用下的竖向振动不容忽略,有必要采取竖向隔振装置进行减振控制。考虑人体与结构耦合作用后不仅使隔振动力模型更加真实,还可以直接获得人体的动力响应。采用碟形弹簧支座对结构进行基础竖向隔振,并根据国际标准ISO5982规定的不同姿势下的人体动力模型,建立了考虑具有非经典阻尼的人与隔振结构耦合运动方程,利用复模态分析实现了方程的解耦,通过算例分析了竖向隔振以及人体作用对结构响应的影响。结果表明:对于一般的质量和刚度分布均匀的结构,人体对结构具有微弱的减振作用。碟形弹簧支座可以显著地降低结构的竖向振动并改善居住舒适度。     

单自由度超弹性SMA减振结构随机振动控制理论研究

利用形状记忆合金（Shape Memory Alloy,简称SMA）丝的超弹性,提出了一种具有复位功能的阻尼器。在SMA丝的Graesser本构模型基础上,建立了阻尼器恢复力的滑移双线性模型;假定滞回面积相等,提出了恢复力的滑移刚塑性模型以近似简化滑移双线性模型。采用等价线性化法建立了单自由度超弹性SMA减振结构在高斯白噪声激励下的平稳随机振动分析公式。通过一算例,考虑不同激励谱密度和结构阻尼比：比较了等价线性法和蒙特卡罗（Monte Carlo）模拟法计算的结构振动响应（位移标准差和速度标准差）,证明了SMA减振结构随机振动控制理论的有效性;比较了等价线性减振结构和无控结构的动力特性（刚度和阻尼比）和振动响应,说明了SMA阻尼器能提高结构的刚度和阻尼比,因而可有效抑制结构的振动。     

剪切阀式磁流变减振器力学特性实验研究

本文对剪切阀式磁流变减振器的结构和工作原理作了介绍,基于平板模型对其结构进行简化,采用叠加法得出了其阻尼力的理论计算模型。利用材料试验机(MTS)分别在不同电流、振幅、速度和频率等条件下,对自行研制的剪切阀式磁流变减振器的动态特性进行了实验研究,得出了相应的实验曲线。实验结果表明剪切阀式磁流变减振器具有优良的电控阻尼力特性,且振幅、速度和频率等因素对其阻尼力有着重要影响,另外也对其阻尼力的理论计算公式作了验证。     

交错式扇贝阻尼密封动力特性研究

建立交错式扇贝阻尼密封三维数值分析模型,基于动网格及多频椭圆涡动模型研究密封动力特性沿轴向分布规律,计算分析错开角度(α=0°、11.25°、22.5°、33.75°)与密封腔深度(h=2.8、3.3、3.8和4.3 mm)对密封动力特性的影响. 结果表明:上游腔室(C1~C4)具有较大的正直接刚度和有效阻尼,对抑制转子涡动、提升系统稳定性的贡献相对较大. 相对并列式(α=0°)结构,交错式扇贝阻尼密封流体周向速度较小、湍流耗散增加,系统稳定性提升,同时密封泄漏量降低. 错开角度为33.75°时的有效阻尼约为0°时的111%~121%;错开角度为22.5°时的泄漏量相较于0°时约降低了2.11%. 有效阻尼随密封腔深度减小而增大,密封腔深度为2.8 mm时的有效阻尼约为4.3 mm时的146%~211%;密封泄漏量随密封腔深度增大而降低,密封腔深度为4.3 mm时的泄漏量相较于2.8 mm时降低了约3.73%.      

负刚度时滞反馈控制动力吸振器的等峰优化

相比于传统动力吸振器, 负刚度动力吸振器同时具有更好的减振能力和更宽的有效减振频带宽度, 为了进一步降低共振峰幅值, 在负刚度吸振器系统耦合时滞反馈控制. 对负刚度时滞反馈控制动力吸振器系统进行等峰优化设计, 优化设计的准则是:第一和第二共振峰的峰值相等; 同时兼顾两个目标, 一个目标是在优化时的最大共振峰幅值小于被动负刚度吸振器系统的反共振峰幅值, 另一目标是在优化时共振峰幅值与反共振峰幅值差小于被动吸振器系统. 接着, 通过设计和调节负刚度系数、吸振器阻尼系数和时滞反馈控制系数对控制系统进行等峰优化设计. 最后, 在降低幅值的同时, 分析结构参数对有效减振频带宽度的影响. 经过等峰优化之后, 选择本文的一组结构参数与两个典型的模型进行对比. 为了定量比较不同模型的降幅效果, 定义了减幅百分比, 研究发现在有效减振频带区间内减幅百分比超过40%以上. 结果表明, 通过等峰优化准则对结构参数进行优化设计和调节增益系数和时滞量, 共振峰幅值的减幅百分比也近似达到40%, 也可以调节增益系数和时滞量, 使得幅频响应曲线具有较宽的有效减振频带和较低的共振峰幅值与反共振峰幅值的差值.      

Rheological–dynamical analogy: Prediction of damping parameters of hysteresis damper

This research aims to predict the damping parameters of hysteresis damper based on an analytical rheological–dynamical (RDA) visco-elasto-plastic solution of one-dimensional longitudinal continuous vibrations of a bar. A visco-elasto-plastic bar or damper is an energy dissipation device. An attempt is made to estimate quantitatively the influence of material physical parameters of materials on the damping ratio in both the linear visco-elastic analysis and the nonlinear visco-elasto-plastic analysis of damper subjected to external vibration forces. Two types of damping are considered: viscous damping in the case of linear analysis, defined as stiffness and/or mass proportional and, in the case of nonlinear analysis, hysteresis damping caused by inelastic deformations of damper. Owing to the visco-elastic nature of the materials of the damper and the frequency dependence of the viscous damping ratio ξ, it is useful to consider separately the situations arising when ξ is positive (the system is stable) and when it is negative. A negative damping ratio means that the complementary solution of the response would not die away (the system is unstable because of factor e^{ξ · ω · t}). In the case of nonlinear analysis, the force–displacement relation is nonlinear, so it is very difficult to predict the actual damping and stiffness coefficients, even if the force–displacement characteristic is simply perfect elasto-plastic. Using the RDA method, which takes into account the rate of release of visco-elasto-plastic energy of the dissipation devices; nonlinear behaviors are linearized, enabling to obtain the equivalent damping and stiffness coefficients and the effective period for the damper.     

Dynamics and control of an active pendulum system

The work focuses on autoparametric vibrations of system composed of a non-linear oscillator with an attached pendulum. A combination of semi-active damper together with a non-linear spring mounted in the suspension of system is proposed. The spring is made from a shape memory alloy (SMA) while damping is realized through a magnetorheological (MR) damper. The MR damper is used for controlling damping of the system, SMA spring is used to change system׳s stiffness. The system is solved numerically and verified experimentally on a custom made experimental rig. Specifically, non-linear resonances are investigated, and their influence on the system dynamics and absorption effect.     

四种不同约束形式隔板式铅耗能器的试验研究

铅耗能器主要利用金属铅塑性耗能,是一种构造简单、耗能性能优良而又经济的耗能减震元件。本文提出了一种隔板式铅耗能器。根据其构造和耗能原理,设计了四种不同约束形式的耗能元件,并通过EHF-EM电液伺服疲劳试验机进行了低周循环试验,分析了这四种约束形式对隔板式铅耗能器的力学性能与耗能性能的影响,揭示了其耗能机制。研究结果表明:隔板式铅耗能器主要具有屈服位移小、造价低廉、构造简单、工作性能稳定、耗能性能优良的特点,在建筑结构和大型机械减振控制方面具有广泛的应用前景;对比分析表明,其中B型耗能器力学性能尤为优越,耗能能力大且随位移增大刚度增强,同时对结构振动还具有限位功能。     

Dynamics of a spacecraft with large flexible appendage constrained by multi-strut passive damper

This paper is concerned with the dynamics of a spacecraft with multi-strut passive damper for large flexible appendage.The damper platform is connected to the spacecraft by a spheric hinge,multiple damping struts and a rigid strut.The damping struts provide damping forces while the rigid strut produces a motion constraint of the multibody system.The exact nonlinear dynamical equations in reducedorder form are firstly derived by using Kane’s equation in matrix form.Based on the assumptions of small velocity and small displacement,the nonlinear equations are reduced to a set of linear second-order differential equations in terms of independent generalized displacements with constant stiffness matrix and damping matrix related to the damping strut parameters.Numerical simulation results demonstrate the damping effectiveness of the damper for both the motion of the spacecraft and the vibration of the flexible appendage,and verify the accuracy of the linear equations against the exact nonlinear ones.     

电流变阻尼器的动态特性实验研究

设计制造了一种多层滑动极板式电流变阻尼器，使用自制的电流变液，采用正弦激励，进行了这种电流变阻尼器的阻尼特性试验。研究了电流变阻尼器的载荷－位移迟滞特性和载荷－速率迟滞特性，同时研究分析了这种电流变阻尼器的周期能耗特性及等效粘性阻尼特性。结果表明，阻尼器的周期能耗量随外加电场强度的增加而增加，外加电场强度越大，阻尼器的等效阻尼系数越大。阻尼器的阻尼特性体现为库仑阻尼和粘性阻尼的组合，其中随外加电场强度可控的主要是库仑阻尼力，而且库仑阻尼力不仅与外加强度有关，也与阻尼器的运动速度有关。该阻尼器系统是一个强非线性系统，极板间电流变液在低剪切应变率时表现为Bingham塑性流体，在高剪切应变率时流变性态比较复杂，导致载荷－速率迟滞环出现多区域闭合现象。     

基于胡聿贤谱的带支撑广义Maxwell阻尼隔震结构随机响应分析

工程中通过设置支撑将阻尼器和建筑结构连接, 但常为了简化分析, 将支撑的水平刚度看成无穷大, 即不考虑支撑对耗能结构随机地震响应的影响. 实际上, 考虑有限水平刚度的支撑对耗能结构响应的影响更加符合工程实际, 为考虑支撑影响的广义Maxwell耗能隔震结构在胡聿贤谱地震激励下的响应分析, 提出一种求解随机地震响应的简明解析解法. 将带支撑广义Maxwell阻尼器等效本构关系、隔震结构运动方程以及胡聿贤谱滤波方程联合组成非经典阻尼系统, 运用复模态法对该非经典阻尼系统解耦, 通过不同响应模态获得耗能隔震系统系列响应基于白噪声激励的Duhamel积分表达式; 利用Dirac函数的性质, 将系统系列响应协方差简化为无积分运算的表达式, 根据功率谱密度函数与其协方差函数的Wiener-Khinchin关系, 得到耗能隔震系统系列响应功率谱和地面加速度功率谱, 基于随机振动理论中谱矩的定义, 得到耗能隔震系统系列响应0 ~ 2阶谱矩. 算例通过与虚拟激励法对比分析, 验证所提方法在该耗能隔震系统分析的正确性和高效性, 并讨论了不同支撑刚度对阻尼器减震效果的影响.      

Testing and modeling of a CLEMR damper and its application in structural vibration reduction

In this paper, a new kind of combined lead extrusion magnetorheological (CLEMR) damper is proposed. First, tests on CLEMR damper at different currents, excitation amplitudes, and frequencies are carried out. Experimental results show that even when power fails, CLEMR damper can still absorb and dissipate vibration energy of the structure effectively, and its damping force can also be well adjusted in a large range of damping force. Then a mathematical model employing the current, excitation amplitude, and frequency as inputs is proposed and verified by comparing experimental and numerical results. Comparison results show that the proposed model can describe the effects of current, amplitude, and frequency on properties of CLEMR damper. Finally, elastic-plastic dynamic time-history analyses on frame structure with and without CLEMR damper are carried out to evaluate the effectiveness of CLEMR damper in reducing seismic responses of the structures; dynamic responses of the uncontrolled and the controlled structures are then compared. Comparison results show that the displacement responses of each floor of the controlled structure, as well as the number of the cracking point and yielding point of the member, reduce significantly, which implies that the proposed CLEMR damper holds promise in reducing and suppressing the vibration responses of the civil structures.     

架空输电线防振锤阻尼特性实验研究

本文利用梁的振动理论对防振锤的阻尼特性进行研究。通过正弦激励下的共振驻留法,分别对不同型号以及同种型号不同锤头质量的防振锤进行振动实验,应用能量平衡原理得到了防振锤的阻尼特性曲线,分析了不同模态响应在阻尼耗能中的贡献。考虑不同类型阻尼对于减振性能的作用,在Lazan阻尼假设的基础上,利用经验公式推导了阻尼系数计算公式。结果表明,钢绞线变形大小直接影响防振锤的阻尼值大小;阻尼对减小共振频率附近的受迫振动幅值作用明显,验证了防振锤的减振性能;同时锤头质量的变化可以影响阻尼曲线的变化。以上结论可为防振锤的防振设计和应用提供参考。     

基于加速度响应控制时MTMD的地震特性

研究了由多个刚度和阻尼保持为常量且频率呈线性分布的TMD形成的MTMD的地震特性。基于虚拟激励法和Kanai Tajimi及Clough Penzien地震谱 ,建立了结构 MTMD系统的加速度传递函数 ,进而导出了设置MTMD时结构的加速度动力放大系数 (ADMF)明确表达式。于是MTMD的优化准则选择为 :结构最大加速度动力放大系数的最小值的最小化 [Min .Min .Max .ADMF]。通过最优搜寻得MTMD的最优频率间隔、平均阻尼比、调谐频率比和相应的控制有效性指标。选择结构受控频率与地震卓越频率比的不同取值 ,研究地震卓越频率对MTMD最优参数及有效性的影响     

Behavior explanation and a new model for nonlinear viscous fluid dampers with a simple annular orifice

Viscous fluid dampers have been used in many building and bridge construction projects for earthquake damage mitigation. Previous study has shown that silicone oil properties, such as the fluid shear-thinning and relaxation effects, play important roles for the annular-orificed fluid damper behavior, and the Navier-Stokes equations based on these mechanisms were developed. In the current study, attempts are made to explain the effects of frequency, damper dimensions, and viscosity of silicone oil on the damper stiffness behavior using the developed equations. It is found that the developed equations successfully explain the observed phenomena. To avoid the complicated fluid dynamics analyses for damper parameters, such as the damping factor and the velocity power exponent, a new four-parameter equation considering both the fluid shear-thinning and stiffness effects, with a form similar to the widely used two- or three-parameter equation is proposed. The results of the new model successfully capture the damper behavior both at low and high frequencies and show an advantage that better consistent results can be obtained in the velocity range for the building and bridge applications.     

Fluid formulae for damping changeability conceptual design of railway semi-active hydraulic dampers

Damping changeability design and evaluation is the most fundamental issue at the beginning of any new railway semi-active hydraulic damper development. Therefore, physical fluid mechanics for the calculation of basic structure and resistance parameters of the damper should be carefully studied in the conceptual phase. Fluid formulae for changeable damping performance evaluation of two commercial railway semi-active hydraulic dampers are established. Simulation results show that the damper switched by high-speed solenoid valves obtains a wide range of changeable damping coefficients, which guarantees the absorption of a wide spectrum of vibrations; however, a different low cost damper regulated with an inversely proportional relief valve, whose Force-velocity characteristics share the same rising curve, is relatively limited in damping ability. In order to overcome the drawback of the latter one with no obvious cost increase, a new semi-active hydraulic damper which is regulated by a simple proportional throttle valve is proposed. Continued fluid formulation and simulation suggests that the damper can change its damping force rising curves or “effective” damping coefficients continuously, within a considerably wide range. Thus, fluid formulae explicitly established in this study are of significance in the damping changeability conceptual design, further refinement and control design for the three semi-active hydraulic dampers. The proposed new damper, which has both a simple configuration and an easy-to-control ability, might be feasible for industry applications.     

表面织构对界面接触参数影响的实验研究

机械接触表面的接触刚度和接触阻尼是直接影响界面振动水平的两个重要动力学参数。本文介绍了一种测试机械连接界面接触刚度和接触阻尼的实验装置和方法,并针对用两种不同加工方法(激光加工及线切割)加工出的具有不同尺寸织构的试样与光滑平面相接触的界面进行了测量,初步探索了平面接触刚度和接触阻尼的表面织构效应,并得出结论：织构及润滑对接触刚度会产生一定影响,而实验中均未观察到这两者对接触阻尼有明显影响。