任意荷载作用下液体粘滞阻尼器在桥梁工程中减震作用探讨

在桥梁工程中，当需要限制梁端的碰撞或过大的相对位移，经常会在梁端设置液体粘滞阻尼器。由于技术原因，液体粘滞阻尼器在桥梁设计中的参数选取基本上是通过全桥模型的地震非线性时程分析得到的。而在寿命期内，桥梁需要承受各种随机荷载，在具有不同力学特性荷载的激励作用下引起梁端纵向大的响应时，液体粘滞阻尼器是否始终起有利的减震作用，一直困扰着其在桥梁工程中的实践。在液体粘滞阻尼器力学特性研究的基础上，通过矩阵变换得到关于阻尼器的局部动力方程，从变形和受力两个方向对此问题进行探讨，得到液体粘滞阻尼器对于梁端的相对位移、相对速度、相对加速度均有减震作用。但不会得出始终对所有构件的受力有利的结论，并进行了验证。     

Nonlinear modeling and experimental characterization of hydraulic dampers: effects of shim stack and orifice parameters on damper performance

A nonlinear model of monotube hydraulic dampers is presented with an emphasis on the shim stack properties and their effects on the overall damper performance. There has been no published detailed analysis of the effects of shim stack design in a hydraulic damper to date. Other damper models have used simplifying assumptions for the shim stack deflection and effects of the shim stack have not been completely studied. Various parameters affecting the nonlinear characteristics of monotube dampers such as the hysteresis region are studied. The model presented in this paper can be used for design purposes and helps in developing controllable valvings based on shim stacks. It can also be used to design controllable bypasses in hydraulic dampers. The mathematical model is validated by comparison against experimental test results carried out on an OHLINS CCJ 23/8 monotube damper, in CVeSS test facilities.     

高速铁路连续箱型梁桥的动力响应与减振分析

根据列车具体的轴距和轴重,建立了和谐号动车组CRH380AL型列车简化模型;对高速铁路两跨连续梁桥采用多自由度欧拉伯努利梁单元进行主梁的模拟,并将液体黏滞阻尼器模拟为有限元阻尼单元;采用Newmark直接积分方法求解了高速列车作用下的连续梁桥运动方程,数值分析了列车车速以及液体黏滞阻尼器的阻尼系数对于高速铁路连续梁桥振动响应的影响。结果表明:黏滞阻尼器对于桥梁具有明显的减振效果,阻尼力不仅与阻尼系数有关还与列车时速有关;同一黏滞阻尼器条件下,桥梁的最大加速度并不随列车速度的增加而单调增加,而是在某些特定列车车速下桥梁的最大加速度出现了峰值,且随着黏滞阻尼器的阻尼系数增大,桥梁振动响应峰值处的最大加速度减幅不同;同一列车时速的条件下,桥梁的减振效果并不是随着阻尼系数的递增呈正比递增,而是随着阻尼系数的增大,阻尼器的减振效果增幅在减小。     

Design and mechanical characteristics analysis of a new viscous damper for piping system

In this paper, the design of a new viscous damper is presented and its mechanical characteristics are investigated experimentally. The motion equation of a system consisting of a drop machine and the damper is set up. By numerically simulating this equation, the curve of the damper cavity generatrix is obtained on the assumption that the resisting force is constant. Then the new damper with big capacity and high-energy dissipation rate is designed. Drop tests using this damper and a Pro225-damper bought in the market are performed, respectively. On one hand, the experimental resisting forces of the new damper approximate constants, which illustrates that the simulation is viable. On the other hand, some advantages of the new damper over the Pro225-damper are found.     

Suppression of multiple modal resonances of a cantilever beam by an impact damper

Impact dampers are usually used to suppress single mode resonance. The goal of this paper is to clarify the difference when the impact damper suppresses the resonances of different modes. A cantilever beam equipped with the impact damper is modeled. The elastic contact of the ball and the cantilever beam is described by using the Hertz contact model. The viscous damper between the ball and the cantilever beam is modeled to consume the vibrational energy of the cantilever beam. A piecewise ordinary differential-partial differential equation of the cantilever beam is established, including equations with and without the impact damper. The vibration responses of the cantilever beam with and without the impact damper are numerically calculated. The effects of the impact absorber parameters on the vibration reduction are examined. The results show that multiple resonance peaks of the cantilever beam can be effectively suppressed by the impact damper. Specifically, all resonance amplitudes can be reduced by a larger weight ball. Moreover, the impacting gap is very effective in suppressing the vibration of the cantilever beam. More importantly, there is an optimal impacting gap for each resonance mode of the cantilever beam, but the optimal gap for each mode is different.     

流体阻尼器中粘性发热的反馈作用与热平衡研究

主要针对长阻尼孔形式下的流体阻尼器进行分析,在三参数模型的基础上研究了流体粘性发热对流体阻尼力的反馈作用,从而建立了含热能转换与热交换的阻尼器的动力学模型,同时对系统的热平衡状态进行了分析。最后通过数值分析对该时变系统从时域和频域上讨论了粘性发热对隔振效果的影响,发现温度变化对共振频率的漂移及幅值大小的影响较大。     

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.     

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.     

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.     

Analytical investigation of an SDOF building structure equipped with a friction damper

The purpose of this study is to investigate analytically a single-degree-of-freedom (SDOF) building structure equipped with a friction damper for assessing its vibration control effect. Friction dampers are installed between stories to reduce inter-story displacements of building structures subjected to external loading. They are in general regarded to generate damping forces characterized by Coulomb damping, of which the directions are opposite to the inter-story velocities of building structures. Hence, the building structure model with friction dampers can be represented by a mass-spring-viscous-Coulomb damping system. The building response reduction as a result of damper installation can be provided by observing the damping ratio rather than the friction force contributed by the dampers. Since a large friction damper force is required to attenuate the response of the building due to strong excitation, friction force ratio is directly related to building response reduction, which is the friction force of the damper versus external force. Therefore, damping and friction force ratios are key parameters, playing a main role in selecting an optimal friction damper, which satisfies target response reduction. This study first identifies an SDOF building structure installed with a friction damper for free vibration with initial conditions. A?closed-form expression of normalized displacement is derived in terms of friction force ratio in the time domain. Peak and valley of displacements are also found and then the time when the structure stops is derived with recursive interval number. This study is extended to identify steady-state vibration of the structure by deriving closed-form solution in case of resonance in terms of friction force ratio. Then, the dissipated energy balance is identified for both free and steady-state vibrations. Finally, equivalent viscous damping ratios are derived by using friction force ratio based on dissipated energy balance equation. The derived equations in terms of viscous damping ratio and friction force ratio can provide insight to design a friction damper for reducing structural displacement under external loadings.     

Rheology and dynamics of repulsive clathrates

The physical and thermodynamic properties of a repulsive clathrate used as a working body for the dissipation, storage, and conversion of energy in thermomechanical systems are studied. In repulsive clathrates, use is made for the first time of the molecular repulsive forces acting in large interfacial areas in a system consisting of a fluid and a capillary-porous matrix not wetted by this fluid. Based on experimental studies of a car damper with a repulsive clathrate, a rheological model of energy dissipation was developed which can be used to design compact high-performance dampers for different purposes and anti-seismic systems of new generation.     

阻尼耗能减振框架结构地震作用振动方程求解及地震反应分析Calculation of vibration equation and analysis of seismic response for damping energy dissipation frame structure

研究了设置耗能阻尼器框架的地震作用振动方程求解及该结构的地震反应。框架结构设置耗能阻尼器后，振动方程的阻尼矩阵不再对振型具有正交性，本文对该振动方程给出了状态方程直接积分法，并与传统强制解耦法进行了比较分析，结果表明强制解耦法对结构第一阶振动反应求解偏差较小，而对于高阶振动反应差别较大，并且强制解耦法高估了阻尼器的减震效果。继而采用状态方程直接积分法对设置有粘滞阻尼器的框架结构进行了地震反应分析，探讨了阻尼器位置对框架结构地震反应的影响，结果表明设置有阻尼器的楼层减振效果明显，未设置阻尼器的楼层减振效果差别较大，甚至有可能出现楼层层间侧移增大的现象，由此提出耗能阻尼器应在结构中合理设置。     

A direct experimental–numerical method for investigations of a laboratory under-platform damper behavior

Under-platform dampers are commonly adopted in order to mitigate resonant vibration of turbine blades. The need for reliable models for the design of under-platform dampers has led to a considerable amount of technical literature on under-platform damper modeling in the last three decades.Although much effort has been devoted to the under-platform damper modeling in order to avail of a predictive tool for new damper designs, experimental validation of the modeling is still necessary. This is due to the complexity caused by the interaction of the contacts at the two damper-platform interfaces with the additional complication of the variablity of physical contact parameters (in particularly friction) and their nonlinearity. The traditional experimental configuration for evaluating under-platform damper behavior is measuring the blade tip response by incorporating the damper between two adjacent blades (representing a cyclic segment of the bladed disk) under controlled excitation. The effectiveness of the damper is revealed by the difference in blade tip response depending on whether the damper is applied or not. With this approach one cannot investigate the damper behavior directly and no measurements of the contact parameters can be undertake. Consequently, tentative values for the contact parameters are assigned from previous experience and then case-by-case finely tuned until the numerical predictions are consistent with the experimental evidence. In this method the physical determination of the contact parameters is obtained using test rigs designed to produce single contact tests which simulate the local damper-platfom contact geometry. However, the significant limitation of single contact test results is that they do not reveal the dependence of contact parameters on the real damper contact conditions. The method proposed in this paper overcomes this problem.In this new approach a purposely developed test rig allows the in-plane forces transferred through the damper between the two simulated platforms to be measured, while at the same time monitoring in-plane relative displacements of the platforms. The in-plane damper kinematics are reconstructed from the experimental data using the contact constraints and two damper motion measurements, one translational and one rotational. The measurement procedures provide reliable results, which allow very fine details of contact kinematics to be revealed. It is demonstrated that the highly satisfactory performance of the test rig and the related procedures allows fine tuning of the contact parameters (local friction coefficients and contact stiffness), which can be safely fed into a direct time integration numerical model.The numerical model is, in turn, cross-checked against the experimental results, and then used to acquire deeper understanding of the damper behavior (e.g. contact state, slipping and sticking displacement at all contact points), giving an insight into those features which the measurements alone are not capable of producing. The numerical model of the system is based on one key assumption: the contact model does not take into account the microslip effect that exists in the experiments.Although there is room for improvement of both experimental configuration and numerical modeling, which future work will consider, the results obtained with this approach demonstrate that the optimization of dampers can be less a matter of trial and error development and more a matter of knowledge of damper dynamics.     

DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.     

汽车液压阻尼器的四段线性化模型

通过对现有某车用液压阻尼器的实验研究和车辆悬架系统动力学仿真研究，发现这种阻尼器的动力学特性存在复杂的非线性行为。为准确描述这类阻尼器的动力学特性和进行汽车悬架系统的动力学仿真研究，本文根据阻尼器的实验数据，提出一种新型四段线性化阻尼器模型，并建立其相应的数学模型。通过汽车悬架系统的动力学仿真研究表明，采用四段线性化阻尼器模型，汽车悬架系统簧载质量在不同路面不平度函数作用下的加速度响应和均方根加速度响应随频率变化不会出现大的波动。与等效线性化阻尼器模型相比，四段线性化阻尼器模型，能较好降低汽车悬架系统簧载质量的加速度响应和均方根加速度响应，有利于提高汽车乘坐舒适性和行驶稳定性，并为新型阻尼器设计提供一个新的思路。     

结构振动的滑模变结构半主动控制

研究应用磁流变阻尼器(MRD)对结构振动半主动控制的算法和原理。研制并对磁流变阻尼器进行了阻尼特性实验，采用非线性滞回双粘性模型描述磁流变阻尼器的阻尼特性，模型结果与实验结果非常一致。采用滑模控制算法和趋近律方法设计了半主动控制器。利用滑模控制方法所建立的控制器，本文给出了地震激励下结构振动半主动控制算例。计算分析表明，半主动滑模控制具有控制效果明显、鲁棒性好等优点，是一种非常有发展前途的控制方法。     

An analytical approach to optimally design of electrorheological fluid damper for vehicle suspension system

This work develops an analytical approach to optimally design electrorheological (ER) dampers, especially for vehicle suspension system. The optimal design considers both stability and ride comfort of vehicle application. After describing the schematic configuration and operating principle of the ER damper, a quasi-static model is derived on the basis of Bingham rheological laws of ER fluid. Based on the quasi-static model, the optimization problem for the ER damper is built. The optimization problem is to find optimal value of significant geometric dimensions of the ER damper, such as the ER duct length, ER duct radius, ER duct gap and the piston shaft radius, that maximize damping force of the ER damper. The two constrained conditions for the optimization problem are: the damping ratio of the damper in the absence of the electric field is small enough for ride comfort and the buckling condition of the piston shaft is satisfied. From the proposed optimal design, the optimal solution of the ER damper constrained in a specific volume is obtained. In order to evaluate performance of the optimized ER damper, simulation result of a quarter-car suspension system installed with the optimized ER damper is presented and compared with that of the non-optimized ER damper suspension system. Finally, the optimal results of the ER damper constrained in different volumes are obtained and presented in order to figure out the effect of constrained volume on the optimal design of ER damper.     

高速铁路连续梁桥的共振响应与振动控制研究

以液体粘滞阻尼器为振动控制外部装置，主桥采用欧拉伯努利梁，通过中国和谐号动车组CRH380AL、日本新干线Shinkansen700和欧洲高速列车HSLMA8三种不同类型的高速列车对比，模拟分析了高速列车作用下桥梁结构共振响应的影响因素，以及粘滞阻尼器的阻尼系数与安装位置对桥梁结构振动响应的减振效果。研究结果表明，（1）合理有效地布置列车荷载轴距，可使桥梁结构发生基频共振的列车时速在运营时速之外，避免了桥梁结构发生较大振动峰值响应，即桥梁结构的基频共振；（2）随着粘滞阻尼器阻尼系数的增大，桥梁的加速度峰值在列车不同时速下均在减少，对桥梁振动有着不同程度的减振效果；（3）通过合理安置液体粘滞阻尼器，可有效降低高速列车作用下桥梁结构的共振响应；（4）随着粘滞阻尼器与主梁的连接点位置逐渐远离支座，粘滞阻尼器的减振效果逐渐明显；（5）随着粘滞阻尼器与桥台的连接点位置逐渐靠近支座，粘滞阻尼器的减振效果略有提升，但不明显。     

粘滞阻尼器减震结构非线性随机振动的时域显式降维迭代随机模拟法

粘滞阻尼器在大型复杂结构减震设计中应用广泛。由于粘滞阻尼器的非线性阻尼力特性,粘滞阻尼器减震结构非平稳随机地震反应分析是一个典型的局部非线性随机振动问题。利用减震结构动力响应时域显式表达式的降维列式优势,仅针对与粘滞阻尼器相关的局部自由度进行非线性迭代计算,提出了局部非线性随机振动问题的时域显式降维迭代随机模拟法,为设置粘滞阻尼器的大型复杂减震结构非线性地震反应分析提供一种高效的随机振动方法。以安装了四个纵桥向粘滞阻尼器的某主跨1200m悬索桥为工程实例,开展E2水准地震激励下的非线性随机振动分析。计算结果显示,设置阻尼器后,主梁的纵桥向位移得到明显控制,降幅达到80%,大桥的关键截面内力也有5%左右的降幅。     

Low-frequency model of a granular medium saturated with a viscous fluid

A mathematical model of a granular medium saturated with a viscous homogeneous fluid is constructed. The steady-state one-dimensional oscillations of cylindrical granules and an incompressible fluid under the action of a plane sonic wave whose length is significantly greater than the cell dimensions are investigated. The steady-state flow of the medium across the cell cross-section and the mean fluid velocity (Darcy’s law) are determined by means of passages to the limits with respect to the frequency and granule mass. The expressions obtained for the soil permeability coefficient under the action of a gravitational hydraulic head are compared with the representations of other authors.