Non‐linear‐Maxwell‐element‐type hysteretic control force

A simple non‐linear control law is proposed for reducing structural responses against seismic excitations. This law defines control force dynamics by one differential equation involving a non‐linear term that restrains the control force amplitude. If non‐linearity is neglected, the control force becomes the force in a Maxwell element, so it is called the non‐linear‐Maxwell‐element‐type (NMW) control force. The NMW control force vs. deformation relation plots hysteretic curves. The basic performance of an SDOF model with the NMW control force is examined for various conditions by numerical analyses. Furthermore, the control law is extended to fit an MDOF structural model, and an application example is shown. The computational results show that the NMW control force efficiently reduces structural responses. Copyright © 2000 John Wiley & Sons, Ltd.     

Control strategy for variable damping element considering near‐future excitation influence

A control strategy is proposed for variable damping elements (VDEs) used together with auxiliary stiffness elements (ASEs) that compose a time‐varying non‐linear Maxwell (NMW) element, considering near‐future excitation influence. The strategy first composes a state equation for the structural dynamics and the mechanical balance in the NMW elements. Next, it establishes a cost function for estimating future responses by the weighted quadratic norms of the state vector, the controlled force and the VDEs' damping coefficients. Then, the Euler equations for the optimum values are introduced, and also approximated by the first‐order terms under the autoregressive (AR) model of excitation information. Thus, at each moment t_k, the strategy conducts the following steps: (1) identify the obtained seismic excitation information to an AR model, and convert it to a state equation; and (2) determine VDEs' damping coefficients under the initial conditions at t_k and the final state at t_k+L, using the first‐order approximation of the Euler equations. The control effects are examined by numerical experiments. Copyright © 2000 John Wiley & Sons, Ltd.     

Forced vibration test of a building with semi‐active damper system

The authors developed a semi‐active hydraulic damper (SHD) and installed it in an actual building in 1998. This was the first application of a semi‐active structural control system that can control a building's response in a large earthquake by continuously changing the device's damping coefficient. A forced vibration test was carried out by an exciter with a maximum force of 100 kN to investigate the building's vibration characteristics and to determine the system's performance. As a result, the primary resonance frequency and the damping ratio of a building that the SHDs were not jointed to, decreased as the exciting force increased due to the influence of non‐linear members such as PC curtain walls. The equivalent damping ratio was estimated by approximating the resonance curves using the steady‐state response of the SDOF bilinear hysteretic system. After the eight SHDs were jointed to the building, the system's performance was identified by a response control test for steady‐state vibration. The elements that composed the semi‐active damper system demonstrated the specified performance and the whole system operated well. Copyright © 2000 John Wiley & Sons, Ltd.     

双磁场控制的磁流变减震结构振动台试验研究

传统磁流变减隔振器通常由线圈持续供电,不仅增大耗能,也会减少器件的使用寿命。基于磁流变凝胶(MRG)的剪切工作原理,运用剪切型结构设计一种新型磁流变凝胶减震装置,采用永磁体和线圈共同控制磁场大小和方向,通过改变磁流变凝胶的磁化程度实现阻尼力大小的控制。将该装置安装在一2层钢框架结构模型的底层,采用恒定电流控制法开展磁流变减震结构振动台试验研究,分析不同电流下减震结构系统对不同地震波的振动控制效果。试验结果表明：该磁流变凝胶减震装置能够显著降低结构的动力响应,对于不同的地震波其减震效果有所差异,随着峰值加速度的增加其减震效果有所下降。     

Performance spectra based method for the seismic design of structures equipped with passive supplemental damping systems

A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd.     

Force reduction factor for building structures equipped with added viscous dampers

This research work focuses on the analysis of the hysteretic seismic behaviour of inelastic SDOF systems equipped with viscous dampers. In detail, it is aimed at obtaining a practical tool useful for the seismic design of building structures with added dampers, within the framework of the traditional seismic design based on ductility. The objective is to evaluate the appropriate force reduction factor for highly damped (i.e. damping ratio greater than 5 %) SDOF systems able to guarantee a prescribed level of structural safety.     

常摩擦TMD地震控制效果的理论和实验研究

在TMD中采用摩擦阻尼代替传统的粘滞阻尼,可有效降低TMD的造价,从而促进其推广应用。但摩擦元件是非线性的,给摩擦TMD分析和设计造成了一定的困难。为了研究常摩擦TMD地震控制的特点和规律,文中采用时程分析法进行了简谐激励和地震激励下摩擦TMD对单自由度结构响应控制的理论分析;在理论分析结果的指导下,进行了单自由度主结构和摩擦TMD系统在简谐激励和地震激励下的振动台试验。理论分析和试验结果表明:除了频率比和质量比的影响,摩擦TMD的控制效果和摩擦力大小、激励幅值有关,只要参数设置合适,其控制效果是令人满意的;在设计摩擦TMD时要针对激励大小、目标控制效率进行具体分析。     

Active interaction control of civil structures. Part 1: SDOF systems

This paper presents a family of semi‐active control algorithms termed as active interaction control (AIC) used for seismic response control of civil structures. AIC control algorithms include active interface damping (AID), optimal connection strategy (OCS) and tuned interaction damping (TID). A typical SDOF AIC system consists of a primary structure, an auxiliary structure and an interaction element. The auxiliary structure typically has stiffness comparable to that of the primary structure while its natural frequency is much higher than that of the primary structure. Interactions between the primary and the auxiliary structures are defined by specific AIC control logic such that vibrational energy is extracted from the primary structure into the auxiliary structure during a locking phase and dissipated in the auxiliary structure in the subsequent unlocking phase. The stability of AIC control algorithms is shown using the Lyapunov direct method. The efficacy of AIC control algorithms is demonstrated by the results of numerical simulations of SDOF systems subjected to seismic ground motions. Practical issues such as sampling period and time delay are also investigated in this study. Copyright © 2001 John Wiley & Sons, Ltd.     

大跨铁路钢桁连续梁桥减隔震方案比较研究

为研究适用于大跨铁路钢桁连续梁桥的减隔震方案及合理优化参数,以一座全长504 m的三跨铁路钢桁连续梁特大桥为工程背景,使用非线性结构分析软件SAP2000建立有限元模型,采用快速非线性分析方法分析对比摩擦摆、阻尼器、速度锁定器等减隔震方案在各种装置参数下的减震效率。研究表明:由于大跨铁路钢桁连续梁桥墩身自振导致的地震力较大,摩擦摆方案内力减震效率一般,同时墩底内力对滑动面半径变化并不敏感,在选取滑动半径时应更多地考虑行车平顺性和梁端位移值的限制。速度锁定器会极大地增加此类桥梁地震输入能量,不适用于此类桥型。阻尼器方案对活动墩内力减震效果明显,但不能有效降低固定墩内力。摩擦摆支座附加阻尼器组合减震方案能有效控制此类桥梁的内力和位移响应。研究结论可为大跨度钢桁连续梁桥减隔震设计提供参考。     

长周期地震动强度指标与SDOF体系残余变形相关性分析

为分析两类长周期地震动作用下如何选取合理的强度指标作为结构抗震设计的输入,从2011年东日本9.0级地震、2003年十胜冲8.0级地震和2016年熊本7.3级地震数据库中选取90条可靠的远场长周期地震动。从1994年美国北岭6.7级地震和1999年台湾集集7.6级地震数据库中选取60条近场长周期地震动,以SDOF体系为研究对象,讨论了阻尼比、屈服刚度折减系数和强度折减系数对残余变形与18个地震动强度指标的相关系数的影响,对比分析了两类长周期地震作用下相关系数之间的异同。研究结果表明:在考虑近场长周期地震动作用时,建议应根据结构周期的大小来选择合适的强度指标作为地震动的输入。远场长周期地震动作用下,以PGA、PGV和PGD为代表的强度指标与残余变形的相关程度均较高,PGV稳定性略好于PGA和PGD,建议PGV作为地震动输入的控制指标。残余变形相关系数受阻尼比、屈服刚度折减系数以及强度折减系数影响不大。     

Equivalent damping of SDOF structure with Maxwell damper

To predict the maximum earthquake response of an SDOF structure with a Maxwell fluid damper or supplemental brace-viscous damper system using the seismic design response spectrum technique, a new approach is presented to determine the first- and second-order equivalent viscous damping and stiffness, the peak responses, and the damper force of the above structure. Based on the fact that the dynamic characteristics of a general linear viscoelastically damped structure are fully determined by its free vibration properties and the relaxation time constants of a Maxwell fluid damper and supplemental brace-viscous damper system in engineering practice are all small, the method of improved multiple time scales and the equivalent criterion in which all free vibration properties are the same are used to obtain the first- and second-order equivalent viscous damping and stiffness of the above structure in closed form. The accuracy of the proposed method is higher and significantly better than that of the modal strain energy method. Furthermore, in the parametric range of the requirements of the Chinese "Code for Seismic Design of Buildings", the error of the proposed second-order equivalent system for the above-mentioned engineering structure is not more than 0.5%.     

Effect of soil interaction on the performance of liquid column dampers for seismic applications

The effects of soil–structure interaction (SSI) while designing the liquid column damper (LCD) for seismic vibration control of structures have been presented in this study. The formulation for the input–output relation of a flexible‐base structure with attached LCD has been presented. The superstructure has been modelled by a single‐degree‐of‐freedom (SDOF) system. The non‐linearity in the orifice damping of the LCD has been replaced by equivalent linear viscous damping by using equivalent linearization technique. The force–deformation relationships and damping characteristics of the foundation have been described by complex valued impedance functions. Through a numerical stochastic study in the frequency domain, the various aspects of SSI on the functioning of the LCD have been illustrated. A simpler approach for studying the LCD performance considering SSI, using an equivalent SDOF model for the soil–structure system available in literature by Wolf (Dynamic Soil–Structure Interaction. International Series in Civil Engineering and Engineering Mechanics. Prentice‐Hall: Englewood Cliffs, NJ, 1985) has also been presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Non-linear seismic behavior of structures with limited hysteretic energy dissipation capacity

This paper investigates the non-linear seismic behavior of structures such as slender unreinforced masonry shear walls or precast post-tensioned reinforced concrete elements, which have little hysteretic energy dissipation capacity. Even if this type of seismic response may be associated with significant deformation capacity, it is usually not considered as an efficient mechanism to withstand strong earthquakes. The objective of the investigations is to propose values of strength reduction factors for seismic analysis of such structures. The first part of the study is focused on non-linear single-degree-of-freedom (SDOF) systems. A parametric study is performed by computing the displacement ductility demand of non-linear SDOF systems for a set of 164 recorded ground motions selected from the European Strong Motion Database. The parameters investigated are the natural frequency, the strength reduction factor, the post-yield stiffness ratio, the hysteretic energy dissipation capacity and the hysteretic behavior model (four different hysteretic models: bilinear self-centring, with limited or without energy dissipation capacity, modified Takeda and Elastoplastic). Results confirm that the natural frequency has little influence on the displacement ductility demand if it is below a frequency limit and vice versa. The frequency limit is found to be around 2 Hz for all hysteretic models. Moreover, they show that the other parameters, especially the hysteretic behavior model, have little influence on the displacement ductility demand. New relationships between the displacement ductility demand and the strength reduction factor for structures having little hysteretic energy dissipation capacity are proposed. These relationships are an improvement of the equal displacement rule for the considered hysteretic models. In the second part of the investigation, the parametric study is extended to multi-degree-of-freedom (MDOF) systems. The investigation shows that the results obtained for SDOF systems are also valid for MDOF systems. However, the SDOF system overestimates the displacement ductility demand in comparison to the corresponding MDOF system by approximately 15%.     

Prediction of seismic energy dissipation in SDOF systems

A simple analytical procedure is developed for calculating the seismic energy dissipated by a linear SDOF system under an earthquake ground excitation. The ground excitation is specified by its pseudo-velocity spectra and effective duration whereas the SDOF system is defined by its natural period of vibration and viscous damping ratio. However, the derived relationship for the energy dissipation demand under an earthquake excitation is sensitive neither to the viscous damping ratio nor the ductility ratio when the SDOF system undergoes inelastic response. Accordingly, the proposed relationship can be employed in an energy-based seismic design procedure for determining the required energy dissipation capacity of a structural system.     

Quantification of ground-motion parameters and response spectra in the near-fault region

This study focuses on the characteristics of near-fault ground motions in the forward-direction and structural response associated with them. These ground motions are narrow-banded in nature and are characterized by a predominant period at which structures excited by them are severely affected. In this work, predominant period is defined as the undamped natural period of a single-degree-of-freedom (SDOF) oscillator at which its 5% damped linear elastic pseudo-spectral velocity (PSV) contains a clear and dominant peak. It is found that a linear relationship exists between predominant period and seismic moment. An empirical equation describing this relationship is presented by using a large set of accelerograms. Attenuation equations are developed to estimate peak ground velocity (PGV) as a function of earthquake magnitude and source-to-site distance. In addition, a predictive equation for spectral shapes of PSV (i.e., PSV normalized by PGV) is presented as a continuous function of the undamped natural period of SDOF oscillators. The model is independent of PGV, and can be used in conjunction with any available PGV attenuation relation applicable to near-fault ground motion exhibiting forward-directivity effects. Furthermore, viscous damping of the SDOF is included in the model as a continuous parameter, eliminating the use of so-called damping correction factors. Finally, simple equations relating force reduction factors and displacement ductility of elasto-plastic SDOF systems are presented.     

Seismic cracking and energy dissipation in concrete gravity dams

A finite element method for seismic fracture analysis of concrete gravity dams is presented. The proposed smeared crack analysis model is based on the non-linear fracture behaviour of concrete. The following features have been considered in the development of the model: (i) the strain softening of concrete due to microcracking; (ii) the rotation of the fracture band with the progressive evolution of microcrack damage in finite elements; (iii) the conservation of fracture energy; (iv) the strain-rate sensitivity of concrete fracture parameters; (v) the softening initiation criterion under biaxial loading conditions; (vi) the closing-reopening of cracks under cyclic loading conditions. The seismic fracture and energy response of dams and the significance of viscous damping models to take account of non-cracking structural energy dissipation mechanisms are discussed. The influences of global or local degradation of the material fracture resistance on the seismic cracking response of concrete dams were also studied. Two-dimensional seismic response analyses of Koyna Dam were performed to demonstrate the application of the proposed non-linear fracture mechanics model.     

Dynamic non-linear analysis of reinforced concrete shear wall by finite element method with explicit analytical procedure

A numerical procedure for a dynamic non-linear finite element analysis is proposed here to analyse three-dimensional reinforced concrete shear wall structures subjected to earthquake motions. A shear wall is modelled as a quasi-three dimensional structure which is composed of plane elements considering the in-plane stiffness of orthogonal flange panels. The proposed constitutive model is based on the non-linearity of reinforcement and concrete in which the tension stiffening in tension and the degradation of stiffness and strength in compression of concrete after cracking are considered. The acceleration-pulse method, which is a kind of explicit analytical procedure, is employed to solve the non-linear dynamic equations, where the dynamic equation can be solved without stiffness matrix and so the iterative procedure is not necessary for descending portion of stress–strain relationship caused by cracking and softening after compressive strength in concrete. The damping effect is considered by assuming equivalent viscous damping which can give good cyclic behaviours of inertia force vs. displacement relationships. This analytical method was applied to a test specimen of a reinforced concrete shear wall with a H-shaped section which was vibrated up to failure by using a large-scale shaking table with high -performance in Japan. The test was performed as one of the dynamic model tests for evaluation of seismic behaviour of nuclear reactor buildings. The calculations were performed sequentially from the elastic range to failure. The comparison with the test results shows that this approach has good accuracy. © 1997 by John Wiley & Sons Ltd     

相邻结构地震反应MR阻尼器控制的仿真分析

本文仿真分析了应用磁流变(MR)阻尼器对相邻结构地震反应的控制效果,为进一步开展模型试验研究奠定了基础。建立了地震激励下相邻结构MR阻尼器控制系统的运动方程,提出了描述MR阻尼器阻尼力滞回特性的改进S igmoid模型,分别对应用开关控制、半主动控制以及最小或最大电流被动控制的四种控制方法的相邻结构地震反应的控制效果进行了仿真分析。结果表明,在相邻结构间连接安装MR阻尼器可以有效地控制相邻结构的地震反应,且开关控制方法和半主动控制方法的控制效果均好于两种被动控制方法,体现了MR阻尼器阻尼力可调的优点;在四种控制方法中,半主动控制方法的控制效果最好,体现了MR阻尼器阻尼力具有连续调节能力的优点;若能解决MR阻尼器的剩磁问题,半主动控制方法的控制效果会得到进一步的提高。     

STOCHASTIC SEISMIC PERFORMANCE EVALUATION OF TUNED LIQUID COLUMN DAMPERS

The seismic performance of Tuned Liquid Column Dampers (TLCDs) for the passive control of flexible structures is investigated using random vibration analysis. A non-stationary stochastic process with frequency and amplitude modulation is used to represent the earthquake strong motion, and a simple equivalent linearization technique is used to account for the non-linear damping force in the TLCD. The governing equations of motion for the structure TLCD system are formulated and reduced to a first-order state vector equation, from which the differential equation for the system response covariance matrix is obtained. The TLCD performance is evaluated on the basis of selected structural response statistics, namely, the expected maximum and root-mean-square displacements, and root-mean-square absolute accelerations and interstorey shears. A parametric study and sensitivity analysis are conducted to assess the TLCD performance and identify critical design parameters. Illustrative examples are presented using SDOF and MDOF shear-beam structural models, a wide-banded stationary random base acceleration and two non-stationary random input ground motions representative of long- and short-duration ground accelerations with significant low-frequency content.     

Minimum‐cost optimization of nonlinear fluid viscous dampers and their supporting members for seismic retrofitting

This paper presents an effective approach for achieving minimum‐cost designs for seismic retrofitting using nonlinear fluid viscous dampers. The damping coefficients of the dampers and the stiffness coefficients of the supporting braces are designed by an optimization algorithm. A realistic retrofitting cost function is minimized subject to constraints on inter‐story drifts at the peripheries of frame structures. The cost function accounts for costs related to both the topology and the sizes of the dampers. The behavior of each damper‐brace element is defined by the Maxwell model, where the force–velocity relation of the nonlinear dampers is formulated with a fractional power law. The optimization problem is first posed and solved as a mixed integer problem. For the reduction of the computational effort required in the optimization, the problem is then reformulated with continuous variables only and solved with a gradient‐based algorithm. Material interpolation techniques, which have been successfully applied in topology optimization and in multi‐material optimization, play a key role in achieving practical final design solutions with a reasonable computational effort. Promising results attained for 3‐D irregular frames are presented and discussed. Copyright © 2017 John Wiley & Sons, Ltd.