Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Earthquake response

Investigated are earthquake responses of one‐way symmetric‐plan, one‐storey systems with non‐linear fluid viscous dampers (FVDs) attached in series to a linear brace (i.e. Chevron or inverted V‐shape braces).Thus, the non‐linear damper is viscous when the brace is considered rigid or viscoelastic (VE) when the brace is flexible. The energy dissipation capacity of a non‐linear FVD is characterized by an amplitude‐dependent damping ratio for an energy‐equivalent linear FVD, which is determined assuming the damper undergoes harmonic motion. Although this formulation is shown to be advantageous for single‐degree‐of‐freedom (SDF) systems, it is difficult to extend its application to multi‐degree‐of‐freedom (MDF) systems for two reasons: (1) the assumption that dampers undergo harmonic motion in parameterizing the non‐linear damper is not valid for its earthquake‐induced motion of an MDF system; and (2) ensuring simultaneous convergence of all unknown amplitudes of dampers is difficult in an iterative solution of the non‐linear system. To date, these limitations have precluded the parametric study of the dynamics of MDF systems with non‐linear viscous or VE dampers. However, they are overcome in this investigation using concepts of modal analysis because the system is weakly non‐linear due to supplemental damping. It is found that structural response is only weakly affected by damper non‐linearity and is increased by a small amount due to bracing flexibility. Thus, the effectiveness of supplemental damping in reducing structural responses and its dependence on the planwise distribution of non‐linear VE dampers were found to be similar to that of linear FVDs documented elsewhere. As expected, non‐linear viscous and VE dampers achieve essentially the same reduction in response but with much smaller damper force compared to linear dampers. Finally, the findings in this investigation indicate that the earthquake response of the asymmetric systems with non‐linear viscous or VE dampers can be estimated with sufficient accuracy for design applications by analysing the same asymmetric systems with all non‐linear dampers replaced by energy‐equivalent linear viscous dampers. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic response of linear and non‐linear asymmetric systems with non‐linear fluid viscous dampers

This investigation is concerned with the seismic response of one‐story, one‐way asymmetric linear and non‐linear systems with non‐linear fluid viscous dampers. The seismic responses are computed for a suite of 20 ground motions developed for the SAC studies and the median values examined. Reviewed first is the behaviour of single‐degree‐of‐freedom systems to harmonic and earthquake loading. The presented results for harmonic loading are used to explain a few peculiar trends—such as reduction in deformation and increase in damper force of short‐period systems with increasing damper non‐linearity—for earthquake loading. Subsequently, the seismic responses of linear and non‐linear asymmetric‐plan systems with non‐linear dampers are compared with those having equivalent linear dampers. The presented results are used to investigate the effects of damper non‐linearity and its influence on the effects of plan asymmetry. Finally, the design implications of the presented results are discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Simplified analysis and supplemental damping system design

Investigated is the accuracy in estimating the response of asymmetric one‐storey systems with non‐linear viscoelastic (VE) dampers by analysing the corresponding linear viscous system wherein all non‐linear VE dampers are replaced by their energy‐equivalent linear viscous dampers. The response of the corresponding linear viscous system is determined by response history analysis (RHA) and by response spectrum analysis (RSA) extended for non‐classically damped systems. The flexible and stiff edge deformations and plan rotation of the corresponding linear viscous system determined by the extended RSA procedure is shown to be sufficiently accurate for design applications with errors generally between 10 and 20%. Although similar accuracy is also shown for the ‘pseudo‐velocity’ of non‐linear VE dampers, the peak force of the non‐linear VE damper cannot be estimated directly from the peak damper force of the corresponding linear viscous system. A simple correction for damper force is proposed and shown to be accurate (with errors not exceeding 15%). For practical applications, an iterative linear analysis procedure is developed for determining the amplitude‐ and frequency‐dependent supplemental damping properties of the corresponding linear viscous system and for estimating the response of asymmetric one‐storey systems with non‐linear VE dampers from the earthquake design (or response) spectrum. Finally, a procedure is developed for designing non‐linear supplemental damping systems that satisfy given design criteria for a given design spectrum. Copyright © 2003 John Wiley & Sons, Ltd.     

结构附加粘滞阻尼器的抗震设计

本文结合抗震设计规范反应谱,给出了一个附加非线性流体粘滞阻尼器结构的抗震设计方法。研究了非线性阻尼器的力学特性,引入了非线性流体阻尼器的等效线性阻尼比,给出了计算最大加速度时刻附加非线性流体阻尼器结构反应的荷载组合系数,提出了按阻尼力的水平力分量与楼层剪力成正比的原则分配阻尼器阻尼系数的方法。同时给出了基于抗震规范设计反应谱附加非线性阻尼器结构的设计流程,通过一个算例说明了使用该方法设计附加非线性粘滞阻尼器结构的全过程。算例分析表明,这种设计方法适合于手算,便于设计人员掌握,在初步设计阶段可以快速、有效地设计满足给定性能水平的附加非线性流体阻尼器体系。     

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.     

Concept and performance testing of a high‐capacity oil damper comprising multiple damper units

There has been a significant increase in the size of building structures in recent years. Huge structures such as high‐rise buildings and large‐domed stadiums require high‐performance structural control, including the use of high‐capacity dampers, especially in an earthquake‐prone country like Japan. The objective of the present study was the enhancement of both human and structural safety in such structures through the development of a rate‐dependent type of damper with a high damping capacity. Among the various available types of rate‐dependent dampers, the authors focused on the oil damper owing to its stable performance against long‐duration vibrations. The target maximum damping force was 6000 kN, which is higher than that of any existing oil damper utilized in building structures. The authors developed a novel concept for achieving this high capacity while maintaining the size of the damper within acceptable dimensions from an architectural point of view. The concept involves the use of multiple damper units that produce mechanically parallel damping forces spatially arranged in series. As a prototype, a 1500‐kN oil damper was fabricated by combining three 500‐kN dampers. The 1500‐kN prototype damper was conceived as a full‐scale prototype of a damper that is more slender than comparable commercially available dampers in Japan, and as a scaled model of the proposed 6000‐kN damper. Sinusoidal loading tests were conducted on the prototype damper using a frequency range of 0.1–1.5 Hz and a velocity range of 0.4–300 mm/s. The results confirmed that the damper produced the design damping forces. The results of earthquake loading tests also revealed that the damper exerted a stable damping force against a large earthquake and maintained its performance after the earthquake. The damper is particularly effective against earthquakes with long‐period components that could increase the temperature of a damper. This is afforded by its high heat capacity compared to conventional dampers. Considering that the proposed 6000‐kN damper will generate a damping force that is about 2–3 times that of the strongest conventional oil damper, existing manufacturer test machines would be inadequate for evaluating its full performance characteristics. To address this issue, the authors also propose a test method for evaluating the overall damping force. The method is premised on the fact that the characteristic feature of the proposed damper is its combination of multiple damper units. The overall performance is thus evaluated using the test results for the individual damper units while the other dampers are bypassed. This method was verified by the results of the abovementioned sinusoidal loading tests, with the error for the 1500‐kN prototype damper found to be less than 5%. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental study of the semi‐active control of building structures using the shaking table

A magnetorheological (MR) damper has been manufactured and tested and a non‐linear model is discussed. The parameters for the model are identified from an identification set of experimental data; these parameters are then used to reconstruct the force vs. displacement and the force vs. velocity hysteresis cycles of the MR damper for the hysteretic model. Then experiments are conducted on a three‐storey frame model using impact excitation, which identifies dynamic parameters of the model equipped with and without the MR damper. Natural frequencies, damping ratios and mode shapes, as well as structural properties, such as the mass, stiffness and damping matrices, are obtained. A semi‐active control method such as a variable structure controller is studied. Based on the ‘reaching law’ method, a feedback controller is presented. In order to evaluate the efficiency of the control system and the effect of earthquake ground motions, both numerical analysis and shaking table tests of the model, with and without the MR damper, have been carried out under three different ground motions: El Centro 1940, Taft 1952, and Ninghe 1976 (Tangshan Earthquake in Chinese). It is found from both the numerical analysis and the shaking table tests that the maximum accelerations and relative displacements for all floors are significantly reduced with the MR damper. A reasonable agreement between the results obtained from the numerical analysis and those from the shaking table tests is also observed. On the other hand, tests conducted at different earthquake excitations and various excitation levels demonstrate the ability of the MR damper to surpass the performance of a comparable passive system in a variety of situations. Copyright © 2003 John Wiley & Sons, Ltd.     

Damping reduction factors and code‐based design equation for structures using semi‐active viscous dampers

This study uses a semi‐active viscous damper with three different control laws to reshape the structural hysteresis loop and mitigate structural response, referred to as 1–4, 1–3 and 2–4 devices, respectively. The 1–4 control law provides damping in all four quadrants of the force‐displacement graph (it behaves like a standard viscous damper), the 1–3 control law provides resisting forces only in the first and third quadrants, and the 2–4 control law provides damping in the second and fourth quadrants. This paper first outlines the linear single degree of freedom structural performance when the three types of semi‐active viscous dampers are applied. The results show that simultaneous reduction in both displacement and base‐shear demand is only available with the semi‐active 2–4 device. To enable guidelines for adding a 2–4 device into the design procedure, damping reduction factors (RF_ξs) are developed, as they play an important role and provide a means of linking devices to design procedures. Three methods are presented to obtain RF_ξ and equivalent viscous damping of a structure with a 2–4 semi‐active viscous damper. In the first method, the relationship between RF_ξ and the damping of a semi‐active structure can be obtained by calculating the area under the force‐deformation diagram. The second and third method modified the Eurocode8 formula of RF_ξ and smoothed results from analysis, respectively. Finally, a simple method is proposed to incorporate the design or retrofit of structures with simple, robust and reliable 2–4 semi‐active viscous dampers using standard design approaches. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of peak ground velocity on deformation demands for SDOF systems

The effect of peak ground velocity (PGV) on single‐degree‐of‐freedom (SDOF) deformation demands and for certain ground‐motion features is described by using a total of 60 soil site records with source‐to‐site distances less than 23 km and moment magnitudes between 5.5 and 7.6. The observations based on these records indicate that PGV correlates well with the earthquake magnitude and provides useful information about the ground‐motion frequency content and strong‐motion duration that can play a role on the seismic demand of structures. The statistical results computed from non‐linear response history analyses of different hysteretic models highlight that PGV correlates better with the deformation demands with respect to other ground motion intensity measures. The choice of PGV as ground motion intensity decreases the dispersion due to record‐to‐record variability of SDOF deformation demands, particularly in the short period range. The central tendencies of deformation demands are sensitive to PGV and they may vary considerably as a function of the hysteretic model and structural period. The results provided in this study suggest a consideration of PGV as a stable candidate for ground motion intensity measure in simplified seismic assessment methods that are used to estimate structural performance for earthquake hazard analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic design and evaluation of steel moment‐resisting frames with compressed elastomer dampers

This paper evaluates the hysteretic behavior of an innovative compressed elastomer structural damper and its applicability to seismic‐resistant design of steel moment‐resisting frames (MRFs). The damper is constructed by precompressing a high‐damping elastomeric material into steel tubes. This innovative construction results in viscous‐like damping under small strains and friction‐like damping under large strains. A rate‐dependent hysteretic model for the compressed elastomer damper, formed from a parallel combination of a modified Bouc–Wen model and a non‐linear dashpot is presented. The model is calibrated using test data obtained under sinusoidal loading at different amplitudes and frequencies. This model is incorporated in the OpenSees [17] computer program for use in seismic response analyses of steel MRF buildings with compressed elastomer dampers. A simplified design procedure was used to design seven different systems of steel MRFs combined with compressed elastomer dampers in which the properties of the MRFs and dampers were varied. The combined systems are designed to achieve performance, which is similar to or better than the performance of conventional steel MRFs designed according to current seismic codes. Based on the results of nonlinear seismic response analyses, under both the design basis earthquake and the maximum considered earthquake, target properties for a new generation of compressed elastomer dampers are defined. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic behavior of asymmetric RC wall buildings: principles and new deformation‐based design method

The seismic design of multi‐story buildings asymmetric in plan yet regular in elevation and stiffened with ductile RC structural walls is addressed. A realistic modeling of the non‐linear ductile behavior of the RC walls is considered in combination with the characteristics of the dynamic torsional response of asymmetric buildings. Design criteria such as the determination of the system ductility, taking into account the location and ductility demand of the RC walls, the story‐drift demand at the softer (most displaced) edge of the building under the design earthquake, the allowable ductility (ultimate limit state) and the allowable story‐drift (performance goals) are discussed. The definition of an eccentricity of the earthquake‐equivalent lateral force is proposed and used to determine the effective displacement profile of the building yet not the strength distribution under the design earthquake. Furthermore, an appropriate procedure is proposed to calculate the fundamental frequency and the earthquake‐equivalent lateral force. A new deformation‐based seismic design method taking into account the characteristics of the dynamic torsional response, the ductility of the RC walls, the system ductility and the story‐drift at the softer (most displaced) edge of the building is presented and illustrated with an example of seismic design of a multi‐story asymmetric RC wall building. Copyright © 2005 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.     

Estimation of seismic demands on isolators in asymmetric buildings using non‐linear analysis

A procedure based on rigorous non‐linear analysis is presented that estimates the peak deformation among all isolators in an asymmetric building due to strong ground motion. The governing equations are reduced to a form such that the median normalized deformation due to an ensemble of ground motions with given corner period T_d depends primarily on four global parameters of the isolation system: the isolation period T_b, the normalized strength η, the torsional‐to‐lateral frequency ratio Ω_θ, and the normalized stiffness eccentricity e_b/r. The median ratio of the deformations of the asymmetric and corresponding symmetric systems is shown to depend only weakly on T_b, η, and Ω_θ, but increases with e_b/r. The equation developed to estimate the largest ratio among all isolators depends only on the stiffness eccentricity and the distance from the center of mass to the outlying isolator. This equation, multiplied by an earlier equation for the deformation of the corresponding symmetric system, provides a design equation to estimate the deformations of asymmetric systems. This design equation conservatively estimates the peak deformation among all isolators, but is generally within 10% of the ‘exact’ value. Relative to the non‐linear procedure presented, the peak isolator deformation is shown to be significantly underestimated by the U.S. building code procedures. Copyright © 2003 John Wiley & Sons, Ltd.     

Semi‐active fuzzy control for seismic response reduction using magnetorheological dampers

A semi‐active fuzzy control strategy for seismic response reduction using a magnetorheological (MR) damper is presented. When a control method based on fuzzy set theory for a structure with a MR damper is used for vibration reduction of a structure, it has an inherent robustness, and easiness to treat the uncertainties of input data from the ground motion and structural vibration sensors, and the ability to handle the non‐linear behavior of the structure because there is no longer the need for an exact mathematical model of the structure. For a clipped‐optimal control algorithm, the command voltage of a MR damper is set at either zero or the maximum level. However, a semi‐active fuzzy control system has benefit to produce the required voltage to be input to the damper so that a desirable damper force can be produced and thus decrease the control force to reduce the structural response. Moreover, the proposed control strategy is fail‐safe in that the bounded‐input, bounded‐output stability of the controlled structure is guaranteed. The results of the numerical simulations show that the proposed semi‐active control system consisting of a fuzzy controller and a MR damper can be beneficial in reducing seismic responses of structures. Copyright © 2004 John Wiley & Sons, Ltd.     

Feedback–feedforward control of offshore platforms under random waves

This study investigates the control of jacket‐type offshore platforms. The deck displacement of jacket‐type offshore platforms can be controlled using both passive and active control mechanisms. Among the passive control mechanisms, a tuned mass damper concept is studied in this paper. Active control mechanisms considered here include the active mass damper, the active tendon mechanism and the propeller thruster. An optimal frequency domain approach to active control of wave‐excited platforms is used in which the H₂ norm of the transfer function from the external disturbance to the regulated output is minimized. In this study, the hydrodynamic drag force is evaluated using the JONSWAP wave spectrum. Unlike conventional linearization approaches, the influence of non‐linearity in the drag force is retained in this scheme by expressing the non‐linear force components in terms of higher‐order convolutions of the water‐particle velocities. To demonstrate the effectiveness of this scheme, the platform performance with and without control devices under different sea states is evaluated. It is demonstrated that the control devices are useful in reducing the displacement response of jacket‐type offshore platforms, especially when the wave forces are concentrated at frequencies close to the natural frequencies of the platform. This becomes especially significant in deep waters because the natural frequencies of jacket‐type platforms fall closer to the dominant wave frequencies in deep waters. Adding control devices to deep water platforms will ensure a reduction both in the global response of the platform and in localized effects, such as the fatigue of welded joints. Copyright © 2001 John Wiley & Sons, Ltd.     

Torsional balance of plan‐asymmetric structures with frictional dampers: analytical results

This investigation deals with the torsional balance of the earthquake response and design of elastic asymmetric structures with frictional dampers. Plan asymmetry leads to an uneven lateral deformation demand among structural members and to unbalanced designs with larger capacities in some resisting planes. Frictional dampers are capable of controlling lateral‐torsional coupling by placing the so‐called empirical center of balance (ECB) of the structure at equal distance from all edges of the building. This rule is developed for single‐story systems with linear and inelastic behavior. However, recently obtained theoretical and experimental results demonstrate that this rule carries over to multistory structures. Results show that the peak displacement demand at the building edges and that of resisting planes equidistant from the geometric center may be similar if the damper is optimally placed. It is also shown that torsional amplification of the edge displacements of arbitrary asymmetric structures relative to the displacement of the symmetric counterparts are approximately bound by a factor of 2. Furthermore, frictional dampers are equally effective in controlling lateral‐torsional coupling of torsionally flexible as well as stiff structures. Copyright © 2005 John Wiley & Sons, Ltd.     

金属阻尼器在高烈度区学校建筑的应用研究

提高学校公共建筑在地震作用下的抗震能力是自汶川地震后一直备受关注的研究课题。高烈度地区对地震设防烈度要求较高,该类建筑的结构抗震设计难度较大。通过对常规框架结构方案及增设金属阻尼器的消能减震方案进行对比分析,发现在地震作用下阻尼器发生剪切变形,小震工况即屈服耗能,能够提供1%的附加阻尼比。相比于传统框架结构,消能减震方案能够有效减小结构构件的尺寸,进而满足学校建筑对于净高的要求。在罕遇地震作用下,该结构体系满足"强柱弱梁"的设计准则,结构位移角满足规范要求,抗震性能较纯框架结构好。研究结论可为金属阻尼器的设计和进一步研究提供参考。     

Semi‐explicit rate‐dependent modeling of damage‐avoidance steel connections using HF2V damping devices

A rate‐dependent modeling technique is developed for moment resisting steel connections that utilize non‐linear viscous dampers. First, a model of the Maxwell‐type is developed that considers the non‐linear viscous damper and connection flexibility for translational motion. This model is compared with experimental results at several input motion frequencies to validate the results. The model is then extended to represent an exterior steel beam‐to‐column connection using damage‐avoidance design and non‐linear viscous dampers. By including terms to represent structural member and connection flexibility, using appropriate geometric transformations the model can be formulated to give the overall lateral load‐drift structural performance. Validation analysis shows good agreement between experimental observations and the model predictions. Copyright © 2010 John Wiley & Sons, Ltd.     

持续变刚度摩擦型阻尼器

文中提出了一种具有持续可变滑移后刚度的摩擦型阻尼器。与传统摩擦阻尼器相比,这种阻尼器的滑移后刚度随变形增加而持续增长,承载能力显著提高。使用者可以根据不同地震水平下的性能目标调整输出力的大小,因此也为不同目标值下的结构控制提供了一种切实可行的方法。阻尼器采用套筒-活塞式结构,摩擦片通过橡胶层固化到活塞上,橡胶层同时为摩擦片提供面压。摩擦片与套筒内壁形成滑移面,该滑移面的内径沿轴向呈曲线变化,理论分析、数值模拟与试验结果表明,抛物线形的滑移面可提供呈三次函数关系的力与位移关系曲线,持续增长的刚度和出力,有利于改善结构的抗倒塌性能。     

Prediction of the maximum credible ground motion in Singapore due to a great Sumatran subduction earthquake: the worst‐case scenario

Although Singapore is located in a low‐seismicity region, huge but infrequent Sumatran subduction earthquakes might pose structural problems to medium‐ and high‐rise buildings in the city. Based on a series of ground motion simulations of potential earthquakes that may affect Singapore, the 1833 Sumatran subduction earthquake (M_w=9.0) has been identified to be the worst‐case scenario earthquake. Bedrock motions in Singapore due to the hypothesized earthquake are simulated using an extended reflectivity method, taking into account uncertainties in source rupture process. Random rupture models, considering the uncertainties in rupture directivity, slip distribution, presence of asperities, rupture velocity and dislocation rise time, are made based on a range of seismologically possible models. The simulated bedrock motions have a very long duration of about 250 s with a predominant period between 1.8 and 2.5 s, which coincides with the natural periods of medium‐ and high‐rise buildings widely found in Singapore. The 90‐percentile horizontal peak ground acceleration is estimated to be 33 gal and the 90‐percentile horizontal spectral acceleration with 5% damping ratio is 100 gal within the predominant period range. The 90‐percentile bedrock motion would generate base shear force higher than that required by the current design code, where seismic design has yet to be considered. This has not taken into account effects of local soil response that might further amplify the bedrock motion. Copyright © 2002 John Wiley & Sons, Ltd.