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

Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures under seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deformation characteristics. Among these analytical 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 force-deformation relationship is described by a fractional derivative model. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic system subjected to deterministic or random excitation. Through numerical verification, it is shown that viscoelastic dampers are effective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with fractional derivative.     

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. Supported by: Science Council, Chinese Taipei, grant no. 88-2625-2-002-006     

Dynamic characteristics and seismic response of adjacent buildings linked by discrete dampers

Coupling adjacent buildings using discrete viscoelastic dampers for control of response to low and moderate seismic events is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristics, mainly modal damping ratio and modal frequency, of damper-linked linear adjacent buildings for practical use. Random seismic response of linear adjacent buildings linked by dampers is then determined by a combination of the complex modal superposition method and the pseudo-excitation method. This combined method can effectively and accurately determine random seismic response of non-classically damped systems in the frequency domain. Parametric studies are finally performed to identify optimal parameters of viscoelastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of adjacent buildings. It is demonstrated that using discrete viscoelastic dampers of proper parameters to link adjacent buildings can reduce random seismic responses significantly. Copyright © 1999 John Wiley & Sons Ltd.     

Spring-viscous damper systems for combined seismic and vibration isolation

The coupled lateral-vertical-rocking dynamic response of spring-viscous damper isolated structures is considered. The force-displacement relation of the viscous dampers is described by an experimentally calibrated fractional derivative viscoelasticity model. The equations of motion are derived and reduced to a form for direct solution by the discrete Fourier transform method. The validity and accuracy of the derived solution are demonstrated by comparison with shake table test results. The developed analysis procedure is employed in the seismic analysis of a recently constructed isolated structure. The analytical and experimental results demonstrate that spring-viscous damper isolation systems are capable of providing both effective seismic and vibration isolation.     

Optimal placement of dampers for passive response control

The effectiveness of viscous and viscoelastic dampers for seismic response reduction of structures is quite well known in the earthquake engineering community. This paper deals with the optimal utilization of these dampers in a structure to achieve a desired performance under earthquake‐induced ground excitations. Frequency‐dependent and ‐independent viscous dampers and viscoelastic dampers have been considered as the devices of choice. To determine the optimal size and location of these dampers in the structure, a genetic algorithm is used. The desired performance is defined in terms of several different forms of performance functions. The use of the genetic approach is not limited to any particular form of performance function as long as it can be calculated numerically. For illustration, numerical examples for different building structures are presented showing the distribution and size of different dampers required to achieve a desired level of reduction in the response or a performance index. Copyright © 2002 John Wiley & Sons, Ltd.     

Experimental and analytical study on pounding reduction of base‐isolated highway bridges using MR dampers

Pounding between adjacent superstructures has been a major cause of highway bridge damage in the past several earthquakes. This paper presents an experimental and analytical study on pounding reduction of highway bridges subjected to earthquake ground motions by using magnetorheological (MR) dampers. An analytical model, which incorporates structural pounding and MR dampers, is developed. A series of shaking table tests on a 1:20 scaled base‐isolated bridge model are performed to investigate the effects of pounding between adjacent superstructures on the dynamics of the structures. Based on the test results, the parameters of the linear and the nonlinear viscoelastic impact models are identified. Performance of the semiactive system for reducing structural pounding is also investigated experimentally, in which the MR dampers are used in conjunction with the proposed control strategy, to verify the effectiveness of the MR dampers. Structural responses are also simulated by using the established analytical model and compared with the shaking table test results. The results show that pounding between adjacent superstructures of the highway bridge significantly increases the structural acceleration responses. For the base‐isolated bridge model considered here, the semiactive control system with MR dampers effectively precludes pounding. Copyright © 2009 John Wiley & Sons, Ltd.     

Modal time history analysis of non-classically damped structures for seismic motions

The step-by-step modal time history integration methods are developed for dynamic analysis of non-classically damped linear structures subjected to earthquake-induced ground motions. Both the mode displacement and mode acceleration-based algorithms are presented for the calculation of member and acceleration responses. The complex-valued eigenvectors are used to effect the modal decoupling of the equations of motion. However, the recursive step-by-step algorithms are still in terms of real quantities. The numerical results for the acceleration response and floor response spectra, obtained with these approaches, are presented. The mode acceleration approach is observed to be decidedly better than the mode displacement approach in as much as it alleviates the so-called missing mass effect, caused by the truncation of modes, very effectively. The utilization of the mode acceleration-based algorithms is, thus, recommended in all dynamic analyses for earthquake-induced ground motions.     

近场地震动下偏心结构的减震控制研究

本文选用远场宽频地震Kanai-Tajimi模型与近场地震He-Agrawal速度脉冲模型,对现有的典型近场地震记录进行了非线性数值拟合。通过调整脉冲分量与宽频分量的比值,得到了不同脉冲分量的地震波,分析了在合成近场地震波作用下,设置粘滞阻尼器时偏心结构的动力反应,并与未设置阻尼器时结构的地震响应进行了对比,同时也对能反映结构偏心特性的参数进行了分析研究。通过数值模拟与仿真分析,得到了一些对实际工程设计有意义的结论。     

Large‐scale real‐time hybrid simulation of a three‐story steel frame building with magneto‐rheological dampers

A series of large‐scale real‐time hybrid simulations (RTHSs) are conducted on a 0.6‐scale 3‐story steel frame building with magneto‐rheological (MR) dampers. The lateral force resisting system of the prototype building for the study consists of moment resisting frames and damped brace frames (DBFs). The experimental substructure for the RTHS is the DBF with the MR dampers, whereas the remaining structural components of the building including the moment resisting frame and gravity frames are modeled via a nonlinear analytical substructure. Performing RTHS with an experimental substructure that consists of the complete DBF enables the effects of member and connection component deformations on system and damper performance to be accurately accounted for. Data from these tests enable numerical simulation models to be calibrated, provide an understanding and validation of the in‐situ performance of MR dampers, and a means of experimentally validating performance‐based seismic design procedures for real structures. The details of the RTHS procedure are given, including the test setup, the integration algorithm, and actuator control. The results from a series of RTHS are presented that includes actuator control, damper behavior, and the structural response for different MR control laws. The use of the MR dampers is experimentally demonstrated to reduce the response of the structure to strong ground motions. Comparisons of the RTHS results are made with numerical simulations. Based on the results of the study, it is concluded that RTHS can be conducted on realistic structural systems with dampers to enable advancements in resilient earthquake resistant design to be achieved. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental and analytical studies on the performance of hybrid isolation systems

This paper presents experimental and analytical results on the seismic response of a rigid structure supported on isolation systems that consist of either lead rubber or sliding bearings. Shake table tests are conducted with various levels of isolation damping that is provided from the bearings and supplemental viscous fluid dampers. The table motions originated from recorded strong ground motions that have been compressed to the extent that the mass of the model structure corresponds to the mass of a typical freeway overcrossing. Experimental data are used to validate mechanical idealizations and numerical procedures. The study concludes that supplemental damping is most effective in suppressing displacements of rigid structures with moderately long isolation periods (T_I≤3 sec) without affecting base shears. Friction damping is most effective in suppressing displacement amplifications triggered by long duration pulses—in particular, pulses that have duration close to the isolation period. Copyright © 2001 John Wiley & Sons, Ltd.     

Response prediction,experimental characterization and P‐spectra design of frames with viscoelastic–plastic dampers

Viscoelastic–plastic (VEP) dampers are hybrid passive damping devices that combine the advantages of viscoelastic and hysteretic damping. This paper first formulates a semi‐analytical procedure for predicting the peak response of nonlinear SDOF systems equipped with VEP dampers, which forms the basis for the generation of Performance Spectra that can then be used for direct performance assessment and optimization of VEP damped structures. This procedure is first verified against extensive nonlinear time‐history analyses based on a Kelvin viscoelastic model of the dampers, and then against a more advanced evolutionary model that is calibrated to characterization tests of VEP damper specimens built from commercially available viscoelastic damping devices, and an adjustable friction device. The results show that the proposed procedure is sufficiently accurate for predicting the response of VEP systems without iterative dynamic analysis for preliminary design purposes. A design method based on the Performance Spectra framework is then proposed for systems equipped with passive VEP dampers and is applied to enhance the seismic response of a six‐storey steel moment frame. The numerical simulation results on the damped structure confirm the use of the Performance Spectra as a convenient and accurate platform for the optimization of VEP systems, particularly during the initial design stage. Copyright © 2016 John Wiley & Sons, Ltd.     

A method of calculating the non‐linear seismic response of a building braced with viscoelastic dampers

Buildings are continually subject to dynamic loads, such as wind load, seismic ground motion, and even the load from internal utility machines. The recent trend of constructing more flexible high‐rise buildings underscores the importance of including viscoelastic dampers in building designs. Viscoelastic dampers are used to control the dynamic response of a building. If the seismic design is based only on the linear response spectrum, considerable error may occur when calculating the seismic response of a building; rubber viscoelastic dampers show non‐linear hysteretic damping that is quite different from viscous damping. This study generated a non‐linear response spectrum using a non‐linear oscillator model to simulate a building with viscoelastic dampers installed. The parameters used in the non‐linear damper model were obtained experimentally from dynamic loading tests. The results show that viscoelastic dampers effectively reduce the seismic displacement response of a structure, but transmit more seismic force to the structure, which essentially increases its seismic acceleration response. Copyright © 2003 John Wiley & Sons, Ltd.     

Accuracy of nonlinear static procedures for the seismic assessment of shear critical structures

The nonlinear behavior of reinforced concrete (RC) members represents a key issue in the seismic performance assessment of structures. Many structures constructed in the 1980s or earlier were designed based on force limits; thus they often exhibit brittle failure modes, strength and stiffness degradation, and severe pinching effects. Field surveys and experimental evidence have demonstrated that such inelastic responses affect the global behavior of RC structural systems. Efforts have been made to consider the degrading stiffness and strength in the simplified nonlinear static procedures commonly adopted by practitioners. This paper investigates the accuracy of such procedures for the seismic performance assessment of RC structural systems. Refined finite element models of a shear critical bridge bent and a flexure‐critical bridge pier are used as reference models. The numerical models are validated against experimental results and used to evaluate the inelastic dynamic response of the structures subjected to earthquake ground motions with increasing amplitude. The maximum response from the refined numerical models is compared against the results from the simplified static procedures, namely modified capacity spectrum method and coefficient method in FEMA‐440. The accuracy of the static procedures in estimating the displacement demand of a flexure‐critical system and shear‐critical system is discussed in detail. Copyright © 2015 John Wiley & Sons, Ltd.     

SSI效应对粘弹性阻尼结构减震效果的影响分析

本文以一单跨7层框架结构为研究对象,对不同场地和地震波输入条件下的粘弹性阻尼结构进行了二维有限元时程分析,探讨了SSI（土-结构动力相互作用）效应对粘弹性阻尼结构减震效果的影响。分析结果表明：①在硬土和稍硬土地基条件下,SSI效应明显降低了结构的楼层位移峰值,若在抗震设计中对客观存在的SSI效应加以考虑,设置较少数量的阻尼器（与刚性地基假定条件下确定的阻尼器数量相比）就能使结构的实际地震位移反应满足基于刚性地基假定的地震位移控制目标;②粘弹性阻尼结构的减震效果与场地条件、输入地震动特性密切相关;③与刚性地基相比,SSI效应使粘弹性阻尼结构的减震效果明显降低,且地基越软,降低幅度越大。因此,在实际的工程设计中,应当充分考虑SSI效应,对粘弹性阻尼结构的减震控制效果进行合理的评价,并针对不同的场地条件选用合适的阻尼器类型和性能参数,才有可能达到预期的减震控制效果。     

基于分数阶时间导数常Q黏弹本构关系的含黏滞流体双相VTI介质中波场数值模拟

分数阶微分算子具有描述历史依赖性和全域相关性的特质,本文利用这种特质描述双相介质固体骨架的黏弹性特征.基于Kjartansson常Q理论将含有分数阶时间导数的黏弹固体骨架各向异性本构关系与双相介质理论有机地结合起来,并引入流变学本构关系描述孔隙流体的黏滞性力学行为,提出一种新的基于分数阶时间导数常Q黏弹本构关系的含黏滞流体双相VTI模型.推导了相应的时间域波传播方程,然后对该方程进行了数值模拟.对整数阶导数采用高阶交错网格有限差分算法,对分数阶时间导数采用短时记忆中心差分算法,进行了不同相界、不同品质因子组及双层地质结构情况下该类介质中波场的数值模拟与特征分析.模拟结果表明：将含有分数阶时间导数的常Q黏弹固体骨架各向异性本构关系及孔隙流体的黏滞性本构关系引入双相介质理论是可行的,二者的结合能更好地反映地下介质的黏弹性特征,对于进一步认识波在黏弹各向异性孔隙介质中的传播机理具有重要意义,为反演和重构地下油气储层和结构奠定正演理论基础.     

A new spatial coherence model and analytical coefficients for multi-support response spectrum combination

In this paper, a new spatial coherence model of seismic ground motions is proposed by a fi tting procedure. The analytical expressions of modal combination (correlation) coeffi cients of structural response are developed for multi-support seismic excitations. The coeffi cients from both the numerical integration and analytical solutions are compared to verify the accuracy of the solutions. It is shown that the analytical expressions of numerical modal combination coeffi cients are of high accuracy. The results of random responses of an example bridge show that the analytical modal combination coeff icients developed in this paper are accurate enough to meet the requirements needed in practice. In addition, the computational effi ciency of the analytical solutions of the modal combination coeff icients is demonstrated by the response computation of the example bridge. It is found that the time required for the structural response analysis by using the analytical modal combination coeffi cients is less than 1/20 of that using numerical integral methods.     

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.     

Modal response analysis of multi‐support structures using a random vibration approach

A formulation is developed for modal response analysis of multi‐support structures using a random vibration approach. The spectral moments of the structural response are rigorously decomposed into contributions from spectral moments of uncoupled modal responses. An advantage of the proposed formulation is that the total dynamic response can be obtained on the basis of mode by mode uncoupled analyses. The contributions to the total response from modal responses under individual support ground motions and under cross‐correlated pairs of support ground motions can be recognized explicitly. The application and performance of the formulation is illustrated by means of an example using a well‐established coherency spectrum model and widely known power spectra models, such as white noise and Kanai–Tajimi. The first three spectral moments of displacement, shear, and bending moment responses are computed, showing that the formulation produces the same results as the exact solution. Copyright © 2015 John Wiley & Sons, Ltd.     

Deterministic and probabilistic representation of near-field pulse-like ground motion

The response and damage assessment of engineering structures under near-field ground motions is currently of great interest. Near-field ground motion with directivity focusing or fling effects produces pulse-like ground motion that has characteristics different from those of ordinary records. This paper develops simple deterministic and probabilistic models for near-field pulse-like ground motions. These models belong to the class of engineering models that aim to replicate some of the gross features observed in near-field records. The ground velocity is expressed as a steady-state function or a stationary random process modulated by an envelope function. Both models account for the non-stationarity and the multiple pulses in the ground velocity. While the deterministic model is similar to some of the models developed earlier, the probabilistic model facilitates handling uncertainties in the ground motion and variability in the structure's properties. For instance, this model combined with structural reliability methods can be used for reliability assessment of structures under near-field random ground motion. The reduction of the structural response by adding supplemental dampers is also investigated.