Optimal Parameters Of Tuned Mass Damper Research Articles

Optimal Design of Formulas for a Single Degree of Freedom Tuned Mass Damper Parameter Using a Genetic Algorithm and H2 Norm.

One of the researchers' concerns in structural engineering is to control the dynamic behavior of structures efficiently. The TMD (tuned mass damper) is one of the effective methods of controlling the vibration of structures, and various numerical techniques have been proposed to find the optimal parameters of the TMD. This paper develops a new explicit formula to derive the optimal parameters of the TMD of a single degree of freedom (SDOF) structure under seismic load using a genetic algorithm (GA). In addition, the state-space model and the H2 norm function are used to identify the optimal frequency ratio and damping ratio of the TMD that minimize the overall vibration energy of the structure. The MATLAB curve fitting toolbox is used for the explicit formula proposal, and the validity of the proposed formula is verified through multidimensional performance verification technique. Finally, the TMD parameters of the SDOF structure are applied to the multi-degrees of freedom (MDOF) structure to compare and analyze with the existing research results, and the results of the explicit formula proposed in this paper are confirmed to be excellent. This paper can suggest a new direction for determining the optimal TMD parameters using a GA and can be effectively applied to vibration control problems of various structures.

Optimization of tuned mass dampers for multiple mode vortex-induced vibration mitigation in flexible structures: An application to multi-span continuous bridge

Tuned mass dampers (TMDs) have proven effective in suppressing structural vibration. In existing research on vortex-induced vibration (VIV) control of flexible structures, only one mode is commonly considered at the time, and only basic aerodynamic force models, which can struggle to model amplitude-dependent damping, are considered. However, flexible structures, such as multi-span bridges, exhibit multiple modes with closely spaced frequencies. Neglecting secondary modes may introduce calculation inaccuracies, as these modes can impose additional stiffness, thereby influencing the performance of TMD. This paper presents a framework to optimize the performance of multiple TMDs in the context of multi-mode VIV control for a flexible structure. A multi-span bridge is used as a case study, and the secondary modes and nonlinear aerodynamic effects are considered. The governing equations for the force-structure-MTMDs system are derived in modal coordinates using a polynomial model to model the aerodynamic force. A novel method to calculate the contribution of each mode to determine the minimum number of secondary modes to be considered is proposed. The optimal parameters of MTMDs are obtained using a global optimization method and compared with mode-by-mode design results. Robustness analysis is conducted to verify the effectiveness of the optimization framework. The results show that the polynomial model accurately predicts the amplitude after TMD installation. Secondary modes significantly affect the optimal parameters of TMDs, and the optimized results exhibit better control performance than the mode-by-mode design results.

On the Efficacy of a Novel Optimized Tuned Mass Damper for Minimizing Dynamic Responses of Cantilever Beams

This study examines the optimal design of a tuned mass damper (TMD) in the frequency domain so that the dynamic response of cantilever beams can be decreased. Random vibration theory is applied to identify the mean square acceleration of the endpoint of a cantilever beam as the objective function to be reduced. In addition, to determine the optimal TMD coefficient of mass, stiffness, and damping, a differential evolution (DE) optimization algorithm is employed. The upper and lower limit values of these parameters are taken into account. A majority of the previous studies have concentrated on determining just the stiffness and damping parameters of TMD. Nonetheless, in this study there is also the optimization of TMD mass parameters to determine the mass quantity. In addition, there has been inefficient use of the stochastic DE optimization algorithm method for the optimization of TMD parameters in previous studies. Hence, to obtain optimal TMD parameters, this algorithm is precisely used on the objective function. Tests are carried out on the cantilever beam with the TMD system following this optimization method with harmonic base excitations that resonate the foremost modes of the beam and white noise excitation. The method proposed here is reasonably practical and successful regarding the optimal TMD design. When a TMD is designed appropriately, the response of the cantilever beam under dynamic interactions undergoes a considerable reduction.

Optimization of TMD Parameters in Frequency Domain Including SSI Effect by Means of Recent Metaheuristic Algorithms

This study presents the application of three recent metaheuristic optimization algorithms to design the tuned mass damper (TMD) for a high-rise building structure, taking into account the effect of soil–structure interaction (SSI) in the frequency domain. The algorithms used in this study were grey wolf optimizer (GWO), moth–flame optimization (MFO), and whale optimization algorithm (WOA), and the obtained results were compared with the well-known particle swarm optimization (PSO) and genetic algorithm (GA). The TMD optimization problem was formulated with two objective functions: the H2 and the H∞ norms of the top floor displacement. The frequency, the mass, and the damping ratio of the TMD were optimized within defined bounds for a 40-story benchmark structure. Unlike in previous research, the optimization in this study was performed for different mass ratios. First, the efficiency of the obtained optimum parameters was plotted in the frequency domain and then tested in the time domain by presenting the top floor displacement of the same benchmark structure. The time domain analysis was carried out using the El Centro and Petrolia earthquakes as external disturbances. It was found that the optimal TMD parameters are affected by the soil type. The GWO algorithm reached the optimal solutions faster and more efficiently than the other algorithms. GA limitations were pointed out.

Optimization and sensitivity of TMD parameters for mitigating bridge maximum vibration response under moving forces

In order to effectively reduce the vertical vibration response of the bridge, this paper proposes a frequency-domain analysis method of bridge vibration that can consider the influence of the tuned mass damper (TMD) device. In this method, the time-domain motion equation of bridge-TMD under moving concentrated loads’ excitation is first established. Then, the equation of motion is Fourier transformed to obtain the displacement response spectrum of the bridge with the TMD device installed. Further, the 2-norm of the displacement response spectrum of the bridge is optimized by the augmented Lagrangian optimization method to obtain the optimal TMD parameters. Finally, numerical simulations verify the superiority of this method over the traditional optimization method (Den Hartog’s method) in terms of maximum displacement control. And, the effects of bridge damping ratio, moving load number, and axle-span ratio and moving load speed on the optimal parameters of TMD to control the maximum displacement response of the bridge were studied. The results show that using the augmented Lagrangian optimization method to optimize the 2-norm of the displacement response spectrum of the bridge can not only effectively analyze the influence of each bridge and load parameters on the selection of TMD optimal parameters, but also it can reasonably configure TMD parameters for all kinds of simply supported beam bridges, which can provide references for practical engineering applications.

Optimum design of tuned mass dampers for different earthquake ground motion parameters and models

SummaryTuned mass dampers are frequently used for passive control of vibrations in civil structures subject to seismic and wind actions. Their efficiency depends on selection of their mechanical properties in relation to main system and excitation characteristics. This paper proposes an optimum design strategy of single tuned mass dampers to control vibrations of principal mode of structures excited by earthquake ground motion. The main purpose of the paper is to investigate the influence of the time modulation of earthquake excitation upon the optimal tuned mass dampers design parameters: frequency and damping ratio. The study is based on numerical analyses carried out with different stochastic models for earthquakes: a simple filtered white noise model and two time modulated filtered white noise models. The numerical analyses are carried out to solve an optimization problem with a performance index defined by the reduction of the standard deviation of either the structure displacement or its inertial acceleration as objective function. To complete the work, the influence of the bandwidth excitation over the values of the optimal tuned mass damper parameters is investigated, as well the optimum mass ratio and the structure frequency. The results of the numeral analyses carried out infer that the earthquake excitation characteristics, including its modulation in time domain, highly affect the optimum tuned mass damper design parameters values.

Random vibro-acoustic control of internal noise through optimized Tuned Mass Dampers

Abstract The present work deals with the passive control of interior sound pressure induced by randomly vibrating structure coupled to an enclosure filled with air. The control in the low frequency range is achieved using a Tuned Mass Damper (TMD) device. In order to guarantee an optimal performance of the TMD device, a stochastic acoustic optimization strategy is proposed. In the later, the objective function is the root mean square acoustic pressure measured at a given location inside the cavity. Assuming linear behavior of the vibro-acoustic system, the modal interaction approach is used and the objective function is evaluated by means of spectral analysis. The effectiveness of the proposed strategy is investigated and compared with others from the open literature. The capability of the proposed optimization strategy to deal with multimodal control of interior sound has also been addressed. To this end, multiple TMDs have been used. The optimal TMD parameters have been obtained using a multi-objective optimization approach and the results that have been gathered show significant attenuations in all target resonant modes.

Structural vibration control for the offshore floating wind turbine including drivetrain dynamics analysis

Compared to the onshore wind turbines, the offshore floating wind turbines experience larger loads and displacements due to combined effects of the wind and waves. Suppressing the structural vibration of floating wind turbines with a passive tuned mass damper (TMD) device has the potential to be an effective and economical method. In this study, a barge-type floating wind turbine is chosen as the research object. The SIMPACK multi-body dynamics software is employed to establish the detailed model of the wind turbine. For achieving considerable load reduction performance, the spring stiffness, damping coefficient, and mass of the TMD system are optimized based on a simplified mathematical model. Furthermore, the genetic algorithm (GA) is used to achieve global optimal TMD parameters. To investigate the effect of the detailed drivetrain model on the wind turbine performances and comprehensively evaluate the structural vibration inhibition effect of the designed TMD, a coupled aero-hydro-servo-elastic model is constructed and simulated for different load cases. The time-domain and frequency-domain analysis of simulation results are performed. Moreover, a robustness study for TMD parameters obtained by the GA is also performed. Analysis results indicate that the flexibility and gear contact within the drivetrain has a noticeable effect on the wind turbine performances, and the designed TMD can significantly inhibit the structural loads and stabilize the electrical output power.

Optimisation Design and Damping Effect Analysis of Large Mass Ratio Tuned Mass Dampers

Under harmonic load and random stationary white noise load, the existing fitting formulas are not suitable for calculating the optimal parameters of large mass ratio tuned mass dampers (TMDs). For this reason, the optimal parameters of large mass ratio TMDs are determined by numerical optimisation methods, and a revised fitting formula is proposed herein based on a curve fitting technique. Finally, the dynamic time history analysis method is used to study the control effect of large mass ratio TMDs. The results show that when the mass ratio is large, the error between the existing fitting formula and the actual optimal value is quite large, and the revised fitting formula is applicable to the parameter design of the traditional small mass ratio and large mass ratio (≤1) TMDs. When the ratio of local base soil predominant frequency to structure vibration frequency is greater than 4, the optimal parameters of a TMD under white noise excitation can be calculated according to the revised fitting formula, and the remaining conditions should be determined by numerical optimisation. In addition, a large mass ratio TMD reduces the dynamic response of the main structure effectively compared with a small mass ratio TMD and reduces the relative displacement between the TMD and main structure.

Feasibility of Tuned Mass Damper Approach

His investigation is aimed at exploring the possibility of energy recovery through the suppression of vibrations. The article describes a new type of regenerative suspension using electromagnetic tuned mass damper (TMD) approach. The magnetic part of the device performs the function of the TMD, thereby providing both energy regeneration, and damping properties to the protected structure. Equations of optimal parameters of TMD, such as stiffness and damping coefficient were obtained according to the theory of TMD. Then, optimized TMD was mounted in structure with characteristics typically for car wheel. Therefore, efficiency of using TMD for such structures was revealed by amplitude and acceleration frequency response plot. Equation of velocity of TMD was obtained as well. Further estimated regenerative function of current TMD system was investigated: electromotive force for one coil equals to 0.03V, at 1.13 m/s TMD velocity. Finally, the aims of the further research were determined as well.

Optimal design of tuned mass dampers subjected to continuous stationary critical excitation

Tuned mass dampers (TMD) have been widely used as one of vibration controlled devices in order to reduce the response of buildings subjected to lateral loads such as earthquake loads. Although the optimal design of TMD subjected to earthquake has received much attention of researchers, finding the most severe earthquake for this purpose has been well-known a challenging task. Hence, this paper proposes the optimal design of TMD subjected to continuous stationary critical excitation as the most severe earthquake. The continuous stationary critical excitation is determined by maximizing structural responses. In this study, the optimal parameters of TMD are determined through minimizing the sum root of the mean square of story drifts defined in the frequency domain. For achieving this purpose, at first, the performance of the improved gravitational search algorithm (IGSA) is verified using a ten story shear building with a TMD as a benchmark example. The numerical results demonstrate that IGSA converges to better solutions in comparison with other algorithms. Finally, the optimal design of TMD parameters obtained for the ten story shear building subjected to the continuous stationary critical excitation.

Effects of Tuned Mass Damper on Fixed-Fixed 3D Nonlinear String Resting on Nonlinear Elastic Foundation

This paper studies the vibration of a nonlinear 3D-string fixed at both ends and supported by a nonlinear elastic foundation. Newton’s second law is adopted to derive the equations of motion for the string resting on an elastic foundation. Then, the method of multiple scales (MOMS) is employed for the analysis of the nonlinear system. It was found that 1:3 internal resonance exists in the first and fourth modes of the string when the wave speed in the transverse direction is [Formula: see text] and the elasticity coefficient of the foundation is [Formula: see text]. Fixed point plots are used to obtain the frequency responses of the various modes and to identify internal resonance through observation of the amplitudes and mode shapes. To prevent internal resonance and reduce vibration, a tuned mass damper (TMD) is applied to the string. The effects of various TMD masses, locations, damper coefficients ([Formula: see text]), and spring constants ([Formula: see text]) on overall damping were analyzed. The 3D plots of the maximum amplitude (3D POMAs) and 3D maximum amplitude contour plots (3D MACPs) are generated for the various modes to illustrate the amplitudes of the string, while identifying the optimal TMD parameters for vibration reduction. The results were verified numerically. It was concluded that better damping effects can be achieved using a TMD mass ratio [Formula: see text]–0.5 located near the middle of the string. Furthermore, for damper coefficient [Formula: see text], the use of spring constant [Formula: see text]–13 can improve the overall damping.

Simulation Study on Train-Induced Vibration Control of a Long-Span Steel Truss Girder Bridge by Tuned Mass Dampers

Train-induced vibration of steel truss bridges is one of the key issues in bridge engineering. This paper talks about the application of tuned mass damper (TMD) on the vibration control of a steel truss bridge subjected to dynamic train loads. The Nanjing Yangtze River Bridge (NYRB) is taken as the research object and a recorded typical train load is included in this study. With dynamic finite element (FE) method, the real-time dynamic responses of NYRB are analyzed based on a simplified train-bridge time-varying system. Thereinto, two cases including single train moving at one side and two trains moving oppositely are specifically investigated. According to the dynamic characteristics and dynamic responses of NYRB, the fourth vertical bending mode is selected as the control target and the parameter sensitivity analysis on vibration control efficiency with TMD is conducted. Using the first-order optimization method, the optimal parameters of TMD are then acquired with the control efficiency of TMD, the static displacement of Midspan, expenditure of TMDs, and manufacture difficulty of the damper considered. Results obtained in this study can provide references for the vibration control of steel truss bridges.

Passive control of bilinear hysteretic structures by tuned mass damper for narrow band seismic motions

Tuned mass damper (TMD) has been extensively used in vibration control of engineering structures. Numerous available results show that TMD can greatly reduce the response of elastic structures under wind, water waves, and earthquakes. The efficiency of TMDs, however, decreases when primary system experiences nonlinear behaviors. In order to make use of TMDs in such situations, this paper investigates the feasibility of adopting TMD in controlling of inelastic structures subjected to seismic motions. The focus is to explore the performance of TMD controlled buildings in areas subjected to long distance earthquakes, where structures usually have low nonlinearity. An optimization criterion is proposed to minimize the maximum nonlinear response within the concerned frequency band of excitations, instead of conventional approach whereby the linear response of the primary system is minimized. The limit on stroke is taken into consideration for practicality. Through numerical studies, it is shown that the primary structures achieve much better damage reduction by adopting the optimal TMD parameters based on the proposed criterion.

Effect of tuned mass damper on displacement demand of base-isolated structures

The third author of this paper has previously proposed the installation of a tuned-mass damper (TMD) to reduce the displacement demand on a base isolated structure. The TMD consists of a mass-dashpot-spring subsystem that is attached to the isolated superstructure, analogous to a pendulum. The present paper examines the effectiveness of this scheme and determines optimal parameters for the design of the TMD. Both the base-isolated structure and the TMD are modeled as single-degree-of-freedom, linear oscillators. The optimal TMD parameters are determined by considering the response of the base-isolated structure, with and without the TMD, to a white-noise base acceleration. Such an excitation is representative of broadband ground motions having a nearly constant intensity over a duration several times longer than the period of the base-isolated structure. It is found that, under such an excitation, a reduction of the order of 15%–25% in the displacement demand of the base-isolated structure can be achieved by adding the TMD. Next, the responses of an example base-isolated structure with and without an optimally designed TMD to selected suites of far- and near-field recorded accelerograms are determined. The study shows that for far-field ground motions the effectiveness of the TMD is more or less similar to that predicted by the white noise model, whereas for near-field ground motions the effectiveness of the TMD is less, i.e. of the order of 10% or less. Reasons for this result are described.

Optimal tuned mass damper for seismic applications and practical design formulas

In seismic retrofit of a long-span truss bridge in Japan, a new retrofit scheme was applied in which the existing bearings of the bridge were replaced by a new floor deck isolation system. The floor decks and isolation system together can be viewed as a giant tuned mass damper (TMD) to reduce the seismic force of the truss. This motivates a study on the optimal design of a TMD for a single-degree-of-freedom structure under seismic loads in this paper. Kanai–Tajimi spectrum is selected to model the earthquake excitation. It is shown that, when ratio of the characteristic ground frequency in the Kanai–Tajimi spectrum to the structural frequency is above three, the ground motion can be assumed to be a white noise to design TMD. For a smaller ground frequency ratio, simple formulas of the optimal TMD parameters are obtained. The dependence of optimal TMD parameters on mass ratio especially for large TMD is highlighted. It is found that the optimal TMD has lower tuning frequency and higher damping ratio as the mass ratio increases. For a large mass ratio, TMD becomes very effective in minimizing the primary structure response and robust against uncertainties in the parameters of the system.