Seismic analysis of structures with a fractional derivative model of viscoelastic dampers

Viscoelastic dampers are now among some of the preferred energy dissipation devices used for passive seismic response control.To evaluate the performance of structures installed with viscoelastic dampers,different analytical models have been used to characterize their dynamic force deformation characteristics.The fractional derivative models have received favorable attention as they can capture the frequency dependence of the material stiffness and damping properties observed in the tests very well.However,accurate analytical procedures are needed to calculate the response of structures with such damper models.This paper presents a modal analysis approach,similar to that used for the analysis of linear systems,for solving the equations of inotion with fractional derivative terms for arbitrary forcing functions such as those caused by earthquake induced ground motions.The uncoupled modal equations still have fractional derivatives,but can be solved by numerical or analytical procedures.Both numerical and analytical procedures are formulated.These procedures are then used to calculate the dynamic response of a multi-degree of fleedom shear beam structure excited by ground motions. Numerical results demonstrating the response reducing effect of viscoelastic dampers are also presented.

Simplified analysis of frame structures with viscoelastic dampers considering the effect of soil-structure interaction

In this study, simplified numerical models are developed to analyze the soil-structure interaction （SSI） effect on frame structures equipped with viscoelastic dampers （VEDs） based on pile group foundation. First, a single degree-of- freedom （SDOF） oscillator is successfully utilized to replace the SDOF energy dissipated structure considering the SSI effect. The equivalent period and damping ratio of the system are obtained through analogical analysis using the frequency transfer function with adoption of the modal strain energy （MSE） technique. Aparametric analysis is carried out to study the SSI effect on the performance of VEDs. Then the equilibrium equations of the multi degree-of-freedom （MDOF） structure with VEDs considering SSI effect are established in the frequency domain. Based on the assumption that the superstructure of the coupled system possesses the classical normal mode, the MDOF superstructure is decoupled to a set of individual SDOF systems resting on a rigid foundation with adoption of the MSE technique through formula derivation. Numerical results demonstrate that the proposed methods have the advantage of reducing computational cost, however, retaining the satisfactory accuracy. The numerical method proposed herein can provide a fast evaluation of the efficiency of VEDs considering the SSI effect.

Stochastic seismic response of structures with added viscoelastic dampers modeled by fractional derivative

Viscoelastic dampers,as spplementary energy dissipation devices,have been used in building structures un- der seismic excitation or wind loads.Different analytical models have been proposed to describe their dynamic force deform- ation characteristics.Among these analytieal models,the fractional derivative models have attracted more attention as they can capture the frequency dependence of the material stiffness and damping properties observed from tests very well.In this paper,a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose foree-detormation relationship is described by a fractional derivative mod- el.Then,a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamie system subjected to deterministic or random excitation.Through numerical verification,it is shown that viscoelastic dampers are ef- fective in reducing structural responses over a wide frequency range,and the proposed schmnes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model wills frac- tional derivative.

An alternative practical design method for structures with viscoelastic dampers

Viscoelastic dampers（VEDs） are one of the most common passive control devices used in new and retrofit building projects which reduce the structure responses and dissipate seismic energy during an earthquake.Various methods to design this kind of dampers have been proposed based on the desired level of additional damping,eigenvalue assignment,modal strain energy,linear quadratic regulator control theories,and other approaches.In the current engineering practice,the popular method is the one based on the modal strain energy that uses the inter-story lateral stiffness as one of the main variables for damper design.However,depending on the configuration of the structure,in some cases the resulting interstory lateral stiffness can be very large.Consequently,the dampers size would also be large producing much more damping than that effectively necessary,resulting in an increase of the overall cost of the supplemental damping system and causing excessive stress on the structural elements connected to the dampers.In this paper an alternative practical design method for structures with VEDs is proposed.This method uses the inter-story shear forces as one of the main variables to accomplish the damper design compared to what was done in previous studies.Nonlinear time-history analyses were conducted on a 7-story reinforced concrete（RC） structure to check the reliability and effectiveness of the proposed method.Comparisons on the seismic performance between the structure without dampers and that equipped with VEDs were carried out.It is concluded that the proposed method results in a very suitable size of dampers,which are able to improve the performance of the structure at all levels of earthquake ground motions and satisfying the drift requirement prescribed in the codes.

Experimental and analytical study on design performance of full-scale viscoelastic dampers

Viscoelastic（VE） dampers, with their stiffness and energy dissipation capabilities, have been widely used in civil engineering for mitigating wind-induced vibration and seismic responses of structures, thus enhancing the comfort of residents and serviceability of equipment inside. In past relevant research, most analytical models for characterizing the mechanical behavior of VE dampers were verified by comparing their predictions with performance test results from small-scale specimens, which might not adequately or conservatively represent the actual behavior of full-scale dampers, especially with regard to the ambient temperature, temperature rise, and heat convection effects. Thus, in this study, by using a high-performance testing facility with a temperature control system, full-scale VE dampers were dynamically tested with different displacement amplitudes, excitation frequencies, and ambient temperatures. By comparing the analytical predictions with the experimental results, it is demonstrated that adopting the fractional derivative method together with considering the effects of excitation frequencies, ambient temperatures, temperature rises, softening, and hardening, can reproduce the design performance of full-scale VE dampers very well.

Higher-mode effect on the seismic responses of buildings with viscoelastic dampers

In conventional modal analysis procedures,usually only a few dominant modes are required to describe the dynamic behavior of multi-degrees-of-freedom buildings.The number of modes needed in the dynamic analysis depends on the higher-mode contribution to the structural response,which is called the higher-mode effect.The modal analysis approach, however,may not be directly applied to the dynamic analysis of viscoelastically damped buildings.This is because the dynamic properties of the viscoelastic dampers depend on their vibration frequency.Therefore,the structural stiffness and damping contributed from those dampers would be different for each mode.In this study,the higher-mode effect is referred to as the response difference induced by the frequency-dependent property of viscoelastic dampers at higher modes.Modal analysis procedures for buildings with viscoelastic dampers distributed proportionally and non-proportionally to the stiffness of the buildings are developed to consider the higher-mode effect.Numerical studies on shear-type viscoelastically damped building models are conducted to examine the accuracy of the proposed procedures and to investigate the significance of the higher-mode effect on their seismic response.Two damper models are used to estimate the peak damper forces in the proposed procedures. Study results reveal that the higher-mode effect is significant for long-period viscoelastically damped buildings.The higher-mode effect on base shear is less significant than on story acceleration response.Maximum difference of the seismic response usually occurs at the top story.Also,the higher-mode effect may not be reduced by decreasing the damping ratio provided by the viscoelastic dampers.For practical application,it is realized that the linear viscous damping model without considering the higher-mode effect may predict larger damper forces and hence,is on the conservative side.

Application of Lead Viscoelastic Dampers to Wind Vibration Control on Big-Span Power Transmission Tower

To study the wind vibration response of power transmission tower, the lead viscoelastic dampers （LVDs） were applied to a cup tower. With time history analysis method, the displacement, velocity, acceleration and force response of the tower was calculated and analyzed. The results show that the control effect of lead viscoelastic dampers is very good, and the damping ratio can reach 20% or more when they are applied to the tower head.

Optimal Vibration Control of Adjacent Building Structures Interconnected by Viscoelastic Dampers

The objective of this paper is to investigate the dynamic characteristics of two adjacent building structures interconnected by viscoelastic dampers under seismic excitations. The computational procedure for an analytical model including the system model formulation, complex modal analysis and seismic time history analysis is presented for this purpose. A numerical example is also provided to illustrate the analytical model. The complex modal analysis is conducted to determine the optimal damping ratio, the optimal damper stiffness and the optimal damper damping of the viscoelastic dampers for each mode of the system. For the damper stiffness and damping with optimal values, the responses can be categorized into underdamped and critically damped vibrations. Furthermore, compared to the viscous dampers with only the energy dissipation mechanism, the viscoelastic dampers with both the energy dissipation and redistribution mechanisms are more effective for increasing the damping ratio of the system. The seismic time history analysis is conducted to assess the effectiveness of the viscoelastic dampers for vibration control. Based on the optimal damping ratio, the optimal damper stiffness, the optimal damper damping of the viscoelastic dampers for a certain mode of the system, and the viscoelastic dampers can be used to effectively suppress the root-mean-square responses as well as the peak responses of the two adjacent buildings.

铅黏弹性阻尼器增强钢管约束钢筋混凝土柱节点抗震性能研究

针对钢管约束钢筋混凝土(steel tubed reinforced concrete,STRC)柱节点抗震性能薄弱的现状,提出采用改良的铅黏弹性阻尼器进行增强。基于ABAQUS工作平台对铅黏弹性阻尼器试件建立有限元模型,将数值计算所得滞回和骨架曲线、耗能性能及疲劳性能与试验结果进行对比,两者吻合较好。在此基础上探讨了铅芯直径、铅芯布置形式及复合黏弹性体厚度比值对铅黏弹性阻尼器力学性能的影响。结果表明:相较于扇形铅黏弹性阻尼器,改良后的四边形铅黏弹性阻尼器表现出更好的力学性能;随着铅芯直径的增大,阻尼器的耗能能力指标均得到大幅提高;建议铅芯个数取2个,铅芯面积与复合黏弹性层面积比值取6%~8%,复合黏弹性体厚度比值约为0.67。建立不同布置方案的铅黏弹性阻尼器增强STRC柱节点试件模型,对其破坏形态、滞回特性和箍筋应力进行对比分析,给出合理的布置方案,为实际工程提供参考。

带支撑广义Maxwell粘弹性阻尼耗能结构风振响应分析

工程中粘弹性阻尼器的安装通过支撑与结构进行连接,但在安装粘弹性阻尼器的耗能结构随机响应分析中,为了简化计算过程,将支撑的刚度看作无穷大或者忽略支撑刚度的影响。实际上,对支撑刚度的影响加以考虑更能符合工程实际。针对考虑支撑刚度影响的粘弹性阻尼耗能结构风振响应分析过程复杂的问题,提出了一种求解考虑支撑影响的广义Maxwell粘弹性阻尼耗能结构基于Davenport谱风振响应的简明解析解法。在广义Maxwell粘弹性阻尼器微分型本构模型基础上,给出了考虑支撑刚度的粘弹性阻尼器等效本构关系。将粘弹性阻尼器等效本构关系与结构运动方程联立,采用复模态法将其解耦,获得结构风振响应的统一表达式。将耗能结构在Davenport风速谱下的系列响应功率谱密度函数分解为频域响应函数与Davenport功率谱密度函数的乘积形式,基于随机振动理论中谱矩的定义,对响应功率谱密度函数积分后获得无积分项的系列响应谱矩表达式。在算例中通过与虚拟激励法计算结果对比,验证了所提解法的准确性,并分析了支撑刚度在耗能系统中的影响。

设置侧向限位阻尼器的层间隔震结构减震性能研究

对在隔震层设置侧向限位黏弹性阻尼器组成混合耗能结构随机激励下的减震性能进行了系统研究.首先,建立混合耗能结构的地震动方程,利用双过滤白噪声激励地震动的滤波方程,将该类激励下混合耗能结构的动力学问题精确转化为基于易于获得简明封闭解的白噪声激励问题.其次,基于复模态法和白噪声激励的Dirac函数性质推导了混合耗能结构系列响应(结构位移、层间位移和阻尼器阻尼力)的方差和0~2阶谱矩的简明封闭解.最后,通过算例在验证所提封闭解正确的基础上研究了混合耗能结构减震性能的影响因素.研究表明:层间隔震层以上楼层的结构响应量随着隔震层刚度的增大而增大;黏弹性阻尼器阻尼参数对隔震层以上楼层的影响特征为,结构位移在一定阻尼参数下可达到最小,而层间位移则随着阻尼参数的增大而增大.该研究可为层间隔震混合耗能结构的设计提供参考.

我国黏弹性阻尼器抗震疲劳性能检验标准研究

我国黏弹性阻尼器在生产和应用过程中均需要进行抗震疲劳性能检验。我国现行的消能阻尼器标准中均对黏弹性阻尼器的抗震疲劳性能检验方法进行了规定。对现行标准中相关的试验加载制度和性能评价方法进行了汇总和比较,并基于此,对四种黏弹性阻尼器进行了抗震疲劳性能试验和性能参数分析。结果表明,基于不同标准得到的阻尼器力学性能参数的变化率不同,是否满足15%限值的结论也不相同。

胶泥缓冲器与高射机枪动力学性能优化匹配

为了改善机枪的射击稳定性从而提高射击精度,设计一款应用于12.7 mm重型机枪的单出杆式黏弹性胶泥缓冲器,用变刚度Kelvin模型对其进行数学建模.用正交试验法对黏弹性胶泥缓冲器的刚度、阻尼系数和预压力进行优化匹配分析,获得胶泥缓冲器与高射机枪动力学匹配最好的一组性能优化参数.优化匹配的黏弹性胶泥缓冲器与弹簧缓冲器动力学性能仿真比较结果表明,使用胶泥缓冲器的12.7 mm重型机枪后坐力更小,后坐速度变化更平稳,枪口波动更小.

弱非线性系统下的耗能减震结构随机地震响应分析

本文研究了结构刚度弱非线性和滞变弱非线性的耗能减震结构的随机地震响应问题。首先利用整体本构关系建立单自由度弱非线性耗能结构的运动方程;然后结合带支撑黏弹性阻尼器的等效阻尼原理和随机等效线性化法对其进行等效;最后基于FPK(Fokker-Planck-Kolmogorov)方程法推导出结构刚度弱非线性耗能结构随机地震响应值的解析解,基于等效Duffing体系法推导出结构刚度滞变弱非线性耗能结构随机地震响应值的解析解,并对这2种方法的误差进行了分析。算例分析表明:计算结果可靠、有效;相较于现有的随机等效线性化法的求解方法,FPK法和等效Duffing体系法具有更高的精度。

支撑刚度对黏弹性阻尼耗能结构的随机风振响应特性研究

针对随机风振激励下实用黏弹性阻尼耗能系统的响应分析复杂且支撑刚度影响研究不足的问题,提出了考虑安装支撑的黏弹性阻尼耗能结构的随机风振响应谱矩及方差的计算方法,并分析了支撑刚度对结构的动力响应特性。首先,依据黏弹性阻尼器与安装支撑的串联关系,建立六参数实用黏弹性阻尼器等效微分型本构方程。其次,综合运用复模态法、虚拟激励法和功率谱二次分解法,推导出耗能结构响应量(位移、层间位移、阻尼力、支撑位移)0~2阶谱矩的解析解。最后,通过算例验证了所提方法的精确性,并研究了支撑刚度对黏弹性阻尼器减震性能与结构可靠度的影响。研究表明,阻尼器支撑刚度越大,阻尼器减震性能越能得到发挥,工程应用时有必要考虑支撑刚度的不利影响。

带支撑六参阻尼器隔震结构基于李鸿晶谱的简明解法研究

考虑带支撑六参数黏弹性阻尼器耗能隔震结构在李鸿晶谱激励下求解地震响应较为复杂,提出了一种能够获得随机地震响应的简明解法。采用带支撑六参数黏弹性阻尼器分析模型,以微分本构方程实现黏弹性阻尼器隔震结构的数学建模,结合复模态法与虚拟激励法,获得了隔减震体系系列响应(位移、速度以及阻尼器受力)频域解的统一表达式;以李鸿晶谱作为激励功率谱,将激励功率谱与结构频率响应特征值函数进行简化,获得了该随机激励下系统响应功率谱、响应谱矩及响应方差的简明解;给出算例,与此类问题传统的常用分析方法进行对比,验证所提方法在该系统下分析动力响应的合理性和高效性,并讨论了不同支撑刚度对阻尼器减震效果的影响。

VED支承转子的模态频率及稳定性研究

为了研究两端黏弹性橡胶阻尼器(VED)支承单盘转子系统的动力学特性,建立了轮盘位于1/3轴跨处的转子系统有限单元模型.通过求解转子系统的复特征根问题,获得转子系统的模态振型.分析模态频率和阻尼比随转速的变化规律,讨论阻尼器支承刚度、损耗因子和质量参数对模态频率和阻尼比的影响.结果表明,转子系统的阻尼器支承刚度和损耗因子分别存在一个最优值,使得工作转速远离模态频率,并提高了转子系统的稳定性;质量参数对一阶模态阻尼比的影响较小;当质量参数超出某有效区间时,系统将失去对高阶模态响应的衰减作用.

设置F-Ved建筑结构空间协同工作控制研究

根据粘弹性阻尼器和摩擦阻尼器各自的特点 ,提出一种新型粘弹性 -摩擦阻尼器 (F- Ved)耗能装置。推导了粘弹性 -摩擦阻尼器和人字型支撑的组合层间单元刚度矩阵和控制力向量 ;并基于框架结构的空间特性 ,建立了设置 F-Ved框架结构在考虑空间协同分析的基础上地震反应时程分析的控制方法 ;应用此方法 ,对设置 F- Ved的钢筋混凝土框架结构进行了在罕遇地震和多遇地震作用下的时程分析 。

黏弹性阻尼器的耗能比研究

黏弹性阻尼器是一种典型的被动控制装置,它可以通过黏弹性材料的剪切滞回耗能起到减小结构地震或风振响应的作用。本文采用阻尼器耗能占地震总输入能量比值(耗能比)评估黏弹性阻尼器的减震效率,相比采用水平位移比的评价指标更能直观地反映阻尼器耗能能力。本文采用Kelvin模型推导出结构弹性和弹塑性2种状态下附加黏弹性阻尼器耗能比计算公式,算例计算结果表明:推导的计算公式有很好的精度和准确性,可供工程设计使用。

黏弹性阻尼器加固穿斗式平面外木排架的抗震性能

为研究穿斗式木结构的抗震性能及其加固方法,选取杉木和松木两种木材,设计并制作四榀穿斗式木结构平面外框架,采用黏弹性阻尼器加固试件,对加固和未加固的木框架分别进行低周往复荷载试验,研究结构的抗震性能及阻尼器的加固效果.研究结果表明:加固后木排架滞回曲线的滑移和捏缩现象大幅减轻,滞回环面积增大,等效黏滞阻尼比增加,耗能能力增强,杉木和松木排架耗能能力分别提高83.31%和286.34%;加固后试件的骨架曲线斜率和极限承载力均得到大幅提升,斜率大致随加载幅值增大而增大,极限承载力杉木排架最大提升218.32%,松木排架最大提升458.89%;加固后木结构框架的刚度储备增高,初始刚度杉木试件提升46.9%,松木试件提升264.1%;杉木试件在安装阻尼器后节点的残余拔榫量减少15.06 mm,松木试件减少31.96 mm.