Inner mass impact damper for attenuating structure vibration

The behaviors of a vibration system suppressed with an impact damper are investigated, where the impact damper is simplified as a combination of spring and viscous damping. The analytical theory for the optimal impact control algorithms for impact damper is developed, and the accurate expressions are derived for the optimal values of the impact damper damping and initial displacement in a single-degree-of-freedom structure. The relation between coefficient of restitution and impact damping ratio is obtained. The investigation shows that the effective reduction of the vibration response is nearly independent of the number of impacts, but primarily related to the type of collision which the impact mass collides with the main mass face-to-face. This theory is generalized to continuous structures. An example of an impact damper in a rotating cantilever beam demonstrates that the impact dampers are suitable for attenuating the impulse response of structures unconditional stable without the requirement of the accuracy of the modal information.     

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 ordina...     

质量阻尼器的发展

广泛评述了调谐质量阻尼器(TMD)、多重调谐质量阻尼器(MTMD)、主动质量阻尼器(AMD)、半主动 TMD(SATMD)、主动调谐/主被动调谐/混合质量阻尼器(ATMD/APTMD/HMD)的研究现状.TMD, MTMD, AMD, SATMD, ATMD/APTMD/HMD能够有效地减小结构的风振与地震反应.指出强震下结构设置TMD, MTMD, AMD, SATMD, ATMD/APTMD/HMD的主要目的是限制结构屈服的进一步发展.因此,基于非线性结构模型的TMD, MTMD, AMD, SATMD, ATMD/APTMD/HMD研究具有重要意义.指出了TMD, MTMD, AMD, SATMD, ATMD/APTMD/HMD 有待于进一步研究的若干问题.提出了结构主动多重调谐质量阻尼器(AMTMD)和多重主被动调谐质量阻尼器(MAPTMD)的新控制策略.介绍了AMTMD和MAPTMD的研究进展并指出了进一步研究的发展方向.      

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。     

Transient dynamics,damping, and mode coupling of nonlinear systems with internal resonances

In this paper, we study and compare performance and robustness of linear and nonlinear Lanchester dampers. The linear Lanchester damper consists of a small mass attached to a primary system through a linear dashpot, whereas the nonlinear Lanchester damper is linked to the primary mass through dry friction forces. In each case, we propose a semi-analytical method for computing the frequency response, for different values of the design parameters, in order to evaluate the performance and robustness of the two kinds of damper. Overall, it is shown that linear Lanchester dampers perform better than nonlinear damper both in terms of attenuation and robustness. Moreover, the nonlinear frequency response curves, that include the intrinsic non-smooth nature of the friction force, may serve as reference curve for further numerical studies.

     

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.     

Nonlinear dynamics of mistuned bladed disks with ring dampers

In turbomachinery applications, rotating bladed disks (blisks) are often subject to high levels of dynamic loading, such as traveling wave excitations, which result in large response amplitudes at resonance. To prevent premature high cycle fatigue, various dry friction dampers are designed for blisk systems to reduce the forced responses. Ring dampers are located in the disk, underneath the blades, and are held in contact with the blisk by centrifugal loading. Energy is dissipated by nonlinear friction forces when relative motions between the ring damper and the blisk take place. To investigate the dynamic responses of blisk–damper systems in the presence of the nonlinear frictional contacts, conventional methods based on numerical time integration are not suitable since they are computationally expensive. This paper presents a reduced-order modeling technique to efficiently capture the nonlinear dynamic responses of the blisk–damper systems. Craig–Bampton component mode synthesis (CB-CMS) serves as the first model reduction step. A novel mode basis that mimics the contact behavior under sliding and sticking conditions is developed to further reduce the CB-CMS model while maintaining its accuracy. The resulting reduced nonlinear equations of motion are solved by a hybrid frequency/time domain (HFT) method. In the HFT method, the contact status and friction forces are determined in the time domain by a three-dimensional contact model at each contact point, whereas the reduced equations of motion are solved in the frequency domain according to a harmonic balance formulation. Moreover, to investigate the effects of blade mistuning, which can lead to drastic increase of forced responses, an extension of the reduced-order models (ROMs) is developed based on component mode mistuning. Forced responses computed by the proposed ROMs are validated for both tuned and mistuned systems. A statistical analysis is performed to study the effectiveness of ring dampers under random blade mistuning patterns.     

MR减振驱动器用于结构振动控制的算法研究

提出了四种半主动控制算法 ;针对安装有MR减振驱动器的三层剪切型结构仿真分析了各种半主动控制算法和被动控制策略的控制效果。仿真分析结果表明 ,MR减振驱动器作为一种半主动控制装置可以有效地控制结构的反应 ;施加最大磁场作为被动控制装置时 ,也对结构反应有很好的控制效果     

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.     

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。     

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.     

桥梁多模态耦合抖振控制方法研究

目前已证实调谐质量阻尼器(TM D)可以有效控制桥梁抖振响应,并已在工程中得到应用。然而,传统桥梁抖振被动控制理论是基于单模态叠加SRSS法,无法考虑多模态参与作用和模态间气动耦合效应,本文基于Scan lan多模态耦合抖振理论和多重调谐质量阻尼器(M TM D)被动控制理论,提出一种桥梁多模态耦合抖振M TM D控制方法,该方法可以考虑多模态参与作用、模态间气动耦合效应和单模态中各模态位移分量的气动耦合,且对各TM D在主梁上的安装位置没有任何限制。本文最后采用时域仿真方法对该方法进行了验证,两者计算结果吻合良好,表明本文所提出的方法的正确性。     

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.      

The effect of underplatform dampers on the forced response of bladed disks by a coupled static/dynamic harmonic balance method

Friction contacts are often used in turbomachinery design as passive damping systems. In particular, underplatform dampers are mechanical devices used to decrease the vibration amplitudes of bladed disks.Numerical codes are used to optimize during designing the underplatform damper effectiveness in order to limit the resonant stress level of the blades. In such codes, the contact model plays the most relevant role in calculation of the dissipated energy at friction interfaces. One of the most important contact parameters to consider in order to calculate the forced response of blades assembly is the static normal load acting at the contact, since its value strongly affects the area of the hysteresis loop of the tangential force, and therefore the amount of dissipation.A common procedure to estimate the static normal loads acting on underplatform dampers consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to get the static contact/gap status to use in the calculation, assuming that it does not change when vibration occurs.In this paper, a novel approach is proposed. The static and the dynamic displacements of the system (bladed disk+underplatform dampers) are coupled together during the forced response calculation. Static loads acting at the contacts follow from static displacements and no preliminary static analysis of the system is necessary.The proposed method is applied to a numerical test case representing a simplified bladed disk with underplatform dampers. Results are compared with those obtained with the classical approach.     

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.     

斜拉索振动控制中MR阻尼器选型的研究

以全索全时段振动响应的均方根(RMS)评价MR阻尼器对斜拉索的减振效果。计算结果表明MR阻尼器型号是影响斜拉索减振效果的最主要因素。斜拉索的减振效果在选用合适的MR阻尼器时达到最佳。进而研究了MR阻尼器型号与阻尼器安装位置、施加的电压、斜拉索基频(张力、索长、质量)、激励荷载(类型、频率、幅值)等各种因素的关系,为MR阻尼器合理选型提供了优化设计的方法。型号选用主要是与斜拉索基频和MR阻尼器安装位置有关。在引起索基频变化的因素中,索质量对型号的选取影响最大;而索长对型号影响不大。对于索质量较大、张力较大、MR阻尼器安装位置较低、外界激励较大、频谱特征多变、低频为主时需要较强的MR阻尼器。进一步研究表明,半主动控制与开环控制的最优MR阻尼器型号有较好的一致性,因此半主动控制所选用的MR阻尼器型号可参照被动控制时最优MR阻尼器型号。     

Dynamic properties of automotive damper modules

This paper addresses the dynamic properties of automotive shock absorber modules. Analyzing an equivalent linear system, a set of characteristic dimensionless numbers are introduced in order to qualify the dynamic performance of the damper and the damper module. The dependency of these numbers on the main parameters of the module like the damping constant, the spring stiffness of the damper, the top mount stiffness and the piston rod mass is shown. These numbers may also serve as similarity coefficients for quite different dampers regarding their dynamic behavior. Furthermore, they can be used to adjust the stiffness of the different force elements of the damper module to achieve an optimal damping quality.     

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.     

A novel scheme for nonlinear displacement-dependent dampers

In this paper, a novel scheme for nonlinear displacement-dependent (NDD) damper is introduced. The damper is attached to a simple mass-spring-damper vibration system. The vibration system equipped with a NDD damper is mathematically modeled and the nonlinear governing differential equation of the system is derived. To obtain the displacement of the system, the approximate analytical solution of the governing equation is elaborated using the multiple scales method. The advised approximate analytical algorithm is performed for several case studies and is also verified by the numerical fourth-order Runge?CKutta method. In addition, the performance of the NDD damper is analyzed and compared with the performance of the traditional linear damper. It is found that the proposed NDD damper scheme along with the multiple scales method is not only feasible for vibration reduction but also yields satisfactory response performance rather than the existing traditional linear damper.     

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。