斜拉桥塔-索-桥面耦合参数振动模型及响应分析

针对大跨度斜拉桥拉索与桥塔、桥面的协同振动问题,考虑拉索垂度、阻尼、倾角以及重力弦向分力的影响,引入拉索高精度抛物线形,建立了桥塔-索-桥面连续非线性精细化振动模型,推导了桥塔和桥面共同激励作用下斜拉索耦合振动方程,对比分析了2种激振模式下斜拉索的参数振动特性,并编制程序研究了桥面与拉索的频率比、桥面激励幅值、索力及阻尼对结构耦合振动特性的影响规律。结果表明：桥面与拉索频率比对系统振动的影响较大,频率比为1:2和2:1时拉索均产生强烈振动,但2:1激振模式下拉索振幅更大,达到共振时间较长;随着桥面激励幅值的增大,2:1亚谐波共振模式下的拉索振幅增长速率更快;拉索振幅随索力的增大呈非线性减小趋势;斜拉索阻尼超过2%时,继续提高自身阻尼不能有效减小其振动幅值,需要通过设置附加阻尼才能更好地抑制其振动。     

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.     

考虑阻尼影响时结构动载荷问题的冲击计算

在考虑阻尼影响的基础上,采用线性振动理论研究了动载荷问题的冲击计算. 利用振动方程推导出了结构动位移、动载荷系数、冲击时间的表达式,并讨论分析了结构阻尼对动载荷问题的影响.     

FREQUENCY-SHAPING LQR CONTROL OF WHOLE-SPACECRAFT VIBRATION ISOLATION PLATFORM BASED ON MR DAMPER1)

设计磁流变六杆隔振平台,以改善星箭界面低频振动环境.采用牛顿-欧拉法建立整星隔振平台动力学模型,利用固定界面模态综合法得到卫星和隔振平台动力学模型.由于星箭界面低频振动环境在特定频段存在振动量级较大的问题,采用频域加权LQR (linear quadratic regulator)方法,利用直接分解法扩展系统状态变量,进行磁流变阻尼器半主动控制系统设计.仿真结果表明,相对传统控制方法,频域加权LQR方法在特定频段减振效果明显改善,且在其他频段没有恶化,验证了算法有效性.     

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。     

NEURAL NETWORK MODEL OF MAGNETORHEOLOGICAL DAMPER FOR VIBRATION ISOLATION PLATFORM OF WHOLE-SPACECRAFT

为改善星箭界面振动环境,设计六杆隔振平台,采用磁流变阻尼器作为半主动控制元件,替代原有锥壳过渡支架.对整星隔振平台用磁流变阻尼器进行性能测试,得到反映磁流变阻尼器阻尼特性的实验数据.建立具有两个隐含层的反向传播神经网络对阻尼器进行建模,用于预测磁流变阻尼器阻尼特性以及控制系统设计.提出一种串行算法优化网络结构、权值和阈值,保证网络具有较好的泛化能力和稳定性.仿真结果表明,与参数化模型相比,提出的神经网络模型具有较小的训练误差和较强的泛化能力,能够很好地预测阻尼器的阻尼特性.     

分布振子复合板的模态阻尼及多点激励下阻尼减振相关性

分布阻尼振子可拓宽结构减振频带,因此可将振子分布于板中以形成复合板（简称“分布振子复合板”）,进而实现较宽的减振频带．对于多点支撑处受到宽频非一致激励（例如在不同激励点处的激励频率、幅值与相位有差异）的分布振子复合板,目前还缺乏有效简便的优化控制指标．在作者之前的研究中,针对含分布振子的梁推导了基于模态应变能的模态阻尼计算理论,讨论了模态阻尼与单点激励下梁的减振效果的相关性,并应用于宽频减振设计优化．本文进一步将模态阻尼计算理论推广到分布振子复合板,并将研究从梁的单点激励扩展到板的多点非一致激励下的阻尼减振相关性．首先,在利用模态应变能法推导得到分布振子复合板的模态阻尼计算公式后,从理论上讨论了不同边界条件与模态阶次对计算结果的影响,以及计算理论的适用性．而后,进一步通过有限元参数分析了边界条件、频率比、模态阶次与质量比的影响．最后,通过算例分析了无振子板或分布振子复合板在四个激励点具有多种幅值与相位组合情况下的稳态响应．结果表明,推导的模态阻尼计算公式可正确预测不同边界条件下的模态阻尼,且理论预测的模态阻尼与基板的稳态平均加速度减小率、稳态峰值应变能减小率均有较高的相关性．     

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。     

High-order layerwise mechanics and finite element for the damped dynamic characteristics of sandwich composite beams

A high-order discrete-layer theory and a finite element are presented for predicting the damping of laminated composite sandwich beams. The new layerwise laminate theory involves quadratic and cubic terms for approximation of the in-plane displacement in each discrete layer, while interlaminar shear stress continuity is imposed through the thickness. Integrated damping mechanics are formulated and both laminate and structural stiffness, mass and damping matrices are formed. A finite element method and a beam element are further developed for predicting the free vibration response, including modal frequencies, modal loss factors and through-thickness mode shapes. Numerical results and evaluations of the present model are shown. Modal frequencies and damping of sandwich composite beams are measured and correlated with predicted values. Finally, parametric studies illustrate the effect of core thickness and face lamination on modal damping and frequency values.     

Adaptive tuning of elasto-plastic damper

Hysteretic dampers are frequency independent, and thereby potentially effective for several structural vibration modes, provided that the inherent amplitude dependence can be controlled. An adaptive tuning procedure is proposed, aiming at elimination of the amplitude dependence by adjusting the damper parameter(s) with respect to the magnitude of the damper motion. The procedure is demonstrated in terms of the bilinear elasto-plastic damper model, and optimality corresponds to maximum modal damping. A parametric solution for the damping ratio is obtained by a two-component system reduction technique, and maximization leads to an amplitude dependent expression for the optimal yield level. The amplitude is predicted from the most recent extremum of the damper response, and simultaneously used to adjust the yield level. Numerical examples demonstrate that the adaptive tuning procedure succeeds in controlling the amplitude dependence, resulting in equal damping for the first vibration modes.     

斜拉桥中斜拉索的面内外耦合内共振分析

研究了桥面侧振引起的斜拉索非线性振动问题。基于Hamilton原理建立了拉索的非线性振动控制方程,并利用多尺度法得到了斜拉索振动方程的二阶近似解。通过具体算例分析了斜拉索面内一阶模态与面外一阶模态相互耦合发生内共振的可能性,讨论了拉索倾斜角对拉索振动的影响,比较了在零初始条件和非零初始条件下拉索振动响应的区别。研究发现:拉索内共振发生在一定的激励频率和激励幅值区域内;改变倾斜角度,会影响拉索发生内共振时激励频率区域的大小;初始条件的不同,拉索的振动形式会相差很大。     

捷联惯导系统减振设计

机抖激光陀螺的捷联惯性导航系统结构设计的关键在于惯性测量单元（IMU）的减振设计。文章描述了一种IMU减振系统设计的方法,并在实际应用当中获得良好的效果。IMU减振系统的设计方法主要分为三大内容。首先是对减振系统中减振器的布局方案进行仿真分析,建立减振系统的六自由度振动响应模型,研究减振器布局方案的频谱特性,比较得到减振效果较优的减振器方案。然后针对获得的减振器布局方案,设计IMU结构框架和各向同性的减振器,并采用有限元的方法,对IMU的减振系统进行模态分析,获得IMU减振系统的前20阶模态频率和振型,用有限元仿真分析的方法来验证减振设计。目前这种IMU减振系统的设计方法已应用到某新型捷联惯导系统当中,减少了系统陀螺精度的降低。     

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。     

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.      

CALCULATION OF DYNAMIC LOAD IMPACT OF BIMODULOUS BEAM WITH CONSIDERATION OF SHEAR EFFECT AND DAMPING

在考虑剪切效应及阻尼的基础上,采用线性振动理论研究了双模量梁动载荷问题的冲击计算. 建立了双模量梁动载荷问题的振动微分方程,推导出了双模量梁动载荷问题的动位移、动载荷系数、冲击时间的表达式,并讨论分析了剪切效应及阻尼对双模量梁动载荷冲击问题的影响. 算例分析表明,对于某些双模量梁动载荷冲击问题,剪切效应及阻尼的影响是不能忽略的.     

Active TLCGD control of plane asymmetric buildings under earthquake excitation

The sealed,tuned liquid column gas damper (TLCGD) with gas-spring effect extends the frequency range of application and efficiently increases the modal structural damping.Active tuned liquid column gas damper (ATLCGD) is developed for the vibration control of plane asymmetric buildings subjected to earthquake excitation,improving the performance of the passive control scheme.The active behaviour is obtained by adjusting the pressure at the end of the liquid column using a pressurised reservoir.The classical linear quadratic regulator (LQR) design is presented as a straightforward approach to optimal control.Numerical simulations indicate a significant vibration reduction of plane asymmetric buildings by active control within the strong motion of the dynamic response.     

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.     

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。     

Performance evaluation of electronic control suspension featuring vehicle ER dampers

This paper presents ride comfort and driving stability performances of electronic control suspension (ECS) equipped with controllable electrorheological (ER) damper and appropriate control strategy. In order to achieve this goal, a cylindrical type ER damper which is applicable to Macpherson strut type suspension of a mid-sized passenger vehicle is designed and manufactured on the basis of the required damping force level of an existing passenger vehicle. After experimentally evaluating the field-dependent damping force and dynamic characteristics of the controllable ER damper, ECS consisting of sprung mass, spring, tire and controller is established in order to investigate the ride comfort and driving stability performances. On the basis of the governing equation of motion of the suspension system, five control strategies (soft, hard, comfort, sports and optimal mode) are formulated. The proposed control strategies are then experimentally realized with the quarter-vehicle ECS system. Control performances such as vertical acceleration of the car body and tire deflection are evaluated in both time and frequency domains under various road conditions. In addition, a comparative work is undertaken to investigate inherent control characteristics of each control strategy.     

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.