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1

Rahman, Mohammad Sabbir, Md Kamrul Hassan, Seongkyu Chang, and Dookie Kim. "Adaptive multiple tuned mass dampers based on modal parameters for earthquake response reduction in multi-story buildings." Advances in Structural Engineering 20, no. 9 (November 24, 2016): 1375–89. http://dx.doi.org/10.1177/1369433216678863.

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The primary objective of this research is to find the effectiveness of an adaptive multiple tuned mass damper distributed along with the story height to control the seismic response of the structure. The seismic performance of a 10-story building was investigated, which proved the efficiency of the adaptive multiple tuned mass damper. Structures with single tuned mass damper and multiple tuned mass dampers were also modeled considering the location of the dampers at the top of the structure, whereas adaptive multiple tuned mass damper of the structure was modeled based on the story height. Selection of the location of the adaptive multiple tuned mass damper along with the story height was dominated by the modal parameters. Participation of modal mass directly controlled the number of the modes to be considered. To set the stage, a comparative study on the displacements and modal energies of the structures under the El-Centro, California, and North-Ridge earthquakes was conducted with and without various types of tuned mass dampers. The result shows a significant capability of the proposed adaptive multiple tuned mass damper as an alternative tool to reduce the earthquake responses of multi-story buildings.
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2

Gutierrez Soto, Mariantonieta, and Hojjat Adeli. "Tuned Mass Dampers." Archives of Computational Methods in Engineering 20, no. 4 (October 19, 2013): 419–31. http://dx.doi.org/10.1007/s11831-013-9091-7.

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3

Štěpánek, Jan, and Jiří Máca. "OPTIMIZATION OF TUNED MASS DAMPERS ATTACHED TO DAMPED STRUCTURES - MINIMIZATION OF MAXIMUM DISPLACEMENT AND ACCELERATION." Acta Polytechnica CTU Proceedings 30 (April 22, 2021): 98–103. http://dx.doi.org/10.14311/app.2021.30.0098.

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A tuned mass damper is a device, which can be highly helpful while dealing with dynamic behaviour of structures. Its proper design is conditioned by knowledge of both loading and the structure properties. In many cases, the structure can be represented by single degree of freedom model, which simplifies the design and optimization of tuned mass dampers. Most of studies focus only on minimization of displacement of the main structure under harmonic force load, however, in many cases, different frequency response function would be more appropriate. This paper presents an extension of design formulas for the H∞ optimization of tuned mass dampers for damped structures and various frequency response functions.
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4

Wang, Zhihao, Hui Gao, Hao Wang, and Zhengqing Chen. "Development of stiffness-adjustable tuned mass dampers for frequency retuning." Advances in Structural Engineering 22, no. 2 (August 28, 2018): 473–85. http://dx.doi.org/10.1177/1369433218791356.

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Tuned mass damper is an attractive strategy to mitigate the vibration of civil engineering structures. However, the performance of a tuned mass damper may show a significant loss due to the frequency detuning effect. Hence, an inerter-induced negative stiffness (apparent mass effect) and magnetic-force-induced positive/negative stiffness are proposed to integrate a stiffness-adjustable vertical tuned mass damper and pendulum tuned mass damper for frequency retuning, respectively. Based on the established differential equations of motion for a vertical tuned mass damper coupled with an inerter and a pendulum tuned mass damper integrated with a magnetic-force-induced positive-/negative-stiffness device, the frequency retuning principles of a vertical tuned mass damper and a pendulum tuned mass damper are, respectively, demonstrated. The frequency retuning strategies for both the vertical tuned mass damper and the pendulum tuned mass damper are confirmed and clarified by model tests. Furthermore, the performance of a retuned vertical tuned mass damper for mitigating vibration of a linear undamped single-degree-of-freedom primary structure is discussed, and the effects of the amplitudes of the pendulum tuned mass damper on magnetic-force-induced stiffness as well as the frequency of the pendulum tuned mass damper are also investigated. Both theoretical analysis and experimental investigations show that the proposed frequency tuning methodologies of tuned mass dampers are efficient and cost-effective with relatively simple configurations.
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5

Wang, Min, Yan Lin Zhang, and Tao Zan. "Performance Optimization and Comparison of TMD, MTMD and DTMD for Machining Chatter Control." Advanced Materials Research 199-200 (February 2011): 1165–70. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.1165.

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This paper investigates and analyzes the performances of several types of tuned mass damper (TMD) including common single TMD(STMD), multiple tuned mass dampers (MTMD) and dual tuned mass dampers (DTMD) on the machining chatter control. Considering the special nature of the machining stability problem, the optimal design parameters of the dampers are defined as those that minimize the magnitude of the real part of the FRF of the damped machining system. This paper demonstrates the performance of the optimally designed different TMDs for machining stability improvement by calculating the stability diagrams for the turning processes. The calculation results show that a more than 60% improvement in the critical limiting cutting depth can be obtained for the optimally designed MTMD (2 TMDs) compared to the optimally designed STMD, and a more than20% improvement for the optimally designed DTMD compared to the optimally designed MTMD(2 TMDs).
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6

Khazaei, Mohsen, Reza Vahdani, and Ali Kheyroddin. "Optimal Location of Multiple Tuned Mass Dampers in Regular and Irregular Tall Steel Buildings Plan." Shock and Vibration 2020 (September 16, 2020): 1–20. http://dx.doi.org/10.1155/2020/9072637.

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Tuned mass dampers are one of the most common devices for the passive control of structures subjected to earthquakes. The structure of these dampers consists of three main parameters: mass, damping, and stiffness. Tuned mass dampers reduce the amplitude of the responses affecting on a mode. In most cases, only a single TMD (tuned mass damper) or a few dampers at several points above the building height are installed on the roof of the building, requiring considerable mass and space in some parts of the structure as overhead. It is also more important to predict the elements that will meet the required mass. In this research, the performance of multiple tuned mass dampers (MTMDs) is investigated in L- and U-shaped regular and irregular tall steel buildings with 10 and 20 floors, under the near- and far-field records. Nonlinear time history analysis is also applied to evaluate the multiple tuned mass dampers effects on the seismic responses of the structures. The SAP2000 API and MATLAB genetic algorithm are used to determine the optimal location of the MTMDs in the roof plans of the buildings. The results show the effects of multiple tuned mass dampers in reducing the seismic response of acceleration, displacement, and base shear up to 50, 40, and 40% in average, respectively. The results of determining the optimum location of MTMDs in the models indicate the importance of the symmetry of the dampers relative to the centre of mass of the building.
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7

LI, CHUNXIANG. "PERFORMANCE OF DUAL-LAYER MULTIPLE TUNED MASS DAMPERS FOR STRUCTURES UNDER GROUND EXCITATIONS." International Journal of Structural Stability and Dynamics 06, no. 04 (December 2006): 541–57. http://dx.doi.org/10.1142/s0219455406002106.

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The dual-layer multiple tuned mass dampers (DL-MTMD) with a uniform distribution of natural frequencies are proposed, which consist of one large tuned mass damper (L-TMD) and an arbitrary number of small tuned mass dampers (S-TMD). The structure is represented by a generalized system corresponding to the specific vibration mode to be controlled. The criterion for assessing the optimum parameters and effectiveness of the DL-MTMD is based on the minimization of the minimum values of the maximum dynamic magnification factors (DMF) of the structure installed with the DL-MTMD. Also considered is the stroke of the DL-MTMD. The proposed DL-MTMD system is demonstrated to show higher effectiveness and robustness to the change in frequency tuning, in comparison to the multiple tuned mass dampers (MTMD) with equal total mass ratios. It is also demonstrated to be more effective than the dual tuned mass dampers (DTMD) with one large and one small tuned mass damper, but they maintain the same level of robustness to the change in frequency tuning. The DL-MTMD system can be easily manufactured as the optimum value for the linking dashpots between the structure and L-TMD is shown to be zero.
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8

Chawhan, Rechal L., Nikhil H. Pitale, S. S. Solanke, and Mangesh Saiwala. "Use of Tuned Liquid Damper to Control Structural Vibration Structural." IOP Conference Series: Materials Science and Engineering 1197, no. 1 (November 1, 2021): 012053. http://dx.doi.org/10.1088/1757-899x/1197/1/012053.

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Abstract The aim of this paper is to study the tuned liquid damper and it’s effectivness. The tunned liquid dampers are simply tuned mass damper where the liquid (usually water) replaces the mass.Tuned liquid dampers is a water tank placed over the structure which is able to reduce the dynamic structural response subjected to stimulation through sloshing effect. The effectiveness of tuned liquid damper depends upon various parameters. Tuned liquid damper are suitable for high rise building rather than short building. The tuned liquid damper decreases effect of harmonic excitation by Dissipating the energy of excitation through sloshing phenomenon.
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9

Kopylov, Semen, Zhaobo Chen, and Mohamed AA Abdelkareem. "Back-iron design-based electromagnetic regenerative tuned mass damper." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 234, no. 3 (June 14, 2020): 607–22. http://dx.doi.org/10.1177/1464419320932350.

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Implementation of tuned mass dampers is the commonly used approach to avoid excessive vibrations in civil engineering. However, due to the absence of the compact dimension, there are still no practical applications of the tuned mass dampers in automotive industry. Meanwhile, recent investigations showed the benefit of utilizing a tuned mass damper in a vehicle suspension in terms of driving comfort and road holding. Thus, the current investigation aimed to explore a novel compact dimension tuned mass damper, which can provide both sufficient vibration mitigation and energy harvesting. This paper presents a prototype of a back-iron-based design of an electromagnetic regenerative tuned mass damper. The mathematical model of the tuned mass damper system was developed and has been validated by the experimental results of the tuned mass damper prototype implemented in a protected mass test-bench. The indicated results concluded that the attenuation performance dramatically deteriorated under random excitations and a reduction in the root-mean-square acceleration of 18% is concluded compared to the case with undamped tuned mass damper. Under harmonic excitations, the designed tuned mass damper prototype is able to reduce the peak acceleration value of the protected structure by 79%. According to the experimental results, the designed tuned mass damper prototype revealed a peak regenerative power of 0.76 W under a harmonic excitation of 8.1 Hz frequency [Formula: see text]m amplitude. Given the simulated random road profiles from C to E, the back-iron electromagnetic tuned mass damper indicated that root-mean-square harvested power from 0.6 to 6.4 W, respectively.
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10

Ahmad, Aabas. "Analysis of Load Reduction of Floating Wind Turbines Using Passive Tuned Mass Dampers." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1340–45. http://dx.doi.org/10.22214/ijraset.2021.38179.

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Abstract: An efficient method for restraining the large vibration displacements and loads of offshore floating wind turbines under harsh marine environment is proposed by putting tuned mass dampers in the cabin. A dynamics model for a barge-type offshore floating wind turbine with a fore–aft tuned mass damper is established based on Lagrange’s equations; the nonlinear least squares Leven berg–Marquardt algorithm is employed to identify the parameters of the wind turbine; different parameter optimization methods are adopted to optimize tuned mass damper parameters by considering the standard deviation of the tower top longitudinal displacement as the objective function. Aiming at five typical combined wind and wave load cases under normal running state of the wind turbine, the dynamic responses of the wind turbine with/without tuned mass damper are simulated and the suppression effect of the tuned mass damper is investigated over the wide range of load cases. The results show that when the wind turbine vibrates in the state of damped free vibration, the standard deviation of the tower top longitudinal displacement is decreased approximately 60% in 100 s by the optimized tuned mass damper with the optimum tuned mass damper mass ratio 1.8%. The standard deviation suppression rates of the longitudinal displacements and loads in the tower and blades increase with the tuned mass damper mass ratio when the wind turbine vibrates under the combined wind and wave load cases. When the mass ratio changes from 0.5% to 2%, the maximum suppression rates vary from 20% to 50% correspondingly, which effectively reduce vibration responses of the offshore floating wind turbine. The results of this article preliminarily verify the feasibilities of using a tuned mass damper for restraining vibration of the barge-type offshore floating wind turbine
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11

Setareh, Mehdi. "Floor vibration control using semi-active tuned mass dampers." Canadian Journal of Civil Engineering 29, no. 1 (February 1, 2002): 76–84. http://dx.doi.org/10.1139/l01-063.

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This paper discusses the application of a new class of semi-active tuned mass dampers, called ground-hook tuned mass dampers (GHTMD), for the reduction of floor vibrations due to human movements. The TMD introduced uses a continuously variable semi-active damper (ground-hook damper) to achieve reduction in the floor acceleration. Here, the GHTMD is applied to a single degree of freedom system representative of building floors. The GHTMD design parameters are defined in terms of non-dimensional values. The optimum values of these parameters are found based on the minimization of the acceleration response of the floor for different GHTMD mass ratios and floor damping ratios. The performance of the GHTMD is compared to that of the equivalent passive TMD. In addition, the effects of off-tuning due to variations in the mass ratios and frequency ratios of the TMD and GHTMD are studied. Comparison of the results demonstrates the efficiency and robustness of GHTMD with respect to equivalent TMD. Finally, a guide for the design of GHTMDs is presented.Key words: floor vibrations, semi-active tuned mass dampers, tuned vibration absorbers, vibration control, ground-hook dampers, human-induced vibrations, annoying vibrations, optimum design parameters.
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12

Tophøj, Laust, Nikolaj Grathwol, and Svend Hansen. "Effective Mass of Tuned Mass Dampers." Vibration 1, no. 1 (September 15, 2018): 192–206. http://dx.doi.org/10.3390/vibration1010014.

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Tuned Mass Dampers (TMDs) are widely used for the control and mitigation of vibrations in engineering structures, including buildings, towers, bridges and wind turbines. The traditional representation of a TMD is a point mass connected to the structure by a spring and a dashpot. However, many TMDs differ from this model by having multiple mass components with motions of different magnitudes and directions. We say that such TMDs have added mass. Added mass is rarely introduced intentionally, but often arises as a by-product of the TMD suspension system or the damping mechanism. Examples include tuned pendulum dampers, tuned liquid dampers and other composite mechanical systems. In this paper, we show how a TMD with added mass can be analyzed using traditional methods for simple TMDs by introducing equivalent simple TMD parameters, including the effective TMD mass, the mass of the equivalent simple TMD. The presence of added mass always reduces the effective TMD mass. This effect is explained as a consequence of smaller internal motions of the TMD due to the increased inertia associated with the added mass. The effective TMD mass must be correctly calculated in order to predict the TMD efficiency and in order to properly tune the TMD. The developed framework is easy to apply to any given general linear TMD system with a known motion. Here, we demonstrate the approach for a number of well-known examples, including tuned liquid dampers, which are shown to use only a small fraction of the total liquid mass effectively.
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13

Kim, Young Moon, Ki Pyo You, Jang Youl You, Sun Young Paek, and Byung Hee Nam. "LQG Control of Along-Wind Responses of Tall Building Using Composite Tuned Mass Dampers." Key Engineering Materials 723 (December 2016): 753–59. http://dx.doi.org/10.4028/www.scientific.net/kem.723.753.

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A composite tuned mass damper(CTMD) is a vibration control device consisting of an active-passive tuned mass dampers supported on the primary vibrating structure. The performance of CTMD in mitigating wind-induced vibration of tall building is investigated. Optimum parameters of a passive tuned mass damper(PTMD)for minimizing the variance response of the damped primary structure under random loads, with different mass ratio of an active tuned mass damper(ATMD) to a PTMD have been used for the optimum parameters of CTMD. The active control force generated by ATMD actuator was estimated by using linear quadratic Gaussian(LQG) controller, and the fluctuating along-wind load, treated as a stationary random process ,was simulated numerically using the along-wind load spectrum proposed by Solari .Comparing the along-wind rms response of tall building without a CTMD, the CTMD is effective in reducing the response to 40%~45% of the response without the CTMD. Therefore, the CTMD system was effective in reducing wind-induced vibration of tall building.
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14

Cong, Cong. "Using active tuned mass dampers with constrained stroke to simultaneously control vibrations in wind turbine blades and tower." Advances in Structural Engineering 22, no. 7 (December 21, 2018): 1544–53. http://dx.doi.org/10.1177/1369433218817892.

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Simultaneous control of wind turbine blades and tower vibrations is studied in this article. Four active tuned mass dampers have been incorporated into each blade and tower to reduce vibrations. A decentralized constrained H∞ velocity output feedback which restricts the tuned mass damper stroke as a hard constraint is proposed by solving linear matrix inequality. Each active tuned mass damper is driven individually by the output of the corresponding velocity signal. Considering the structural dynamics subjected to gravity, variable rotor speed, and aerodynamic loadings, a model describing dynamics of rotating blades coupled with tower, including the dynamics of active tuned mass dampers, was developed by Euler–Lagrangian formulation. A numerical simulation is carried out to verify the effectiveness of the proposed decentralized control scheme. Investigations show promising results for the active tuned mass damper in simultaneous control blade vibrations and tower vibrations by decentralized control approach. Numerical results demonstrate that the decentralized control has the similar performance compared to centralized control and effectively reduce the displacement of vibrations.
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15

Yadav, Ajay, Devangkumar Talaviya, Ankit Bansal, and Mohit Law. "Design of Chatter-Resistant Damped Boring Bars Using a Receptance Coupling Approach." Journal of Manufacturing and Materials Processing 4, no. 2 (June 3, 2020): 53. http://dx.doi.org/10.3390/jmmp4020053.

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Deep hole boring using slender bars that have tuned mass dampers integrated within them make the boring process chatter vibration resistant. Dampers are usually designed using classical analytical solutions that presume the (un)damped boring bar which can be approximated by a single degree of freedom system, and the damper is placed at the free end. Since the free end is also the cutting end, analytical models may result in infeasible design solutions. To place optimally tuned dampers within boring bars, but away from the free end, this paper presents a receptance coupling approach in which the substructural receptances of the boring bar modelled as a cantilevered Euler–Bernoulli beam are combined with the substructural receptances of a damper modelled as a rigid mass integrated anywhere within the bar. The assembled and damped system response thus obtained is used to predict the chatter-free machining stability limit. Maximization of this limit is treated as the objective function to find the optimal mass, stiffness and damping of the absorber. Proposed solutions are first verified against other classical solutions for assumed placement of the absorber at the free end. Verified models then guide prototyping of a boring bar integrated with a damper placed away from its free end. Experiments demonstrate a ~100-fold improvement in chatter vibration free machining capability. The generalized methods presented herein can be easily extended to design and develop other damped and chatter-resistant tooling systems.
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16

Li, Lu-yu, and Tianjiao Zhang. "Analytical analysis for the design of nonlinear tuned mass damper." Journal of Vibration and Control 26, no. 9-10 (January 9, 2020): 646–58. http://dx.doi.org/10.1177/1077546319889840.

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A tuned mass damper is a passive control device that has been widely used in aerospace, mechanical, and civil engineering as well as many other fields. Tuned mass dampers have been studied and improved over the course of many years. In practical engineering applications, a tuned mass damper inevitably produces some nonlinear characteristics due to the large displacement and the use of the limiting devices, but this nonlinearity is often neglected. The simulation results in this study confirm that neglecting the nonlinearity in the design process can produce adverse effects on the control performance. This paper takes into account the nonlinearity of the tuned mass damper produced in the process of vibration and deduces an optimum formula for the frequency of a tuned mass damper by the complexification averaging method and multiscale method. Based on this formula, a modified design method for the frequency of a tuned mass damper is presented. The numerical results show that the nonlinear tuned mass damper after modification is better than a linear tuned mass damper in terms of control performance.
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17

Fu, Bo, Huanjun Jiang, and Jin Chen. "Substructure Shake Table Testing of Frame Structure–Damper System Using Model-Based Integration Algorithms and Finite Element Method: Numerical Study." Symmetry 13, no. 9 (September 18, 2021): 1739. http://dx.doi.org/10.3390/sym13091739.

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Substructure shake table testing (SSTT) is an advanced experimental technique that is suitable for investigating the vibration control of secondary structure-type dampers such as tuned mass dampers (TMDs). The primary structure and damper are considered as analytical and experimental substructures, respectively. The analytical substructures of existing SSTTs have mostly been simplified as SDOF structures or shear-type structures, which is not realistic. A common trend is to simulate the analytical substructure via the finite element (FE) method. In this study, the control effects of four dampers, i.e., TMD, tuned liquid damper (TLD), particle damper (PD) and particle-tuned mass damper (PTMD), on a frame were examined by conducting virtual SSTTs. The frame was modeled through stiffness-based beam-column elements with fiber sections and was solved by a family of model-based integration algorithms. The influences of the auxiliary mass ratio, integration parameters, time step, and time delay on SSTT were investigated. The results indicate that the TLD had the best performance. In addition, SSTT using model-based integration algorithms can provide satisfactory results, even when the time step is relatively large. The effects of integration parameters and time delay are not significant.
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18

He, Er-Ming, Ya-Qi Hu, and Yang Zhang. "Optimization design of tuned mass damper for vibration suppression of a barge-type offshore floating wind turbine." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 231, no. 1 (August 3, 2016): 302–15. http://dx.doi.org/10.1177/1475090216642466.

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An efficient method for restraining the large vibration displacements and loads of offshore floating wind turbines under harsh marine environment is proposed by putting tuned mass dampers in the cabin. A dynamics model for a barge-type offshore floating wind turbine with a fore–aft tuned mass damper is established based on Lagrange’s equations; the nonlinear least squares Levenberg–Marquardt algorithm is employed to identify the parameters of the wind turbine; different parameter optimization methods are adopted to optimize tuned mass damper parameters by considering the standard deviation of the tower top longitudinal displacement as the objective function. Aiming at five typical combined wind and wave load cases under normal running state of the wind turbine, the dynamic responses of the wind turbine with/without tuned mass damper are simulated and the suppression effect of the tuned mass damper is investigated over the wide range of load cases. The results show that when the wind turbine vibrates in the state of damped free vibration, the standard deviation of the tower top longitudinal displacement is decreased approximately 60% in 100 s by the optimized tuned mass damper with the optimum tuned mass damper mass ratio 1.8%. The standard deviation suppression rates of the longitudinal displacements and loads in the tower and blades increase with the tuned mass damper mass ratio when the wind turbine vibrates under the combined wind and wave load cases. When the mass ratio changes from 0.5% to 2%, the maximum suppression rates vary from 20% to 50% correspondingly, which effectively reduce vibration responses of the offshore floating wind turbine. The results of this article preliminarily verify the feasibilities of using a tuned mass damper for restraining vibration of the barge-type offshore floating wind turbine.
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19

Štepánek, Jan, and Jiří Máca. "DESIGN OF TUNED MASS DAMPERS FOR LARGE STRUCTURES USING MODAL ANALYSIS." Acta Polytechnica CTU Proceedings 26 (March 17, 2020): 100–106. http://dx.doi.org/10.14311/app.2020.26.0100.

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Tuned mass damper is a device, which can be highly useful when dealing with excessive vibration and is widely used in many engineering fields. However, its proper design and optimization is a complicated task. This study uses mode superposition method to speed up the evaluation of dynamic response. The speed of response calculation allows for a quick calculation of frequency response function and numerical optimization of tuned mass dampers. This optimization method is demonstrated on a numerical example of a cable stayed footbridge. The example compares a simplified and widely used design method of tuned mass damper with numerical optimization.
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20

Zhang, Zhi Qiang, and Fei Ma. "Research on Seismic Response Vibration Hybrid Control of Hefei TV Tower." Advanced Materials Research 243-249 (May 2011): 5197–203. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.5197.

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In this paper, Hefei TV Tower is used as an analytical case to examine the Hybrid control method on seismic response. Firstly, on the basis of the other’s work, a bi-model dynamic model is proposed to study the seismic response vibration hybrid control, using tuned mass damper and viscous fluid dampers. Then the optimal coefficient is obtained by considered the seismic response of upper turret as optimization objectives. According to analysis, it’s showed that the seismic responses of the tower are decreased greatly with tuned mass damper and viscous fluid dampers, and the vibration reduction effectiveness of the tower is sensitive to the spectral characteristics of earthquake wave.
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21

Ying Zhang, Sara, Yi-Yuan Li, Jason Zheng Jiang, Simon A. Neild, and John H. G. Macdonald. "A methodology for identifying optimum vibration absorbers with a reaction mass." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2228 (August 2019): 20190232. http://dx.doi.org/10.1098/rspa.2019.0232.

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Tuned mass dampers (TMDs), in which a reaction mass is attached to a structural system via a spring–parallel–damper connection, are commonly used in a wide range of applications to suppress deleterious vibrations. Recently, a mass-included absorber layout with an inerter element, termed the tuned mass damper inerter (TMDI), was introduced, showing significant performance benefits on vibration suppression. However, there are countless mass-included absorber layouts with springs, dampers and inerters, which could potentially provide more preferred dynamic properties. Currently, because there is no systematic methodology for accessing them, only an extremely limited number of mass-included absorber layouts have been investigated. This paper proposes an approach to identify optimum vibration absorbers with a reaction mass. Using this approach, a full class of absorber layouts with a reaction mass and a pre-determined number of inerters, dampers and springs connected in series and parallel, can be systematically investigated using generic Immittance-Function-Networks. The advan- tages of the proposed approach are demonstrated via a 3 d.f. structure example.
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22

Kwon, Oh Hoon, and Shin Hyoung Park. "Comparing the Effectiveness of Friction Damper and Tuned Mass Damper Using Numerical Simulation." Applied Mechanics and Materials 835 (May 2016): 455–60. http://dx.doi.org/10.4028/www.scientific.net/amm.835.455.

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The purpose of this study is to evaluate and compare the effectiveness of friction dampers and tuned mass dampers (TMD) using numerical simulations. Wind and earthquake loads are simulated on a 15-story model building structure in which a friction damper and/or a TMD are installed. The idealized one-dimensional structure with a friction damper at each story and/or a TMD at the top of the building is subjected to a simulated load, and the displacement and acceleration responses of the structure are measured. The outcomes show that a TMD is more useful to control the vibration of the building from a wind load and a friction damper is more suitable for loads created by large accelerations such as those found during seismic events. This study provides verification on the performance of friction dampers and TMDs according to each of the two load types, wind and earthquake, through numerical simulations.
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23

Xu, Ruotian, Jun Chen, and Xinqun Zhu. "A hybrid approach for parameter optimization of multiple tuned mass dampers in reducing floor vibrations due to occupant walking: Theory and parametric studies." Advances in Structural Engineering 20, no. 8 (January 27, 2017): 1232–46. http://dx.doi.org/10.1177/1369433216684351.

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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.
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24

Wang, Xiong Jiang, Jia Yun Xu, and Ji Chen. "Study on the Indiscrete Tuned Mass Damper for Buffeting Control of Long Span Cable-Stayed Bridges." Applied Mechanics and Materials 160 (March 2012): 405–9. http://dx.doi.org/10.4028/www.scientific.net/amm.160.405.

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A study of buffeting control of the E-dong Bridge Using an indiscrete tuned mass damper (ITMD) system is performed in this paper. Different from the traditional multiple tuned mass damper (MTMD) system which is fixed along the main span of bridge discretely, this indiscrete tuned mass damper is attached to the centre region of the bridge’s main span continuously. A three-dimensional finite element model of E-dong Bridge, is completed by the software of ANSYS. By comparing the vertical and lateral buffeting response of bridge without dampers, the control efficiency of ITMD and MTMD is confirmed.
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Cetin, Huseyin, Ersin Aydin, and Baki Ozturk. "Optimal damper allocation in shear buildings with tuned mass dampers and viscous dampers." International Journal of Earthquake and Impact Engineering 2, no. 2 (2017): 89. http://dx.doi.org/10.1504/ijeie.2017.089038.

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Ozturk, Baki, Huseyin Cetin, and Ersin Aydin. "Optimal damper allocation in shear buildings with tuned mass dampers and viscous dampers." International Journal of Earthquake and Impact Engineering 2, no. 2 (2017): 89. http://dx.doi.org/10.1504/ijeie.2017.10010008.

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27

Sikora, Marian. "Modeling and Operational Analysis of an Automotive Shock Absorber with a Tuned Mass Damper." Acta Mechanica et Automatica 12, no. 3 (September 1, 2018): 243–51. http://dx.doi.org/10.2478/ama-2018-0038.

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Abstract Recently, the topic of energy dissipation efficiency of vehicle suspension dampers has become a research and engineering problem due to structural requirements of vehicle manufacturers and the introduction of electric/hybrid cars. By principle, any disturbances in the damping force generation process translate into pressure fluctuations to be then transferred to the body of the vehicle. The effect known as rattling within the damper engineering community is perceived as detrimental to ride comfort. To improve the performance of a vehicle damper several methods can be devised and used. One approach is to optimize the settings of the valves in the damper. The approach, however, often influences the force output of the damper. Another technique involves the application of add-on systems. One such system is the tuned mass damper concept originally developed by Frahm for structural engineering applications. In the paper the author proposes a damper concept equipped with an external/internal tuned mass damper component for improving the dynamic characteristics of vehicle dampers. The author presents modeling details followed by simulations of the damper with the tuned mass damper concept subjected to oscillatory inputs, and a critical analysis of the presented results.
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Murakami, Katsuhide, Masato Ishii, Kentaroh Miyazaki, and Yasuhiro Tsuneki. "Proposal for an Efficient Damping System for High-Rise Buildings in Major Earthquakes." Journal of Disaster Research 11, no. 1 (February 1, 2016): 106–17. http://dx.doi.org/10.20965/jdr.2016.p0106.

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Recent vibration resistant designs for buildings in Japan often adopt a vibration control structure with dampers arranged in the framework. Generally, the dampers are arranged in the building’s core in a geometry that works most effectively to protect against story shearing deformation. It is already known, however, that the above-mentioned arrangement of dampers does not provide good damping effects for the upper stories of high-rise buildings with large aspect ratios, because the protection mechanism is designed to decrease the shearing deformation components of the building’s horizontal deformation caused by its horizontal loads. A new type of dampers, called force-restricted tuned viscous mass dampers (FRTVMD), has been recently developed for such circumstances, amplifying the deformation of viscous dampers with their tuned mass effects. This paper, therefore, first presents a tuned mass damper (TMD) system, effective for high-rise buildings with large aspect ratios against great earthquakes, and then proposes a new vibration control structural system capable of generating better damping effects with FRTVMD. In addition, we review its characteristics and effects by analyzing its vibration response, as well as verify that a combined use of such vibration control structural systems will generate far greater damping effects than an individual system.
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Ahmad, Aabas. "Load Reduction of Floating Wind Turbines Using Tuned Mass Dampers." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1298–303. http://dx.doi.org/10.22214/ijraset.2021.38178.

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Abstract: Offshore wind turbines have the potential to be an important part of the United States’ energy production profile in the coming years. In order to accomplish this wind integration, offshore wind turbines need to be made more reliable and cost efficient to be competitive with other sources of energy. To capitalize on high speed and highquality winds over deep water, floating platforms for offshore wind turbines have been developed, but they suffer from greatly increased loading. One method to reduce loadsin offshore wind turbines is the application of structural control techniques usuallyused in skyscrapers and bridges. Tuned mass dampers are one structural control system that have been used to reduce loads in simulations of offshore wind turbines. This thesis adds to the state of the art of offshore wind energy by developing a set of optimum passive tuned mass dampers for four offshore wind turbine platforms and byquantifying the effects of actuator dynamics on an active tuned mass damper design. The set of optimum tuned mass dampers are developed by creating a limited degree-of-freedom model for each of the four offshore wind platforms
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30

Lu, Zheng, Dianchao Wang, and Peizhen Li. "Comparison Study of Vibration Control Effects between Suspended Tuned Mass Damper and Particle Damper." Shock and Vibration 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/903780.

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The vibration control performance and its influencing factors of a tuned mass damper and a particle damper are examined by a single degree of freedom structure with such devices. The vibration control effects between these two dampers are also investigated. Increasing the mass ratio of the damper can improve the damping effects; under the condition of tuning frequency, the damping effects are remarkable. However, the more the deviation from the tuned frequency, the less controlling effects can be obtained. The damping effect of a particle damper is generally better than that of a tuned mass damper. For this test model, the particle damper can improve primary structure’s equivalent damping ratio 19 times to the original one’s, while the tuned mass damper can be 13 times. The reason lies in the fact that the particle damper can dissipate input energy by tuning mass, collision, impact, and friction between particles and the container and the momentum exchange effects between the secondary damper mass and the primary structure.
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31

Makino, Akifumi. "High-Rise Building Seismic Vibration Control Using Large Tuned Top-Floor Mass Damper." Journal of Disaster Research 4, no. 3 (June 1, 2009): 246–52. http://dx.doi.org/10.20965/jdr.2009.p0246.

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This paper details the design of a high-rise reinforced concrete building whose top floor is isolated and used as the mass for a large-scale mass damper, describing the effect of the vibration control realized. Conventional mass dampers with additional weight at the building tops have been installed to improve environmental vibration against strong wind. Mass dampers have rarely been used, however, as measure against earthquakes. We developed large-scale vibration control using the top floor building weight to serve as a mass damper. The building is a high-rise reinforced concrete structure, 162 meters high, with 43 above-ground stories. Based on seismic response analysis using artificial earthquake waves, the natural vibration period of the mass damper was tuned to decrease story drift in the entire building. The mass damper reduced maximum story drift angle by 20%.
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32

Nagarajaiah, Satish, and Hyung-Jo Jung. "Smart tuned mass dampers: recent developments." Smart Structures and Systems 13, no. 2 (February 25, 2014): 173–76. http://dx.doi.org/10.12989/sss.2014.13.2.173.

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33

Mrad, Charbel, Magdalini D. Titirla, and Walid Larbi. "Comparison of Strengthening Solutions with Optimized Passive Energy Dissipation Systems in Symmetric Buildings." Applied Sciences 11, no. 21 (October 28, 2021): 10103. http://dx.doi.org/10.3390/app112110103.

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The aim of this study is to compare the seismic response of reinforced concrete (RC) symmetric buildings, with a varied number of stories, strengthening with three types of passive energy dissipation systems, as tuned mass dampers, viscous dampers, and friction dampers. The paper presents an overview of design optimization with the object of minimizing certain functions: (i) the maximum displacement at the top of the structures, (ii) the base shear loads, and (iii) the maximum interstory drift. The objective functions were evaluated in three residents’ buildings (a four-story building, a nine-story building, and a sixteen-story building) subjected to seven (real and artificial) seismic recorded accelerograms. For this purpose, 94 nonlinear dynamic analyses were carried out. The effects of each strengthening solution are presented, and from this innovative comparison (optimal design, three different passive energy systems, three different story numbers), further useful results were observed. The outcomes of the study show the effectiveness of a tuned mass damper (TMD) system, and how it might be better for tall and flexible structures than for stiffer structures. However, the response of the pendulum tuned mass damper (TMD) configuration is better than the conventional one because it acts in all directions. The viscous dampers (VDs) provide a significant reduction for mid-rise buildings, while friction dampers (FDs) boost the performance of all structures under seismic action, especially in terms of displacement, and they are more suitable for low-rise buildings.
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34

Wang, Xiuli, and Di Yun. "Force Feedback Control Method of Active Tuned Mass Damper." Shock and Vibration 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/9659425.

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Active tuned mass dampers as vibration-control devices are widely used in many fields for their good stability and effectiveness. To improve the performance of such dampers, a control method based on force feedback is proposed. The method offers several advantages such as high-precision control and low-performance requirements for the actuator, as well as not needing additional compensators. The force feedback control strategy was designed based on direct-velocity feedback. The effectiveness of the method was verified in a single-degree-of-freedom system, and factors such as damping effect, required active force, actuator stroke, and power consumption of the damper were analyzed. Finally, a simulation study was performed by configuring a main complex elastic-vibration-damping system. The results show that the method provides effective control over modal resonances of multiple orders of the system and improves its dynamics performance.
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35

BAKRE, S. V., and R. S. JANGID. "OPTIMUM MULTIPLE TUNED MASS DAMPERS FOR BASE-EXCITED DAMPED MAIN SYSTEM." International Journal of Structural Stability and Dynamics 04, no. 04 (December 2004): 527–42. http://dx.doi.org/10.1142/s0219455404001367.

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The optimum parameters of multiple tuned mass dampers (MTMD) for suppressing the dynamic response of a base-excited damped main system are investigated by a numerical searching technique. The criterion selected for the optimality is the minimization of the steady state displacement of the main system under harmonic base acceleration. The parameters of the MTMD that are optimized include: the damping ratio, the tuning frequency ratio and the frequency bandwidth. The optimum parameters of the MTMD system and corresponding displacement are obtained for different damping ratios of the main system and different mass ratios of the MTMD system. The explicit formulas for the optimum parameters of the MTMD (i.e. damping ratio, bandwidth and tuning frequency) are then derived using a curve-fitting scheme that can readily be used in engineering applications. The error in the proposed explicit expressions is investigated and found to be negligible. The effectiveness of the optimally designed MTMD system is also compared with that of the optimum single tuned mass damper. It is observed that the optimally designed MTMD system is more effective for vibration control than the single tuned mass damper. Further, the damping in the main system significantly influences the optimum parameters and the effectiveness of the MTMD system.
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36

Sahu, Reena, and Anurag Wahane. "Numerical Analysis and Validation of Irregularity in Moment Frame Structure Due to Varying Location of Tuned Mass Damper." International Journal for Research in Applied Science and Engineering Technology 10, no. 8 (August 31, 2022): 345–51. http://dx.doi.org/10.22214/ijraset.2022.46193.

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Abstract: Within the construction industry, the number of higher and lighter structures that are adaptable and have a low damping value has been steadily increasing in recent years. Those constructions will simply fail as a result of earthquake and wind-induced structural vibrations. There are a variety of approaches available today to reduce structural vibration, and one of the oldest is the use of dampers. The tuned mass damper is tuned to the structural frequency of the structure if the stiffness and damping values are kept constant. The main goal is to investigate the mass and torsional irregularity in the structure. This study is divided into two phases - first phase involves the investigation and validation of structure having tuned damper with varying location along the height of building. The second phase involves the location of tuned mass damper with the plan projection of the building. Non-Linear Time history analysis is used to identify the behavior of frame elements in the structure based on considered cases using ETABS. The parameters such as displacement was evaluated. The result shows that the dampers should be carefully placed in order to tune the frequency of the structure.
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Sundar, K. P. Shiyam, Johny Sebastian, M. K. Shrimali, and S. D. Bharti. "Dynamic Response Reduction of Reinforced Concrete Structure using Tuned Mass Damper and Tuned Liquid Damper." Proceedings of the 12th Structural Engineering Convention, SEC 2022: Themes 1-2 1, no. 1 (December 19, 2022): 1699–705. http://dx.doi.org/10.38208/acp.v1.707.

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Damping devices are used to reduce the dynamic response of a structure by energy dissipation. Common types of damping devices are fluid viscous dampers, tuned mass dampers, and tuned liquid dampers. This project aims to study the effectiveness of TMD and TLD in controlling the response of the structure when it is subjected to acceleration records of different earthquakes. A 20-storey reinforced concrete bare frame structure has been subjected to two earthquake acceleration records with and without dampers in SAP 2000. The dampers are modelled using link elements. The structure is attached with TMD and TLD having a mass of 0.5%, 2%, 4%, 6%, 8% and 10% of the modal mass. The analysis procedure used is nonlinear modal time history analysis (FNA). The variation in base shear and top storey displacement has been obtained and plotted.
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38

Tian, Li, Qian Wang, Qiqi Yu, and Nuwen Xu. "Wind-induced Vibration Optimal Control for Long Span Transmission Tower-line System." Open Civil Engineering Journal 7, no. 1 (October 31, 2013): 159–63. http://dx.doi.org/10.2174/1874149501307010159.

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In this paper, tuned mass dampers with optimal parameters for long span transmission tower-line system are investigated. Equations of motion for a structure-TMD system are derived, and the parameters of TMD, stiffness and damping are optimized, respectively. According to a real project, three-dimensional finite element models of both transmission tower and transmission tower-line system are created and their vibration performances are analyzed using SAP2000 software, respectively. Wind load time history is simulated based on wind theory. Using numerical simulation, vibration control with optimal tuned mass damper installed in transmission tower-line system is carried out. Time history curves and the maximum responses of system without and with tuned mass damper under wind excitation are analyzed and discussed. The results show that the optimal tuned mass damper could effectively decrease the wind-induced response of long span transmission tower-line system.
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39

Ahmad, Afham Zulhusmi, Aminudin Abu, Lee Kee Quen, Nor’azizi Othman, and Faridah Che In. "EXPERIMENTAL ANALYSIS OF THE VISCOUS TUNED MASS DAMPER FOR THE ATTENUATION OF STRUCTURAL RESPONSES." Jurnal Teknologi 83, no. 6 (September 27, 2021): 125–39. http://dx.doi.org/10.11113/jurnalteknologi.v83.17151.

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This paper presents a systematic experimental investigation on the performance of a Multiple Tuned Mass Dampers (MTMDs) attached to a structural system under dynamic load excitation. A Modal Experimental Analysis (EMA) of a three-story structural frame equipped with a viscous damper system was carried out through a series of shaking table tests to evaluate the performance and verify the analysis approach. Each of the TMDs consists of a mass attached to a structural floor via Thermoplastic Polyurethane (TPU) viscous bearing. Initially, the TMD was designed solely to control single mode vibration and then the mechanism is extended for the application of controlling multimode responses. The experiment demonstrated that the proposed viscous dampers exhibit good performance in reducing the response of structures under dynamic loads, and able to control both fundamental and higher vibration modes of a Multiple Degree of Freedom (MDOF) primary system effectively. It was also evident that the attachment of the air dashpot dampers to each of TMDs lead to better efficiency on controlling the amplification of the damper mass and significantly contribute to better structural modal tuning.
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40

Liang, Dong, and Ji Xiang Song. "Theoretical Study on Cable’s Vibration Control by Single TMD." Advanced Materials Research 935 (May 2014): 211–14. http://dx.doi.org/10.4028/www.scientific.net/amr.935.211.

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The commonly used viscous dampers for cable’s vibration mitigation have some unfavorable factors, such as the damping effect is not obvious for super long stay cable, the limitation of installation position, coupling vibration, etc. The cable-tuned mass damper system vibration model is put forward to solve this problem. The optimal cable-tuned mass damper system modal damping ratio and optimum design parameters, including cable vibration order, TMD’s stiffness, TMD’s mass, and TMD’s damping, were obtained by the method of complex models. The results can provide important reference for the design of TMD for stay cable.
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41

Tang, Xiudong, and Lei Zuo. "Simultaneous energy harvesting and vibration control of structures with tuned mass dampers." Journal of Intelligent Material Systems and Structures 23, no. 18 (November 20, 2012): 2117–27. http://dx.doi.org/10.1177/1045389x12462644.

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The vibrations of the tall buildings are serious concerns to both engineers and architects for the protection of the safety of the structure and occupant comfort. In order to mitigate the vibration, different approaches have been proposed, among which tuned mass dampers are one of the most preferable and have been widely used in practice. Instead of dissipating the vibration energy into heat waste via the viscous damping element, this article presents an approach to harvest the vibration energy from tall buildings with tuned mass dampers, by replacing the energy-dissipating element with an electromagnetic harvester. This article demonstrates that vibration mitigation and energy harvesting can be achieved simultaneously by the utilization of an electricity-generating tuned mass damper and relevant algorithms. Based on the proposed switching energy harvesting circuit, three control strategies are investigated in this article, namely, semi-active, self-powered active, and passive-matching regenerative. The functions of the energy harvesting circuit on damping force control and power regulation, as well the effectiveness of the control strategies, are illustrated by simulation. The simultaneous energy harvesting and vibration control are demonstrated, for the first time, by experiment based on a three-story building prototype with the electricity-generating tuned mass damper, which is composed of a rotational brushed direct current motor and rack–pinion mechanism.
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42

Li, Chunxiang, and Yanxia Liu. "Further Characteristics for Multiple Tuned Mass Dampers." Journal of Structural Engineering 128, no. 10 (October 2002): 1362–65. http://dx.doi.org/10.1061/(asce)0733-9445(2002)128:10(1362).

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43

Setareh, Mehdi, and Robert D. Hanson. "Tuned Mass Dampers for Balcony Vibration Control." Journal of Structural Engineering 118, no. 3 (March 1992): 723–40. http://dx.doi.org/10.1061/(asce)0733-9445(1992)118:3(723).

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44

Batou, A., and S. Adhikari. "Optimal parameters of viscoelastic tuned-mass dampers." Journal of Sound and Vibration 445 (April 2019): 17–28. http://dx.doi.org/10.1016/j.jsv.2019.01.010.

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45

Leung, A. Y. T., and Haijun Zhang. "Particle swarm optimization of tuned mass dampers." Engineering Structures 31, no. 3 (March 2009): 715–28. http://dx.doi.org/10.1016/j.engstruct.2008.11.017.

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46

Pansare, A. P., and R. S. Jangid. "Tuned mass dampers for torsionally coupled systems." Wind and Structures 6, no. 1 (February 25, 2003): 23–40. http://dx.doi.org/10.12989/was.2003.6.1.023.

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47

Özsarıyıldız, Şaban S., and Ali Bozer. "Finding optimal parameters of tuned mass dampers." Structural Design of Tall and Special Buildings 24, no. 6 (August 12, 2014): 461–75. http://dx.doi.org/10.1002/tal.1174.

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48

Igusa, T., and K. Xu. "Vibration Control Using Multiple Tuned Mass Dampers." Journal of Sound and Vibration 175, no. 4 (August 1994): 491–503. http://dx.doi.org/10.1006/jsvi.1994.1341.

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49

Zhang, Peng, Jie Tan, Haitao Liu, Gang Yang, and Chunyi Cui. "Seismic Vibration Mitigation of a Cable-Stayed Bridge with Asymmetric Pounding Tuned Mass Damper." Mathematical Problems in Engineering 2021 (April 29, 2021): 1–13. http://dx.doi.org/10.1155/2021/6647303.

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In order to mitigate the seismic response of a cable-stayed bridge, a new type damping device named asymmetric pounding tuned mass damper (APTMD) is developed in this paper on the basis of the traditional symmetric pounding tuned mass damper. The novel APTMD has three parameters to be determined: the left-side gap, the right-side gap, and the frequency ratio. A numerical model of the APTMD damping system is established with consideration of both the computational efficiency and accuracy to enable the parametric optimization of the damper. The numerical model is based on a simplified model of the cable-stayed bridge and a nonlinear pounding force model. The genetic algorithm is utilized for the optimization of the damper. Afterwards, the cable-stayed bridge is subjected to 20 recorded ground motions to evaluate the vibration control effectiveness of the APTMD. Four systems are considered: (1) without dampers; (2) with a TMD; (3) with a PTMD; and (4) with an APTMD. Time history analysis reveals the following: (1) those dampers can all effectively suppress the vibration of the bridge and (2) the vibration control effectiveness of the APTMD is slightly better than the TMD and the PTMD.
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50

Tian, Li, and Yujie Zeng. "Parametric Study of Tuned Mass Dampers for Long Span Transmission Tower-Line System under Wind Loads." Shock and Vibration 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/4965056.

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A parametric study of tuned mass dampers for a long span transmission tower-line system under wind loads is done in this paper. A three-dimensional finite element model of transmission tower-line system is established by SAP2000 software to numerically verify the effectiveness of the tuned mass damper device. The wind load time history is simulated based on Kaimal spectrum by the harmony superposition method. The equations of motion of a system with tuned mass damper under wind load excitation are proposed, and the schematic of tuned mass damper is introduced. The effects of mass ratio, frequency ratio, damping ratio, the change of the sag of transmission line, and the robustness of TMD are investigated, respectively. Results show that(1)the change of mass ratio has a greater effect on the vibration reduction ratio than those of frequency ratio and damping ratio, and the best vibration reduction ratio of TMD is not the frequency ratio of 1;(2)the sag-span ratio has an insignificant effect on the vibration reduction ratio of transmission tower when the change of sag-span ratio is not large; and(3)the effect of ice should be considered when the robustness study of TMD is carried out.
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