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.     

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.     

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.     

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.     

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.     

Damping identification of a full‐scale passively controlled five‐story steel building structure

A series of large‐scale dynamic tests was conducted on a passively controlled five‐story steel building on the E‐Defense shaking table facility in Japan to accumulate knowledge of realistic seismic behavior of passively controlled structures. The specimen was tested by repeatedly inserting and replacing each of four damper types, that is, the buckling restrained braces, viscous dampers, oil dampers, and viscoelastic dampers. Finally, the bare steel moment frame was tested after removing all dampers. A variety of excitations was applied to the specimen, including white noise, various levels of seismic motion, and shaker excitation. System identification was implemented to extract dynamic properties of the specimen from the recorded floor acceleration data. Damping characteristics of the specimen were identified. In addition, simplified estimations of the supplemental damping ratios provided by added dampers were presented to provide insight into understanding the damping characteristics of the specimen. It is shown that damping ratios for the specimen equipped with velocity‐dependent dampers decreased obviously with the increasing order of modes, exhibiting frequency dependency. Damping ratios for the specimen equipped with oil and viscoelastic dampers remained constant regardless of vibration amplitudes, whereas those for the specimen equipped with viscous dampers increased obviously with an increase in vibration amplitudes because of the viscosity nonlinearity of the dampers. In very small‐amplitude vibrations, viscous and oil dampers provided much lower supplemental damping than the standard, whereas viscoelastic dampers could be very efficient. Copyright © 2012 John Wiley & Sons, Ltd.     

Simplified design procedure for frame buildings with viscoelastic or elastomeric structural dampers

A simplified design procedure (SDP) for preliminary seismic design of frame buildings with structural dampers is presented. The SDP uses elastic‐static analysis and is applicable to structural dampers made from viscoelastic (VE) or high‐damping elastomeric materials. The behaviour of typical VE materials and high‐damping elastomeric materials is often non‐linear, and the SDP idealizes these materials as linear VE materials. With this idealization, structures with VE or high‐damping elastomeric dampers can be designed and analysed using methods based on linear VE theory. As an example, a retrofit design for a typical non‐ductile reinforced concrete (RC) frame building using high‐damping elastomeric dampers is developed using the SDP. To validate the SDP, results from non‐linear dynamic time history analyses (NDTHA) are presented. Results from NDTHA demonstrate that the SDP estimates the seismic response with sufficient accuracy for design. It is shown that a non‐ductile RC frame building can be retrofit with high‐damping elastomeric dampers to remain essentially elastic under the design basis earthquake (DBE). Copyright © 2005 John Wiley & Sons, Ltd.     

Experimental investigation on a base isolation system incorporating steel–Teflon sliders and pressurized fluid viscous spring dampers

An experimental investigation on a base isolation system incorporating stainless steel–Teflon bearings as sliders, and pressurized fluid viscous spring dampers, is presented in this paper. In the system examined, dampers are connected to the base floor of an isolated building to provide the desired passive control of response in the superstructure, as well as to guarantee that it re‐centres completely after the termination of a seismic action. Two types of experiments were conducted: sinusoidal and random cyclic tests, and a pseudodynamic test in ‘substructured’ configuration. The cyclic tests were aimed at characterizing what follows: the hysteretic and strain‐rate‐dependent response of the considered highly non‐linear spring dampers; the normal pressure‐ and strain‐rate‐dependent frictional behaviour of steel–Teflon bearings, manufactured in compliance with the latest standards for this class of sliders; and the combined response of their assembly. The pseudodynamic test simulated the installation of the protection system at the base of a 2:3‐scale three‐storey steel frame structure, already tested in unprotected conditions by an earlier experimental campaign. Among other findings, the results of the performed tests, as well as of relevant mechanical interpretation and numerical simulation analyses, confirmed the linear additive combination of the dissipative actions of spring dampers and sliders in this mixed installation, and the high protective performance of the considered base isolation/supplemental damping system in a realistic earthquake simulation. Copyright © 2007 John Wiley & Sons, Ltd.     

Probabilistic economic seismic loss estimation in steel buildings using post‐tensioned moment‐resisting frames and viscous dampers

The potential of post‐tensioned self‐centering moment‐resisting frames (SC‐MRFs) and viscous dampers to reduce the economic seismic losses in steel buildings is evaluated. The evaluation is based on a prototype steel building designed using four different seismic‐resistant frames: (i) conventional moment resisting frames (MRFs); (ii) MRFs with viscous dampers; (iii) SC‐MRFs; or (iv) SC‐MRFs with viscous dampers. All frames are designed according to Eurocode 8 and have the same column/beam cross sections and similar periods of vibration. Viscous dampers are designed to reduce the peak story drift under the design basis earthquake (DBE) from 1.8% to 1.2%. Losses are estimated by developing vulnerability functions according to the FEMA P‐58 methodology, which considers uncertainties in earthquake ground motion, structural response, and repair costs. Both the probability of collapse and the probability of demolition because of excessive residual story drifts are taken into account. Incremental dynamic analyses are conducted using models capable to simulate all limit states up to collapse. A parametric study on the effect of the residual story drift threshold beyond which is less expensive to rebuild a structure than to repair is also conducted. It is shown that viscous dampers are more effective than post‐tensioning for seismic intensities equal or lower than the maximum considered earthquake (MCE). Post‐tensioning is effective in reducing repair costs only for seismic intensities higher than the DBE. The paper also highlights the effectiveness of combining post‐tensioning and supplemental viscous damping by showing that the SC‐MRF with viscous dampers achieves significant repair cost reductions compared to the conventional MRF. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

Effect of viscous damping devices on the response of seismically isolated structures

Viscous and other damping devices are often used as elements of seismic isolation systems. Despite the widespread application of nonlinear viscous systems particularly in Japan (with fewer applications in the USA and Taiwan), the application of viscous damping devices in isolation systems in the USA progressed intentionally toward the use of supplementary linear viscous devices due to the advantages offered by these devices. This paper presents experimental results on the behavior of seismically isolated structures with low damping elastomeric (LDE) and single friction pendulum (SFP) bearings with and without linear and nonlinear viscous dampers. The isolation systems are tested within a six‐story structure configured as moment frame and then again as braced frame. Emphasis is placed both on the acquisition of data related to the structural system (drifts, story shear forces, and isolator displacements) and on non‐structural systems (floor accelerations, floor spectral accelerations, and floor velocities). Moreover, the accuracy of analytical prediction of response is investigated based on the results of a total of 227 experiments, using 14 historic ground motions of far‐fault and near‐fault characteristics, on flexible moment frame and stiff braced frame structures isolated with LDE or SFP bearings and linear or nonlinear viscous dampers. It is concluded that when damping is needed to reduce displacement demands in the isolation system, linear viscous damping results in the least detrimental effect on the isolated structure. Moreover, the study concludes that the analytical prediction of peak floor accelerations and floor response spectra may contain errors that need to be considered when designing secondary systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Implementation and application of the unconditionally stable explicit parametrically dissipative KR‐α method for real‐time hybrid simulation

In real‐time hybrid simulations (RTHS) that utilize explicit integration algorithms, the inherent damping in the analytical substructure is generally defined using mass and initial stiffness proportional damping. This type of damping model is known to produce inaccurate results when the structure undergoes significant inelastic deformations. To alleviate the problem, a form of a nonproportional damping model often used in numerical simulations involving implicit integration algorithms can be considered. This type of damping model, however, when used with explicit integration algorithms can require a small time step to achieve the desired accuracy in an RTHS involving a structure with a large number of degrees of freedom. Restrictions on the minimum time step exist in an RTHS that are associated with the computational demand. Integrating the equations of motion for an RTHS with too large of a time step can result in spurious high‐frequency oscillations in the member forces for elements of the structural model that undergo inelastic deformations. The problem is circumvented by introducing the parametrically controllable numerical energy dissipation available in the recently developed unconditionally stable explicit KR‐α method. This paper reviews the formulation of the KR‐α method and presents an efficient implementation for RTHS. Using the method, RTHS of a three‐story 0.6‐scale prototype steel building with nonlinear elastomeric dampers are conducted with a ground motion scaled to the design basis and maximum considered earthquake hazard levels. The results show that controllable numerical energy dissipation can significantly eliminate spurious participation of higher modes and produce exceptional RTHS results. Copyright © 2014 John Wiley & Sons, Ltd.     

Modeling of a large‐scale magneto‐rheological damper for seismic hazard mitigation. Part I: Passive mode

Magneto‐rheological (MR) dampers are a promising device for seismic hazard mitigation because their damping characteristics can be varied adaptively using an appropriate control law. During the last few decades researchers have investigated the behavior of MR dampers and semi‐active control laws associated with these types of dampers for earthquake hazard mitigation. A majority of this research has involved small‐scale MR dampers. To investigate the dynamic behavior of a large‐scale MR damper, characterization tests were conducted at the Lehigh Network for Earthquake Engineering Simulation equipment site on large‐scale MR dampers. A new MR damper model, called the Maxwell Nonlinear Slider (MNS) model, is developed based on the characterization tests and is reported in this paper. The MNS model can independently describe the pre‐yield and post‐yield behavior of an MR damper, which makes it easy to identify the model parameters. The MNS model utilizes Hershel–Bulkley visco‐plasticity to describe the post‐yield non‐Newtonian fluid behavior, that is, shear thinning and thickening behavior, of the MR fluid that occurs in the dampers. The predicted response of a large‐scale damper from the MNS model along with that from existing Bouc–Wen and hyperbolic tangent models, are compared with measured response from various experiments. The comparisons show that the MNS model achieves better accuracy than the existing models in predicting damper response under cyclic loading. Copyright © 2012 John Wiley & Sons, Ltd.     

Semi‐active control of sliding isolated bridges using MR dampers: an experimental and numerical study

Sliding base‐isolation systems used in bridges reduce pier drifts, but at the expense of increased bearing displacements under near‐source pulse‐type earthquakes. It is common practice to incorporate supplemental passive non‐linear dampers into the isolation system to counter increased bearing displacements. Non‐linear passive dampers can certainly reduce bearing displacements, but only with increased isolation level forces and pier drifts. The semi‐active controllable non‐linear dampers, which can vary damping in real time, can reduce bearing displacements without further increase in forces and pier drifts; and hence deserve investigation. In this study performance of such a ‘smart’ sliding isolation system, used in a 1:20 scaled bridge model, employing semi‐active controllable magneto‐rheological (MR) dampers is investigated, analytically and experimentally, under several near‐fault earthquakes. A non‐linear analytical model, which incorporates the non‐linearities of sliding bearings and the MR damper, is developed. A Lyapunov control algorithm for control of the MR damper is developed and implemented in shake table tests. Analytical and shake table test results are compared. It is shown that the smart MR damper reduces bearing displacements further than the passive low‐ and high‐damping cases, while maintaining isolation level forces less than the passive high‐damping case. Copyright © 2005 John Wiley & Sons, Ltd.     

Wavelet‐based non‐stationary response analysis of a friction base‐isolated structure

A wavelet‐based stochastic formulation has been presented in this paper for the seismic analysis of a base‐isolated structural system which is modelled as a two‐degree‐of‐freedom (2‐DOF) system. The ground motion has been modelled as a non‐stationary process (both in amplitude and frequency) by using modified Littlewood–Paley basis wavelets. The proposed formulation is based on replacing the non‐linear system by an equivalent linear system with time‐dependent damping properties. The expressions of the instantaneous damping and the power spectral density function (PSDF) of the superstructure response have been obtained in terms of the functionals of input wavelet coefficients. The proposed formulation has been validated by simulating a ground motion process. The effect of the frequency non‐stationarity on the non‐linear response has also been studied in detail, and it has been clearly shown how ignoring the frequency non‐stationarity in the ground motion leads to inaccurate non‐linear response calculations. Copyright © 2000 John Wiley & Sons, Ltd.     

Experimental testing and numerical modelling of a heavy timber moment‐resisting frame with ductile steel links

This paper presents the development, experimental testing, and numerical modelling of a new hybrid timber‐steel moment‐resisting connection that is designed to improve the seismic performance of mid‐rise heavy timber moment‐resisting frames (MRF). The connection detail incorporates specially designed replaceable steel links fastened to timber beams and columns using self‐tapping screws. Performance of the connection is verified through experimental testing of four 2/3 scale beam‐column connections. All 4 connection specimens met the acceptance criteria specified in the AISC 341‐10 provisions for steel moment frames and exhibit high strength, ductility, and energy dissipation capacity up to storey drifts exceeding 4%. All of the timber members and self‐tapping screw connections achieved their design objective, remaining entirely elastic throughout all tests and avoiding brittle modes of failure. To assess the global seismic performance of the newly developed connection in a mid‐rise building, a hybrid timber‐steel building using the proposed moment‐resisting connection is designed and modelled in OpenSees. To compare the seismic performance of the hybrid MRF with a conventional steel MRF, a prototype steel‐only building is also designed and modelled in OpenSees. The building models are subject to a suite of ground motions at design basis earthquake and maximum credible earthquake hazard levels using non‐linear time history analysis. Analytical results show that drifts and accelerations of the hybrid building are similar to a conventional steel building while the foundation forces are significantly reduced for the hybrid structure because of its lower seismic weight. The results of the experimental program and numerical analysis demonstrate the seismic performance of the proposed connection and the ability of the hybrid building to achieve comparable seismic performance to a conventional steel MRF.     

Evaluation of predictors of non‐linear seismic demands using ‘fishbone’ models of SMRF buildings

Predictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Application of non‐linear multiple tuned mass dampers to suppress man‐induced vibrations of a pedestrian bridge

This paper presents an application of multiple tuned mass dampers (MTMDs) with non‐linear damping devices to suppress man‐induced vibrations of a 34m long pedestrian bridge. The damping force generated by each of these damping devices is simply a drag force from liquid acting on an immersed section. The quadratic non‐linear property of these devices was directly determined from free vibration tests of a simple laboratory set‐up. Dynamic models of the bridge and pedestrian loads were constructed for numerical investigation based on field measurement data. The control effectiveness of non‐linear MTMDs was examined along with its sensitivity against estimation errors in the bridge's natural frequency and magnitude of pedestrian load. The numerical results indicated that the optimum non‐linear MTMD system was as effective and robust as its linear counterpart. Then, a six‐unit non‐linear MTMD system was designed, constructed, and installed on the bridge. Field measurements after the installation confirmed the effectiveness of non‐linear MTMDs, and the measurement results were in good agreement with numerical predictions. After the installation, the average damping ratio of the bridge was raised from 0.005 to 0.036 and the maximum bridge accelerations measured during walking tests were reduced from about 0.80–1.30 ms^?2 to 0.27–0.40 ms^?2, which were within an acceptable range. Copyright © 2003 John Wiley & Sons, Ltd.