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.      

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。     

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。     

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.     

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.     

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.     

复合干摩擦的准零刚度隔振系统的亚谐共振

利用增量平均法研究了复合干摩擦阻尼器的准零刚度非线性隔振系统在外部简谐激励作用下的1/3次亚谐共振. 首先利用平均法得到了复合干摩擦的准零刚度隔振系统的主共振近似解析解, 然后在系统主共振近似解析解的基础上将系统的亚谐共振响应看作增量, 并利用平均法得到了准零刚度隔振系统的亚谐共振近似解析解. 利用李雅普诺夫方法得到了准零刚度隔振系统主共振和亚谐共振稳态解的稳定性条件, 并推导了系统1/3次亚谐共振的存在条件. 根据近似解析解分别得到了复合干摩擦的准零刚度隔振系统的主共振和亚谐共振力传递率. 利用数值解验证了准零刚度隔振系统主共振和亚谐共振近似解析解的准确性. 利用系统的近似解析解详细分析了准零刚度参数和干摩擦力对系统主共振和亚谐共振的幅频响应以及力传递特性的影响. 分析结果表明, 通过选取合适的干摩擦力参数, 可以消除准零刚度隔振系统在主共振区域的亚谐共振. 通过复合干摩擦阻尼器不但可以提高准零刚度隔振系统在低频区域的振幅抑制效果, 而且可以降低准零刚度隔振系统的起始隔振频率, 但是会增大系统在有效隔振频带内的力传递率.      

Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation

The nonlinear behaviors and vibration reduction of a linear system with a nonlinear energy sink(NES)are investigated.The linear system is excited by a harmonic and random base excitation,consisting of a mass block,a linear spring,and a linear viscous damper.The NES is composed of a mass block,a linear viscous damper,and a spring with ideal cubic nonlinear stiffness.Based on the generalized harmonic function method,the steady-state Fokker-Planck-Kolmogorov equation is presented to reveal the response of the system.The path integral method based on the Gauss-Legendre polynomial is used to achieve the numerical solutions.The performance of vibration reduction is evaluated by the displacement and velocity transition probability densities,the transmissibility transition probability density,and the percentage of the energy absorption transition probability density of the linear oscillator.The sensitivity of the parameters is analyzed for varying the nonlinear stiffness coefficient and the damper ratio.The investigation illustrates that a linear system with NES can also realize great vibration reduction under harmonic and random base excitations and random bifurcation may appear under different parameters,which will affect the stability of the system.     

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。     

On some performance characteristics of base excited vibration isolation systems with a purely nonlinear restoring force

Base excited vibration isolation systems with a purely nonlinear restoring force and a velocity nth power damper are considered. The restoring force has a single-term power form with the exponent that can be any non-negative real number. Approximations for the steady-state response at the frequency of excitation are obtained by using the Jacobi elliptic function with a changeable elliptic parameter and by applying an elliptic averaging method. The relative and absolute displacement transmissibility of this system are analysed. These performance characteristics are expressed in terms of the damping parameters, but they are also determined for an arbitrary non-negative real power of geometric nonlinearity, which represent new and so far unknown results. Some examples illustrating the effect of the system parameters on these performance characteristics are also presented.     

Dynamic analysis and performance evaluation of nonlinear inerter-based vibration isolators

This paper investigates a nonlinear inertance mechanism (NIM) for vibration mitigation and evaluates the performance of nonlinear vibration isolators employing such mechanism. The NIM comprises a pair of oblique inerters with one common hinged terminal and the other terminals fixed. The addition of the NIM to a linear spring-damper isolator and to nonlinear quasi-zero-stiffness (QZS) isolators is considered. The harmonic balance method is used to derive the steady-state frequency response relationship and force transmissibility of the isolators subjected to harmonic force excitations. Different performance indices associated with the dynamic displacement response and force transmissibility are employed to evaluate the performance of the resulting isolators. It is found that the frequency response curve of the inerter-based nonlinear isolation system with the NIM and a linear stiffness bends towards the low-frequency range, similar to the characteristics of the Duffing oscillator with softening stiffness. It is shown that the addition of NIM to a QZS isolator enhances vibration isolation performance by providing a wider frequency band of low amplitude response and force transmissibility. These findings provide a better understanding of the functionality of the NIM and assist in better designs of nonlinear passive vibration mitigation systems with inerters.     

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。     

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.     

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.     

Transition sets analysis based parametrical design of nonlinear metal rubber isolator

This research proposes the parametrical design of Metal Rubber (MR) isolation platform based on the investigation of nonlinear vibration properties under different types of excitation. Based on the mechanical model established by experiments, the restoring force of the isolation platform is proposed as a nonlinear function in consideration of the stiffness nonlinearity and Coulomb friction of metal wires. Then, the perturbation method is utilized to solve the steady states whose local stability is studied by singularity theory. The main results obtained by singularity theory show that there are five different types of vibration property, and the critical conditions for the transformation of different vibration properties are defined by transition sets. For impact excitation, the optimum structural parameters are obtained based on the vibration dissipation time via nonlinear backbone analysis; for periodic excitation, the optimum structural parameters are determined according to multiple standards including the bandwidth for effective isolation, bandwidth for multi-steady states, resonance peak and displacement transmissibility in high frequency band etc. The vibration performances for optimum structural parameters are verified by dynamical experiments. In conclusion, this paper carries out a novel sight of choosing optimum parameters, and therefore provides the guidance for the utilization of MR isolation platform for different types of excitation in engineering practices.     

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.     

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.     

Application of non-linear damping to vibration isolation: an experimental study

In a previous study, the authors have proved that in theory the introduction of a cubic non-linear damping can produce ideal vibration isolation such that the system force transmissibility over the resonant frequency region is modified, but the transmissibility over the non-resonant regions remain unaffected. The present study is concerned with both an experimental verification of this theoretical finding and the selection of the cubic damping characteristic parameter required to achieve a desired performance for a single degree of freedom vibration isolation system. These results provide an important basis for the design and practical application of non-linearly damped vibration isolation systems in engineering practice.     

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。