Multiple Tuned Mass Damper System Research Articles

Human-Induced Vibration Control of Floor Structures Using MTMD System Optimized by MATLAB-SAP2000 Interface

Under human-induced excitations, a floor structure may suffer excessive vibrations due to its large span and low damping ratio. Vertical vibrations, in particular, can become intolerable during resonance events. A tuned mass damper (TMD) is a widely used single-degree-of-freedom dynamic vibration absorber. To enhance the serviceability of a floor structure, a multiple TMD (MTMD) system finds broad application. The parameters of the MTMD must be carefully designed to achieve satisfactory performance. However, existing studies often employ a simplified model of the floor structure with closely spaced modes to optimize the parameters of MTMD. Nonetheless, an oversimplified floor model can lead to a reduction in its control effect. To solve this problem, this study utilizes the OAPI facility of SAP2000 to build a connection with MATLAB. A multi-objective optimization algorithm based on the artificial fish swarm algorithm (AFSA) for MTMD is developed in MATLAB, while the finite element model of a real floor structure is built in SAP2000. The locations of the MTMD system are initially specified in SAP2000 and, through the proposed MATLAB–SAP2000 interface, data can be exchanged between them. Based on the structural dynamic responses to external excitations in SAP2000, the optimization process for the MTMD is carried out in MATLAB. Concurrently, the parameters of the MTMD in SAP2000 are iteratively adjusted until they reach their final optimal values. To underscore the enhancements brought about by the proposed interface and optimization method, a comparative case study is conducted. A group of MTMDs, optimized using a conventional method, is presented for reference. The numerical results indicate that, overall, the proposed MTMD system exhibits superior control effectiveness and robustness.

Seismic multi-objective stochastic parameters optimization of multiple tuned mass damper system for a large podium twin towers structure

The lateral-torsional coupled dynamic response under earthquake excitation is a critical problem for eccentric building structures. To control the hazardous coupled seismic response, a tuned mass damper (TMD) is an attractive vibration control device. A multiple TMD (MTMD) system, which is composed by several TMDs with different frequencies and damping ratios, has a better structural control effect under stochastic excitation with a wide frequency range such as earthquake. To improve the lateral-torsional coupled seismic mitigation performance of MTMD for eccentric structures, a multi-objective stochastic parameters optimization method is proposed, and a building with a large podium and twin towers is proposed as the case study. Considering the randomness of earthquakes, a stationary white noise stochastic process based on the Kanai-Tajimi spectrum is used as the input in the optimization. According to structural modal shapes, three TMDs are distributed in the podium, left tower and right tower respectively in the X direction, and two TMDs are in the left tower and right tower respectively in the Y direction, while both the maximum and root mean square (RMS) displacements of top stories of the podium, left tower and right tower are all considered in the optimization. Artificial fish swarm algorithm (AFSA) is used to search optimized parameters of MTMD in this study. For comparison, a MTMD system designed based on the traditional method is presented. Numerical results show that under bi-directional earthquake excitations, the proposed MTMD system has the best seismic mitigation effect generally, in both displacement and acceleration responses. Though the proposed MTMD system is aimed at X- and Y- directional translational responses, it can control torsional responses effectively as well.

Design of parallel multiple tuned mass dampers for the vibration suppression of a parallel machining robot

Parallel machining robots have the potentials of high precision and high flexibility. However, their pose-dependent vibration characteristics may cause accuracy problems during machining, which poses a great challenge to the vibration suppression. Multiple tuned mass dampers (MTMDs) are widely used to suppress the vibration, owing to their significant vibration suppressing effect, great robustness, and compact structure. In this paper, a parallel MTMD system is designed to mitigate the forced vibration of a parallel machining robot. The elasto-dynamic model of the parallel robot is established to identify the modes and natural frequencies of the robot, and the results show that the frequency of the resonant mode varies from 91.0 Hz to 128.1 Hz. Based on the structure and natural frequency scope of the robot, the MTMD system is designed to be a parallel configuration in two directions and the impedance model of the MTMD system is built. Considering the pose-dependent dynamics and compact inner space of parallel robots, a multi-objective optimization method for varied vibration characteristics is proposed based on the impedance model. In this method, the suppression amplitude, robustness, and compactness are the main concerns. In the structural design, small-sized polymer material springs and viscous fluid damping inside the mass blocks are used to compose the MTMD system. Therefore, wide-band vibration suppression is realized in narrow spaces. Finally, verification experiments are performed. Modal tests show that the amplitudes of the resonant modes are decreased by 38.8% along the X axis and 40.7% along the Y axis. Machining tests show that a 20%-30% reduction of the vibration in the feed direction, a 40%-50% reduction in the radial direction, a 48%-55% harmonics reduction at the natural frequency are achieved. Precise surface measurements show a 32% reduction in waviness and a 17% reduction in roughness. This study provides a new structural design and optimization method of MTMDs adapted to vibration suppression for parallel machining robots.

Effective tuned mass damper system for RC tall chimney dynamic wind response control

Tall chimneys have become necessary due to growing industries and changing environmental norms. Chimneys are tall and slender structures and thus they are sensitive towards wind loads. Thus, it becomes necessary to analyze their performance along both the direction i.e. along the wind and across the wind accurately, and to improve their performance by providing suitable measures. Now a days, Tuned Mass Dampers (TMDs) are provided to improve the performance of structures against dynamic loadings However, there are very few reported studies on the effect of TMDs on wind response control of tall chimneys. Hence, it is important to paper the use of different TMD systems and their performance in chimneys. Two RC chimneys of height of 200 m and 220 m of varying thickness are considered for dynamic wind paper using CFD in ANSYS. Modal response of chimney without and with TMD are also studied. The spring mass analogy is used for the connection of chimney and Tuned Mass Dampers. Gust Factor Method as per IS 875 (III) 2015 and IS 4992-1992, for along and across wind load calculation has been studied. Excel Programme file also prepared for the analysis of wind loads using IS codes. Three TMD systems are considered viz. Single Tuned Mass Damper system (s-TMD) and Multiple Tuned Mass Damper system (m-TMD-1 and m-TMD-2).The analysis results of TMD system are compared with the results of without TMD system. The results are compared on the basis of peak displacements of chimney. It has been found that Multiple TMD systems are more effective than Single TMD system. The reduction in deflection of about 25–30% is observed for m-TMD systems.

Lateral Vibration Control of Long-Span Small-Radius Curved Steel Box Girder Pedestrian Bridge with Distributed Multiple Tuned Mass Dampers.

Curved pedestrian bridges are important urban infrastructure with the desired adaptability to the landscape constraints and with aesthetic benefits. Pedestrian bridges feature thin cross-sections, which provide sufficient load capacities but lead to low natural frequencies that make the bridges susceptible to vibration under pedestrian excitation. This study investigates the lateral vibration of a curved bridge with a small radius down to 20 m, proposes an approach to mitigate the lateral vibration of bridges with large curvatures using distributed multiple tuned mass dampers (MTMD), and conducts in-situ bridge tests to evaluate the vibration mitigation performance. The lateral vibration was investigated through in-situ tests and finite element analysis as well as the code requirements. The key parameters of the distributed MTMD system were improved by strategically selecting the mass ratio, bandwidth, center frequency ratio, and damper number. The results showed that the curved bridge was subjected to significant lateral vibration due to the coupling of torque and moment, and the recommended design parameters for the studied bridge were derived, i.e., the total mass ratio is 0.02, bandwidth is 0.15, center frequency ratio is 1.0, and damper number is 3. The proposed approach effectively improves the deployment of MTMD for lateral vibration control of the curved bridge. The field tests showed that the vibration was reduced by up to 82% by using the proposed approach.

Optimization of multiple tuned mass dampers for a two-span continuous railway bridge via differential evolution algorithm

The study aims at proposing a methodology for optimization of multiple tuned mass dampers (MTMD) in reducing the multi-resonance vibrations of continuous bridges due to moving train loads. The equations of motion for time-domain analysis are derived for obtaining train-induced vibrations of a two-span continuous railway bridge with equipped MTMD-1 and MTMD-2 devices when the vehicle-bridge interaction (VBI) is considered. The bridge and the train are modeled as a Bernoulli-Euler beam with constant section and a series of moving sprung masses of identical length, respectively. To reduce the multiple resonance vibrations of a two-span continuous railway bridge, the MTMD-1 and MTMD-2 are tuned to the first mode and the second mode of the bridge, and they are attached to the midspan of each span, respectively. The optimum parameters of the both MTMD systems are investigated using the differential evolution (DE) method. The criterion chosen to obtain the optimum parameters is the minimization of the first two resonance peaks of the bridge. The influence of the different mass ratios and the number of TMD units in the MTMD system on the optimum parameters of the both MTMD systems and corresponding displacement responses of the bridge are also investigated. The results show that the VBI effect does not have much effect on the resonant train speeds and the control performance of TMDs. Therefore, the optimum parameters of TMDs can be obtained quickly by modeling the train as a series of moving forces for the vibration control of railway bridges.

An improved multi-mode seismic vibration control method using multiple tuned mass dampers

Multiple vibration modes of an engineering structure might be excited by earthquake ground motions. Multiple tuned mass dampers (MTMDs) are widely used to control these multi-mode vibrations. However, in the commonly used MTMD system, the mass element in each tuned mass damper (TMD) is normally assumed to be the same. To improve the performance of MTMDs for seismic-induced vibration control, non-uniform MTMD masses are adopted in the present study to improve the mass utilization of TMD, and a location factor is proposed to determine the best location of each TMD in the MTMD system. The effectiveness of the proposed method is validated through numerical study. The results show that the proposed method effectively reduces the seismic responses of the structure induced by multiple vibration modes.

Stochastic design of multiple tuned mass damper system under seismic excitation

Stochastic design of multiple tuned mass damper system under seismic excitation

Optimum placement and design of multiple tuned mass dampers for vibration control of asymmetric buildings

This study proposed a design procedure to determine the optimal location, moving direction, and system parameters of multiple tuned mass dampers systematically for vibration control of asymmetric buildings under dynamic loadings such as earthquake or wind excitations. A piece of computer software was developed as a postprocessor of any commercial structural analysis programs, such as ETABS, SAP2000, and so on. First, the modal parameters of target building structure were extracted from its finite element model. The optimum location and moving direction of the multiple tuned mass dampers system are determined based on the controlled mode shapes and both modal participating mass ratio and modal direction factor. Then, the optimal parameters of the multiple tuned mass dampers system were calculated by minimizing the mean square modal displacement response ratio of the controlled mode for the target building with and without multiple tuned mass dampers system. To evaluate control effectiveness, the responses of the building with and without multiple tuned mass dampers system were compared in both frequency and time domains. The analysis results from a 5-story building with different torsion-coupling degrees and a 46-story real building show that the proposed multiple tuned mass dampers system is quite effective in mitigating excessive floor vibration, base shear, and elapsed time of vibration due to earthquake excitations to enhance both structural safety and resident comfort. It is also concluded that the torsion-coupling effect should be considered in determining the optimum planar location of multiple tuned mass dampers system which is equivalent to mass increase of the multiple tuned mass dampers system and thus improves the control efficacy for asymmetric buildings.

Passive control of jacket–type offshore wind turbine vibrations by single and multiple tuned mass dampers

Vibration control is gaining focuses in the field of offshore wind turbines (OWTs) in recent years as the turbine tower becomes taller and more slender. Although a number of research works have been carried out to control the OWT vibrations, using tuned mass damper (TMD) and multiple tuned mass dampers (MTMDs) to control the jacket–type OWT vibrations is rarely reported, especially for the MTMDs, of which the application in the field of OWTs is still in the initial stage. This study focuses on the performance of TMD and MTMDs in controlling the tower vibrations of the jacket–type OWT subjected to the combined wind, wave and current loads, which are the most common external vibration resources for OWTs. The control effectiveness is numerically investigated and evaluated by the reductions of the standard deviation displacement (σ(d)) and the standard deviation acceleration (σ(a)) of the tower top. After the installation of TMD, σ(d) and σ(a) are reduced by 32% and 29% respectively. Larger TMD mass ratios lead to better control effectiveness, but the improvement becomes less obvious as the mass ratios constantly increase. The control effectiveness of the MTMD system is slightly decreased compared with a single large TMD. However, the robustness of MTMDs is superior since the OWT vibrations can still be controlled effectively even if some TMDs do not function. The control effectiveness of the MTMD system can also be affected by the change in the positions of malfunctioned TMDs.

Study on adaptive-passive multiple tuned mass damper with variable mass for a large-span floor structure

Floor structures, especially large-span floor structures, are sensitive to human-induced vibrations, which might cause a serviceability problem. Multiple tuned mass damper (MTMD) system is often used in the vertical vibration control of large-span floor structures. While it is difficult to determine the design parameters of each TMD in an MTMD system, a passive MTMD system still has the detuning shortcoming. In order to overcome this problem, an adaptive-passive variable mass multiple TMD (APVM-MTMD) system is proposed in this study. Each APVM-TMD in the system has a variable mass configuration and a microcontroller system consisting of an accelerometer, a control circuit board, and a driving device. Under ambient excitation, the control circuit board gathers the signals of the accelerometer on the floor, which can identify the dominant natural frequency of the primary structure where this APVM-TMD is located; this is done through the short time Fourier transformation (STFT)-based frequency identification algorithm. Then, each APVM-TMD can automatically control the driving device to retune itself by varying its mass. After retuning steps of all APVM-TMDs, the previous MTMD system becomes a new MTMD system with a different frequency distribution. A large-span floor structure is proposed as a case study. The original finite element model (FEM) is updated according to the in-situ test. In the updated model, an APVM-MTMD system is designed according to the previous model, then the frequency retuning function is verified. Finally, by applying several kinds of human-induced excitations, the vertical vibration control effect of the retuned MTMD system is compared with the mistuned one. The results show that the APVM-MTMD system can retune itself, and the retuned MTMD system has the best vibration control effect compared to the case without control and the mistuned MTMD system case.

Effect of Multiple Tuned Mass Dampers for Vibration Control in High-Rise Buildings

Tuned mass dampers (TMDs) are one of the strategies implemented in the field of structural vibration control. Most researchers have only focused on the control of one specific mode of vibration by idealizing the structure as a single-degree-of-freedom system. From a practical point of view, the use of a single large TMD within a structure would adversely affect the architectural appeal, usable space, and ease of installation. This study introduces a multiple tuned mass damper (MTMD) system, which is simple and more effective than a conventional single TMD system. The system consists of multiple smaller dampers distributed within the structure either uniformly, varying linearly, or based on the judgment of the designer. TMDs tuned to the first, second, and third natural frequencies are used to control vibrations, thus enabling a wider bandwidth of vibration control and attaining remarkable reductions in floor displacements, floor accelerations, and base shear. A MTMD system was investigated for different base excitations, namely harmonic and seismic. A three-degrees-of-freedom frame model and three mass dampers tuned to all three natural frequencies of the system were fabricated. This building model was studied experimentally and analyzed to investigate the effect of harmonic base excitation on structures. Compared with single TMD systems, the performance of the proposed MTMDs system was found to be excellent in controlling displacements. A five-degrees-of-freedom structure was analyzed for seismic excitation to study the effect of two mass dampers tuned to first two natural frequencies with a mass ratio of 5%. The proposed system significantly reduced the displacement, acceleration, and base shear response at the next-higher-order natural frequency beyond the fundamental. The responses of the structures were compared to assess the optimal placement of dampers to attain highest performance. Vibration control by multiple TMDs was found to be more efficient when dampers are strategically placed on the floors, with the maximum amplitude in the mode shapes corresponding to the respective tuning frequencies.

Vibration control for serviceability enhancement of offshore platforms against environmental loadings

Offshore drilling has become a key process for obtaining oil. Offshore platforms have many applications, including oil exploration and production, navigation, ship loading and unloading, and bridge and causeway support. However, vibration problems caused by severe environmental loads, such as ice, wave, wind, and seismic loads, threaten the functionality of platform facilities and the comfort of workers. These concerns may result in piping failures, unsatisfactory equipment reliability, and safety concerns. Therefore, the vibration control of offshore platforms is essential for assuring structural safety, equipment functionality, and human comfort. In this study, an optimal multiple tuned mass damper (MTMD) system was proposed to mitigate the excessive vibration of a three-dimensional offshore platform under ice and earthquake loadings. The MTMD system was designed to control the first few dominant coupled modes. The optimal placement and system parameters of the MTMD are determined based on controlled modal properties. Numerical simulation results show that the proposed MTMD system can effectively reduce the displacement and acceleration responses of the offshore platform, thus improving safety and serviceability. Moreover, this study proposes an optimal design procedure for the MTMD system to determine the optimal location, moving direction, and system parameters of each unit of the tuned mass damper.

Optimal Design and Application of a Multiple Tuned Mass Damper System for an In-Service Footbridge

Slender steel footbridges suffer excessive human-induced vibrations due to their low damping nature and their frequency being located in the range of human-induced excitations. Tuned mass dampers (TMDs) are usually used to solve the serviceability problem of footbridges. A multiple TMD (MTMD) system, which consists of several TMDs with different frequencies, has a wide application in the vibration control of footbridges. An MTMD system with well-designed parameters will have a satisfactory effect for vibration control. This study firstly discusses the relationship between the acceleration dynamic amplification factor and important parameters of an MTMD system, i.e., the frequency bandwidth, TMD damping ratio, central frequency ratio, mass ratio and the number of TMDs. Then, the frequency bandwidth and damping ratio optimal formulas are proposed according to the parametric study. At last, an in-service slender footbridge is proposed as a case study. The footbridge is analyzed through a finite element model and an in situ test, and then, an MTMD system is designed based on the proposed optimal design formulas. The vibration control effect of the MTMD system is verified through a series of in situ comparison tests. Results show that under walking, running and jumping excitations with different frequency, the MTMD system always has an excellent vibration control effect. Under a crowd-induced excitation with the resonance frequency, the footbridge with an MTMD system can meet the acceleration limit requirement. It is also found that the analysis result agrees well with the in situ test.

Analysis on vibration control of a large-span pedestrian suspension bridge based on a multiple tuned mass damper system

Tuned mass damper is one of the commonly used passive control devices. It is the earliest used device in civil engineering control of vibration control of high-rise buildings and towering structures. For large-span pedestrian bridges, the pedestrian load spectrum covers many modalities of pedestrian bridges. It is difficult to achieve the expected results with a single tuned mass damper device. In order to obtain efficient damping, the multiple modes of a multiple tuned mass damper which may resonate under excitation are controlled. This chapter adopts the pedestrian suspension bridge over Dongtan River as the subject to arrange a multiple tuned mass damper system in the finite element model of the pedestrian suspension bridge, analyze the effectiveness of the multiple tuned mass damper system on the control of human-induced vibration of a large-span pedestrian suspension bridge, and discuss the vibration reduction effect of the multiple tuned mass damper system on the response to human-induced vibration of the pedestrian suspension bridge. The analysis shows that a multiple tuned mass damper system has a significant effect on controlling human-induced vibration of the pedestrian suspension bridge.

Study on vertical vibration control of long-span steel footbridge with tuned mass dampers under pedestrian excitation

This paper aims to study crowd-induced vibration control of long-span steel footbridges with different dynamic characteristics by combining methods of site measurement and numerical simulation. Four kinds of footbridge models with sensitive vertical natural frequencies of easily generating human-bridge resonance under pedestrian loading are designed based on an actual steel footbridge. The numerical models are firstly validated by comparative investigation between the site measurement and the simulation. Detailed study on dynamic responses of the four footbridges with and without controlling systems of tuned mass damper (TMD) and multiple tuned mass damper (MTMD) is then conducted under 13 cases of crowd random excitations, rhythmic running and jumping excitations. Results show that the numerical simulation agrees well with the site measurement data. TMD system is found to be highly efficient in reducing vibration responses only when the excitation frequency is basically consistent with the structural natural frequency, which obviously limits the application of TMD system in footbridges as wider excitation frequency bandwidth is caused by human activities. MTMD system are demonstrated to be with higher vibration absorption robustness appearing predominant and stable capacity of reducing structural vibrations under all the crowd random and rhythmic excitations for the four footbridges.

Multiple tuned mass damper for multi-mode vibration reduction of offshore wind turbine under seismic excitation

With the wide spreads of the wind energy production industry, the demand for the safe and feasible design of wind turbine structures is growing swiftly. The magnificent deployment of wind turbines in hostile environments with high seismic hazard, has lead engineers to consider more comprehensive way of seismic design, and control technics of a gigantic structure like jacket supported offshore wind turbine (OWT). The current research provides an overview to alleviate the dynamic structural responses of the jacket supported OWT due to the seismic loads associated with static wind and wave loads. Multiple tuned mass damper (MTMD) has been installed at the top and base of the turbine tower corresponding to the mode shapes of the structure. The MTMD parameters have been optimized based on response surface methodology (RSM). The performance of MTMD following the multi-mode control strategy seems to be prominent in suppressing the first two vibrational modes. To evaluate the proposed strategy, frequency response function (FRF), fast Fourier transforms (FFT), peak and lateral displacements of the tower, root mean square (RMS), shear and moment have been investigated through the uncontrolled and controlled structures. In addition, the practicability of the MTMD system is also compared with the single tuned mass damper (STMD).

Free parameter search of multiple tuned mass dampers by using artificial bee colony algorithm

Summary In optimization of multiple tuned mass dampers (MTMDs), certain restrictions or preconditions such as uniform distribution of stiffness, mass, or frequency spacing had been applied for simplification, but in turn, solution of individual stiffness and damping parameters are not the true optima. The main purpose of this paper is to obtain the true optima of individual stiffness and damping parameters of MTMD system. In the proposed method, parameters of TMD units are treated as free search optimization variables, and an efficient optimization algorithm, namely, artificial bee colony algorithm has been utilized in obtaining optimum parameters of MTMDs. Performance proposed method with respect to uncontrolled structure is verified through numerical analyses and compared with other reported methods. Comparisons show a superior performance of proposed approach. The basic properties of optimum design, the effectiveness, and robustness with respect to number of dampers are also discussed.

Optimization and application of multiple tuned mass dampers in the vibration control of pedestrian bridges

An effective design approach for Multiple Tuned Mass Dampers (MTMDs) in pedestrian bridges was proposed by utilizing the transfer function to obtain each TMD\'s optimum stiffness and damping. A systematic simulation of pedestrian excitations was described. The motion equation of a typical MTMD system attached to a Multi-degree-of-freedom (MDOF) system was presented, and the transfer function from the input pedestrian excitations to the output acceleration responses was defined. By solving the minimum norm of the transfer function, the parameters of the MTMD which resulted in the minimum overall responses can be obtained. Two applications of lightly damped pedestrian bridges attached with MTMD showed that MTMDs designed through this method can significantly reduce the structural responses when subjected to pedestrian excitations, and the vibration control effects were better than the MTMD when it was considered as being composed of equal number and mass ratios of TMDs designed by classical Den Hartog method.

A hybrid approach for parameter optimization of multiple tuned mass dampers in reducing floor vibrations due to occupant walking: Theory and parametric studies

This article presents a hybrid approach for determining optimal parameters of multiple tuned mass dampers to reduce the floor vibration due to human walking. The proposed approach consists of two parts. The first one is a partial mode decomposition algorithm to efficiently calculate dynamic responses of the coupled floor–multiple tuned mass damper system subjected to moving walking loads. The second one is an adaptive genetic simulated annealing method for the optimization of multiple tuned mass damper parameters. To establish optimization, certain variables must be considered. These include the mass, natural frequency, and damping ratio of each tuned mass damper in a multiple tuned mass damper system. The objective is to minimize floor responses and remove unreasonable requirements, such as uniform mass distribution and symmetric distribution of the tuned mass damper frequency. The proposed hybrid approach has successfully been applied to optimize the multiple tuned mass damper system to reduce the vibration of a long-span floor with closely spaced modes. By the hybrid approach, an extensive parametric study has been carried out. The results show that different walking load models and uncertainties in the dynamic properties of the floor and each tuned mass damper itself can affect the overall performance of the multiple tuned mass damper system. The proposed hybrid optimization approach is very effective and the resulting multiple tuned mass damper system is robust in reducing floor vibrations under various conditions.