Tuned Mass Damper Research Articles

Bidirectional pendulum-type tuned mass damper inerter for synchronously controlling the alongwind and crosswind responses of super-tall buildings

In the context of slender super-tall buildings, which have a high height-to-width ratio and low damping, significant bidirectional vibrations can occur under strong winds. Traditional TMDI device is mainly focused on controlling unidirectional wind-induced vibration responses. To address this issue, the present study introduces a bidirectional pendulum-type tuned mass damper inerter (BPTMDI) designed to synchronously mitigate alongwind and crosswind responses. The study derives nonlinear equations of motion for a multiple degrees of freedom (MDOF) structure integrated with the BPTMDI, using the Euler-Lagrange method. These equations capture the three-dimensional motion characteristics of the BPTMDI. Additionally, linear equations of motion are derived for a simplified planar model. The time-domain responses of the MDOF structure coupled with the BPTMDI are calculated by dividing the system into linear and nonlinear subsystems and applying the state space method and Runge-Kutta method, respectively. The effectiveness of the BPTMDI is evaluated through time history response analysis of a 400 m tall case-study building subjected to bidirectional wind loadings. Results show that the BPTMDI can significantly reduce both alongwind and crosswind responses, with reductions of at least 29.75 % in displacement and 48.64 % in acceleration, regardless of wind direction. Furthermore, the BPTMDI demonstrates improved control efficacy compared to BPTMD systems. Lastly, the simplified planar model of the BPTMDI shows basic similarity to the nonlinear planar-spherical model.

Vibration Suppression of Two Adjacent Cables Using an Interconnected Tuned Mass Damper/Nonlinear Energy Sink

Due to their high flexibility, low damping, and small mass, stay cables are prone to large-amplitude vibrations. Various mechanical measures, typically installed near the cable anchorage to the deck, have been developed to suppress cable vibration. These dampers, however, may not be effective for ultralong cables since the damper is close to the cable anchorage, the cable node. In this paper, a tuned mass damper (TMD)/nonlinear energy sink (NES) are considered for installation between two adjacent stay cables for vibration mitigation. Firstly, the static equilibrium equation of the stay cable–damper system is established, and the influence of the self-weight of the damper on cable shape is investigated. The governing equations describing the motion of the two adjacent cables with a damper are then established using the Hamilton principle, which are then solved by the method of separation of variables. For cases of swept-sine excitation and harmonic excitation, the optimal designs of TMD and NES are achieved with the purpose of suppressing the first- and third-mode-dominated vibrations, respectively. Both optimal TMD and NES may substantially suppress cable vibrations, with each having advantages under certain situations. Finally, the dynamic response characteristics of two adjacent cables with an optimal damper are analyzed. Interesting dynamic behaviors, such as energy input suppression, phase shift, cable frequency shift, and phase diagram boundary rotation, are identified, and their mechanisms are explained.

Comprehensive design strategy of the NSD–TMD controlled system with closed-form frequency-amplitude solutions

A negative stiffness device (NSD) utilizing pre-compressed helical springs has been integrated with diverse vibration control techniques. Recently, the incorporation of NSD has been proposed to enhance the efficacy of a tuned mass damper (TMD) controlled system. This study introduces two design strategies for the NSD–TMD system, which functions either as a TMD with an adjustable operating bandwidth or as a pure non-linear energy sink. First, the non-linear force of NSD was expressed in a Taylor series approximation form incorporating a negative linear stiffness and a positive cubic stiffness term. Second, the equations of motion were formulated, and closed-form solutions were derived using the complexification–averaging method. The accuracy of the Taylor series approximation was substantiated within a specified range through a comparison of force–displacement curves. Third, the accuracy of the dynamic closed-form solutions was affirmed by comparing the amplitude–frequency curves with the numerical simulations. For a case study, an actual timber pedestrian bridge with decaying natural frequency was selected, and the two design strategies were examined individually. The vibration control performance of the TMD and NSD–TMD was also comparatively analyzed. The assessment focused on the peak force transmissibility value and the effective operating frequency bandwidth. Results highlighted a notable enhancement in operational performance, particularly for primary structures exhibiting diminishing modal frequencies. In a TMD-controlled system, the efficacy of vibration control deteriorates and may even amplify the dynamic response when a modal frequency shift occurs in the primary structure. Conversely, both design strategies of NSD–TMD can achieve lower transmissibility and broaden the operating bandwidth.

Control of edgewise vibration of a pre-twisted rotating beam with shunted piezoelectric tuned mass damper

The edgewise vibration control of a pre-twisted beam, rotating in the vertical plane, is considered in this study. A piezoelectric tuned mass damper (PTMD) comprising a spring–mass–damper system and a piezoelectric transducer with its associated shunt circuit is considered the control device. A finite element formulation of the pre-twisted rotating beam with the attached PTMD is developed while considering the effect of centrifugal stiffening due to rotation and the effect of gravity force. The natural frequencies of the beam (without PTMD) obtained using the present formulation are corroborated by comparing them with the results derived from Ansys. A single PTMD attached at the tip end of the beam can effectively suppress the response of the beam subjected to a distributed load in the edgewise direction. The best values of resistance and inductance of the shunt circuit are obtained through a parametric study on the peak and root mean square value of the beam tip response. A qualitative difference in the uncontrolled as well as in the controlled responses can be noticed while considering the effect of the gravity load component in the edgewise direction. Further, it has been observed that the conventional Tuned Mass Damper (TMD) provides better control than the PTMD system for ideally tuned conditions, however, the control performance of TMD degrades rapidly as compared to the PTMD in the presence of detuning. This demonstrates the effectiveness of PTMD in a practical implementation where achieving the perfectly tuned condition is seldom realized. The control performance of PTMD marginally degrades when the beam is subjected to multi-directional excitation. Hence, the proposed control system has the potential for application in rotating beam-type structures, such as wind turbine blades.

Vertical vibration control of structures with tuned liquid column dampers

Conventional tuned liquid column dampers (TLCDs) can only be used to suppress structural vibrations in horizontal directions. However, in reality, the vibration-induced motion of civil engineering structures normally consists of both vertical and horizontal components. In this study, a TLCD-based vibration control system, which is composed of a pair of inclined U-shaped containers, springs, dashpots, as well as supporting slopes, is proposed to control the vertical vibration of an engineering structure. The proposed control system (denoted as vertical TLCD) successfully extends the application of TLCD-type devices to vertical vibration reduction. First, the general configuration and operating principle of the proposed vertical TLCD are illustrated in detail. Second, the equations of motion are derived based on the Lagrange dynamic equations and further verified by two-way fluid–structure coupling numerical simulations using finite element method and finite volume method. Subsequently, the closed-form solution is derived for the optimized design of the vertical TLCD in the frequency domain. The dynamic characteristics of an optimized vertical TLCD-structure system are revealed. The effects of mass ratio, excitation amplitude and structural damping ratio on the optimization results are elaborated, respectively. Under the same optimized parameters, the vertical TLCD is found to be superior, compared to the vertical tuned mass damper (TMD). Finally, the effectiveness of the proposed system is demonstrated by applying it to the control of a bridge experiencing vertical vibrations under seismic loads. The findings of this study provide a comprehensive understanding of TLCD’s capabilities and identify its potential for vertical vibration control, which contributes to the development of more effective and versatile vibration mitigation strategies for a wide range of structures under different engineering scenarios.

Optimization of column-in-column system based on non-conventional TMD concept

Previous studies showed that the non-conventional tuned mass damper (TMD) with large mass ratio outperforms the traditional one in respect to the structural vibration control efficiency and robustness. The authors recently proposed a novel control system based on the non-conventional TMD concept, namely the column-in-column (CIC) system, which was composed of a primary column, a secondary column and a series of interconnected springs/dashpots. In this novel system, the secondary column connected to the primary one with springs/dashpots could act as a large TMD to attenuate adverse vibration of the primary structure, and its control effectiveness was preliminarily verified through numerical investigations. However, the control robustness was found not sufficient based on the existing optimal formulae in the literature for CIC optimization. This paper presents a new design method for optimizing the CIC system for better harnessing its control effectiveness and robustness in reducing structural response. The CIC system consists of two columns with distributed mass and uniform flexural rigidity, connected by springs along the column height. The effective modal mass and modal stiffness of a specific vibration mode of the system can be straightforwardly calculated by using the Euler-Bernoulli beam theory. Considering the fundamental vibration mode of the system as the target response mode for vibration control, the multiple degree-of-freedom (DOF) CIC is simplified into a two DOF with three springs (2DOF3S) structural model, the design parameters, i.e., the optimal tuning frequency ratio and damping ratio of this system are derived to minimize the displacement response of the primary structure. To demonstrate the proposed design method, the effectiveness and robustness of the CIC system in controlling seismic induced structural vibrations are assessed in both the frequency and time domains. Results show that the derived optimum formulae are applicable for optimizing the TMD system with consideration of the distributed mass and deformation of the mass damper, i.e., a column in this study. The optimized CIC system has good control robustness even if the CIC is mistuned with its design parameters deviate from the optimal values by ±50 %. The conventional TMD system with lumped mass as the mass damper is a special case of the proposed CIC system. The optimized CIC system has favorable control efficiency in mitigating the seismic responses of structures with reduction ratios averagely varying within the range of 15 % ∼ 55 % with a probability of 92.67 %. It is concluded that the proposed method is reliable and can be used for the optimum design and control of the CIC system.

Running safety control performance of high-speed trains on bridges under seismic excitation utilizing tuned mass damper

The safety of high-speed trains on bridges during seismic conditions is of paramount concern, especially for high-pier bridges characterized by lower lateral stiffness. The risk of train derailment during earthquakes can increase due to heightened low-frequency excitation. While Tuned Mass Dampers (TMDs) have proven effective in mitigating structural responses, their influence on time-varying vehicle-bridge interactions under earthquakes remains an unexplored area of study. In this research, a 1:10 scale model of a high-speed train-track-bridge coupling system, incorporating a nonlinear wheel-rail interface, was subjected to testing using a four-shaking-table system. This system exhibited good control accuracy and synchronization rates. The experimental results were used to validate the accuracy of the numerical model for the train-track-bridge coupled system under various train speeds. Subsequently, the seismic control performance of TMDs on high-speed trains was assessed through a combination of experimental tests and numerical simulations. Both sets of results, from the experimental and numerical approaches, confirmed the effectiveness of TMDs in controlling acceleration and force-related parameters for both moving and stationary trains. Notably, the control performance is most pronounced when vibrations closely align with the TMD's operating frequency. Additionally, this study delved into the mechanism of train vibration control and conducted a comprehensive parametric investigation, considering factors like pier heights (24 m–50 m), train speeds (0–300 km/h), ground motion intensities (0.04 g–0.21 g), and TMD mass ratios (0.03–0.08). The findings revealed that TMDs have a more significant impact on enhancing the safety index of trains for high-pier bridges characterized by lower frequencies. For instance, in the case of a 50 m pier, the running train's derailment coefficient can be reduced by 34.94 %. However, the control action is narrowband, effectively mitigating train vibrations near the bridge's natural frequency but less effective outside the working frequency range and absolute base acceleration.

Vibration control of structure using inelastic tuned mass damper

Vibration control of structure using inelastic tuned mass damper

Parameter Tuning and Positioning Strategy of VD and TMD Joint Control System for Multi-Modal Vibration of Stay Cables

Stay cables are becoming slender and their fundamental frequencies are becoming lower with the span of bridges increasing, thus leading to the occurrence of multi-modal vibration under various excitations. As a simple and effective strategy for cable vibration mitigation, the external damper is widely used in practice. However, one damper normally can target only fewer modes and poses limited effects on the control of multi-modal vibration. This paper proposed the use of a joint control system combining a viscous damper and a tuned mass damper for mitigating the multi-modal vibration of stay cables, followed by the optimization methodology of tuning and positioning. The control performance of the joint system was evaluated by numerical simulations. The feasibility of the joint control system was validated by analyzing the results of the comparative study, therefore providing a possible solution to multi-modal and high-modal vibration of stay cables.

Analytical optimization of inerter-based dynamic vibration absorbers with negative stiffness (INDVAs) using a reduced 2-degree-of-freedom (2DOF) model

The incorporation of an inerter, with its mass amplification capability, along with a negative stiffness spring characterized by high static-low dynamic stiffness, can significantly enhance the vibration control performance of traditional tuned mass dampers (TMDs). The previous analytical solution for the optimal parameters of inerter-based dynamic vibration absorbers with negative stiffness (INDVAs) is a generalized single-degree-of-freedom (GSDOF) model with INDVAs attached. When utilizing INDVAs for controlling wind-induced responses in high-rise buildings, the accuracy of the GSDOF model is compromised. Therefore, a multi-degree of freedom (MDOF) model is initially reduced to a simplified 2-degree of freedom (2DOF) model using a clustering algorithm in this study. The H-∞ optimization method is then employed to derive simplified analytical solutions for the optimal parameters of the three types of INDVAs. The robustness of the parameters and the control effect of these optimal INDVAs are subsequently compared with those of numerical solutions generated through a multiobjective genetic algorithm and with those of analytical solutions based on the GSDOF model. The results demonstrate that for the same type of INDVA, compared with the multiobjective genetic algorithm, the optimal INDVA calculated by the 2DOF model can achieve the same control effect on the structural wind-induced response, while the time cost is lower. In addition, the optimal INDVA obtained by the 2DOF model has a superior control effect on the wind-induced displacement and acceleration response compared to those of the GSDOF model, especially when the INDVA has a substantial inertance ratio and spans multiple floors.

Experimental investigation on vibration suppression of a new prestressed TMD for wind turbine towers

The pendulum tuned mass damper (PTMD) has been popular for vibration suppression due to its particular configuration form and frequency-tuning pattern. Based on the theoretical and numerical methods, a new prestressed TMD (PSTMD) has recently been presented which has better performances than the PTMD. To verify the improvement advantage and applicability comparatively, a comprehensive experimental study is carried out to investigate the vibration suppression of PSTMD in this paper. A wind turbine tower (WTT) with the lump-mass of the PSTMD can be represented by a two-degrees-of-freedom system, and its optimal design parameters can be analytically derived. Three test specimens, including the uncontrolled WTT, and the WTT with the PTMD or the PSTMD were tested in the laboratory with different equivalent wind and seismic loads via a shaking table. The presence of the PTMD or the PSTMD is noted changing only slightly the natural frequency and mode shape of the WTT, and the PSTMD exhibits the superior vibration suppression capability compared with the traditional PTMD.

Optimal tuning and assessment of non-grounded regenerative tuned mass damper inerter (RE-TMDI) configurations for concurrent motion control and energy harvesting

Optimal tuning and assessment of non-grounded regenerative tuned mass damper inerter (RE-TMDI) configurations for concurrent motion control and energy harvesting

Improved fatigue life of floating offshore wind turbine towers with tuned mass damper inerters (TMDIs)

Improved fatigue life of floating offshore wind turbine towers with tuned mass damper inerters (TMDIs)

Analysis of Pedestrian Steel Bridge Subjected the Seismic Load And Wind Load Using Damper at Different Span

A Pedestrian steel truss bridge model was created by using structural analysis by software. With the similar loading and support condition the 3D model was analyzed for different span like 20m, 25m,30m the basic emphasis has been given decreases the response of structure member by providing damper at different span I section Girder, steel plate thickness. Steel girder and M40 grade of concrete is used for column section in Etab software. The dynamic loading caused by moving pedestrian and earthquake and wind load, Excessive vibration in footbridges usually occurs when they are subjected to rhythmic dynamic loads caused by human activities like walking and running. In order to mitigate the human induced vibrations in footbridges, an increase in the damping ratio is often suggested as the most economical approach. Tuned mass dampers have been widely used for this purpose, however, their installation and maintenance costs are high. This has encouraged researchers to examine the efficiency of the other types of dampers. Viscoelastic dampers have been successfully employed for vibration mitigation of structures against wind and earthquake loads.

Robust damping improvement against the vortex-induced vibration in flexible bridges using multiple tuned mass damper inerters

The tuned mass damper inerter (TMDI) is considered as one of countermeasures to mitigate the very-low-frequency vertical bending vortex-induced vibration (VIV) in flexible bridges. However, the control robustness of the TMDI against the system uncertainty is a serious concern due to the limited inerter span capacity. In this paper, the multiple tuned mass damper inerter (MTMDI) is used instead of identical TMDIs to provide a robust equivalent damping ratio against the uncertain VIV within the entire lock-in wind speed range. A design framework of the MTMDI considering the inerter span length is proposed based on a universal VIV model suitable for the fully closed, centrally slotted, and semi-closed box decks. In the framework, the fluctuation of VIV characteristics with the wind speed, the probability of occurrence of the VIV, and the uncertainties in VIV characteristics and deck dynamics are considered, simultaneously. Two objection functions are defined to focus on the maximizing the equivalent damper ratio and reducing the VIV mitigation failure, respectively. Finally, numerical analysis of a flexible bridge-MTMDI system subjected to the VIV is performed. The results show that the wind speed probability distribution plays a role of weighting coefficient in the MTMDI optimization. The choice of the objective function depends on the mass ratio of the MTMDI and the level of the system uncertainty. The well-optimized MTMDI achieved a more robust control result than the TMDI within the entire lock-in wind speed range.

Active tuned mass damper for a benchmark tall building using an energy-harvesting electromagnetic damper

Among various structural vibration control categories, active control typically provides superior control performance. However, its high energy demand often limits its extensive implementation in large-scale civil structures. Very recently, electromagnetic dampers, which can convert kinetic energy into electrical energy, have emerged as a novel solution for active control with reduced or even zero energy consumption. This study explored the feasibility of an energy-harvesting active tuned mass damper (ATMD) by using an electromagnetic damper for simultaneous vibration suppression and energy harvesting. Numerical simulations were conducted for a full-scale, 76-story benchmark building equipped with the proposed design. The proposed ATMD outperforms the optimised passive counterpart of the same mass, as the former introduces an evident reduction in displacement responses. Furthermore, the proposed ATMD can offer a commensurate control performance to a passive damper with a weight three times heavier. The proposed ATMD also exhibits promising energy-harvesting performance, achieving an average output power at the kilowatt level. The results suggest that electromagnetic devices hold great potential for large-scale applications in civil structures, paving the way for a prosperous future in this field.

Hedge-Algebras-based hybrid control of earthquake-induced buildings using upgraded tuned liquid column dampers

Upgraded Tuned Liquid Column Damper (UTLCD) is an interesting variant of Tuned Liquid Column Damper, which was developed recently. UTLCD consists of a conventional Tuned Liquid Column Damper (TLCD) integrated into an undamped Tuned Mass Damper (TMD). Based on this device, a hybrid type of UTLCD (HUTLCD) is developed to minimize the vibration response of earthquake-induced buildings. HUTLCD is constituted of two independent components, including an active UTLCD (AUTLCD) and a passive UTLCD (PUTLCD). These individual components are connected in parallel to a high-rise building. In this research, the Hedge-Algebras theory (HA) is utilized to design controllers for AUTLCD. This study also uses a new algorithm, Balancing Composite Motion Optimization (BCMO), which has recently been introduced to solve optimization problems. The performance of HUTLCD is compared with that of a pure AUTLCD or a pure PUTLCD, which have the same weight as the HUTLCD. The results achieved from the present work confirm that the HUTLCD is more effective than the pure PUTLCD for the vibration reduction capacity and is better than the pure AUTLCD for both aspects of the vibrational control capacity (for most cases compared with) and saving control energy (for all cases considered). Moreover, the HUTLCD is not more robust than the AUTLCD as the structural stiffness rises, but the HUTLCD still offers higher control effectiveness compared with the AUTLCD or PUTLCD when the structural stiffness decreases. In addition, although the data used to design the optimum HA-based controller is the El Centro earthquake, this controller maintains a high efficiency level for numerous other earthquakes.

Seismic control of tall buildings using vertically distributed multiple tuned mass dampers

SummaryTuned mass damper (TMD) is a seismic vibration control device used to reduce wind and seismic vibrations of structures. Although TMD is attractive to many researchers due to its simplicity, optimizing its parameters and positions is very challenging. The sensitivity of TMD to structure's frequency changes is among its weaknesses and if parameters of this system are not optimally tuned, the efficiency of this system decreases. To solve this problem, multiple tuned mass dampers (MTMDs) have been proposed. In this research, in order to study and compare single tuned mass damper (STMD) with MTMDs vertically distributed according to modal analysis, a 20‐story building is used. The structure is analyzed in OpenSees under seven ground motions with a peak ground acceleration (PGA) of 1.0 g. To optimize TMD parameters, particle swarm optimization (PSO) algorithm is used and the results are compared to those obtained from Den Hartog's approach. To be able to use PSO algorithm and optimize TMD design parameters, Matlab and OpenSees are linked together. In this paper, more than one vibration mode is used to tune and distribute dampers to overcome higher mode effects in high‐rise buildings. The results showed that depending on their different layouts and different optimization methods used, MTMDs reduce the average maximum responses of the structure by up to 12.1%. This is while STMD is able to reduce maximum responses of the structure by 4.3%.

Active vibration control for flexible towers based on displacement observation and reduced-order controller in modal space: Theory and experiment

Active vibration control is not only suitable but also urgently needed in order to mitigate excessive vibration for dynamic systems such as wind turbine towers. However, there is a challenge of directly observing displacement and developing an efficient reduced-order control strategy. With this in view, a reduced-order controller based on displacement observation is developed for the vibration mitigation of flexible high towers, where the problems of low signal-to-noise ratio (SNR) and intricate acceleration-based control algorithms are eliminated completely. The displacement can be measured by laser or modern videometrics technology. A reduced-order model with an active mass damper (AMD) at the top of the tower is created using modal truncation approach based on modal participation factor (MPF), which successfully preserves the dominant modes of the original structure, and reduces the influence of high-frequency uncertainties. Considering structure uncertainties caused by environmental factors and aging process, an unscented Kalman filter (UKF) is introduced to identify the modal stiffness of the reduced-order model. The present study, using a 5 MW onshore wind turbine as an example, investigates active vibration control under wind and seismic loads and compares it with traditional tuned mass damper (TMD). From a dynamic perspective, the simplified model of wind turbine tower takes the form of a multi-degree-of-freedom series model. Consequently, a six-story steel frame platform has been constructed to experimentally validate the efficacy of the reduced-order controller. According to numerical simulation and laboratory testing, the control effect of the reduced-order controller with a few displacement states as feedback can be utilized as an active control strategy for high-rise flexible towers.

H∞ closed-form solution of tuned mass damper enhanced with negative stiffness element (TMD-NS) for structural vibration control

Negative stiffness element has been applied to improve the control performance of tuned mass dampers (TMDs) recently, and two tuned mass dampers enhanced with negative stiffness (TMD-NS) element, namely KDamper (Without loss of generality, it is referred to as TMD-NS I in the present study) and Extended KDamper (EKD, TMD-NS II), have been developed. Previous studies have demonstrated the control effectiveness of TMD-NS I and II. However, there still exist some issues to be addressed: (1) previous studies normally optimize TMD-NS via the intricate and time-consuming numerical methods, the analytical solutions for the optimal design parameters of TMD-NS II remain unknown; (2) a comprehensive and exhaustive evaluation that compares the control effectiveness of TMD-NS I and II is absent from existing literature. To fill these research gaps, this study derives closed-form optimum solutions for TMD-NS II using the H∞ approach. The control effectiveness of TMD-NS I and II in suppressing the seismic responses of structures is investigated systematically. Specifically, the analytical model of an undamped SDOF system equipped with TMD-NS I or II is first developed within a unified framework, and corresponding dynamic equations of motion are formulated. Subsequently, the optimal parameters of TMD-NS I and II are derived based on the classical “fixed-point” theory. Based on the derived optimal parameters, the control effectiveness of TMD-NS I and II are examined by using a damped SDOF system subjected to harmonic excitations and real earthquake ground motions. Finally, a 5-storey isolated benchmark building model is adopted to further investigate the effectiveness of TMD-NS in the seismic protection of engineering structures. The results reveal that the derived closed-form solutions are accurate in capturing the optimal parameters of TMD-NS. In addition, both the optimized TMD-NS I and II outperform the conventional TMD in reducing the seismic responses of structures. Furthermore, TMD-NS I proves more effective in reducing the absolute acceleration of the isolated building, whereas TMD-NS II demonstrates better performance in mitigating the isolating deformation. In a nutshell, both the TMD-NS I and II are highly effective alternatives to conventional TMDs, showcasing superior performance in vibration reduction and robustness.