Tuned Mass Damper Parameters Research Articles

Application of eddy current damper technology for passive tuned mass damper systems within footbridges

Footbridges are prone to vibrations induced by pedestrians depending on the bridgès natural frequencies. Well-known measures to increase the structural damping of a footbridge and hence control the risk of vibrations are Tuned Mass Dampers (TMD). One of the main parameters defining the overall effectiveness of a TMD is its damping mechanism; for this purpose eddy current dampers are an innovative solution, which can improve TMD performance significantly.This paper describes the design of an eddy current damper as part of a passive tuned mass damper. First, the theoretical potential is analyzed analytically. A detailed discussion on the optimization of TMD parameters combined with the characteristics of eddy current dampers shows its advantages. In the second part a TMD construction using an eddy current damper is designed based on a case study of a footbridge.

Tuning of mass dampers for preventing brittle fracture by employing teaching learning based optimization

AbstractIn design of reinforced concrete structures, a ductile design is needed, because the brittle fracture is sudden. Also, the energy absorbed by the structure is effective for ductile structures during earthquake excitations. In design regulations, especially for vertical supporters such as columns, the shear force and axial force capacity is limited, although the strength of the members is not at the limits. For that reason, the shear forces of structures excited by earthquakes can be reduced by adding a tuned mass damper (TMD), but TMD must be optimized and it must not be heavy. If the mass of the TMD is not optimized, the ductile behaviour constraint about the axial force capacity cannot be provided. The compressive strength of the concrete is a measure for the effective application of a TMD to a reinforced concrete structure. Since the mass is limited by the design constraint, the other design variables of TMD such as period and damping ratio are optimized. Using the formulas for frequency and damping ratio related to a preselected mass may not be sufficient and a precise optimum solution for preventing brittle fracture. Metaheuristic methods can be used by using a specific limit. In this study, Teaching Learning Based Optimization (TLBO) is employed to find optimum TMD parameters. Several earthquake excitations were used in the optimization process. A three storey RC frame structures with different compressive strength of concrete is investigated. Three stopping criteria have been used in the proposed methodology. The first criterion is the reduction of the maxi‐mum shear force value for the most critical excitation to the ductile behaviour limit. The second criterion is the reduction of the ratio of maximum first storey displacements of structure with and without TMD. This value is reduced under a user defined value, but the user defined value can be entered as zero. This value can be iteratively increased for minimization. The last criterion is the reduction of the acceleration transfer function of the structure. The proposed method is feasible on finding optimum TMD ensuring ductility conditions. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Tuned mass damper parameters design for structural systems via linear matrix inequality and genetic algorithm

The tuned mass damper parameters designing for structural systems based on combining linear matrix inequality with genetic algorithm is of concern in this paper. Firstly, based on matrix transform, the novel model description with a singular style for structural systems is obtained, in which the possible coupling of those uncertainties is avoided. Secondly, an approach, which combines linear matrix inequality with genetic algorithm, is taken in this work to solving the optimization problems, and the optimized tuned mass damper parameters can be obtained by solving the optimization problems such that the tuned-mass-damper-controlled systems have a prescribed level of vibration attenuation performance. Furthermore, the obtained results are also extended to the uncertain cases. Finally, the effectiveness of the obtained theorems is demonstrated by numerical simulation results.

Optimization design of tuned mass damper for vibration suppression of a barge-type offshore floating wind turbine

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.

Substructure coupling approach to parameterization of passive dynamic auxiliary systems

A physical structure might show undesired forced vibrations when excited by a specific force signal. Moreover, if the resulting deflections influence the acting force, undesired self-excited vibrations can result. In such cases a usual approach is to modify the structure by mounting passive tuned mass dampers (TMD). Different strategies are available to design such TMD. The different approaches have in common, that the original structure is approximated as a single degree of freedom (SDOF) system. This approximation limits the applicability of the design strategies. This paper attempts to solve the abovementioned drawback. Based on a frequency domain substructure coupling approach, it is proposed to apply a sequential quadratic programming algorithm to determine effective parameters of TMD. The approach considers the multiple degrees of freedom (MDOF) character of the original structure. The new method is evaluated by means of a simple finite element model of a simplified milling machine assembly. By means of this analytical example, it is shown that both SDOF TMD and MDOF TMD can be parameterized by the new method. The practical applicability is proven by designing a STMD for a linear axis test bench. Finally, limitations of the method and reasonable subsequent research tasks are discussed.

A new reliability based optimization of tuned mass damper parameters using energy approach

In this work a reliability based optimization (RBO) strategy of Tuned Mass Damper (TMD) parameters is presented. The strategy is based on an energetic approach. The strategy consists to optimize the TMD parameters so that we minimize the failure probability (objective function) characterized by the exceedence of the power dissipated in the primary structure of a certain threshold value during some interval time. The evaluation of the objective function is carried out using the classical Rice’s formula. The strategy is, firstly, applied to linear single-degree of freedom (SDOF) system, subjected to seismic motion, and then extended to linear multi-degree of freedom (MDOF) system. The use of the Rice’s formula requires the knowledge of the joint probability density function (PDF) of the considered processes; to this end, exact expression of the joint PDF is presented for the SDOF system and an approximation is presented for the evaluation of the failure probabilities for the MDOF system. By making use of the obtained joint PDF, for the SDOF system, as the a priori joint PDF, the approximation of the joint PDF, for the MDOF system, has been performed using the Minimum cross-entropy method (MinxEnt). To highlight the good effectiveness of the proposed strategy, a ten-story shear building, subjected to different earthquakes, is considered. The obtained results are compared with other from literature, and it has been shown the superiority of the proposed strategy.

Closed-form optimum tuning formulas for passive Tuned Mass Dampers under benchmark excitations

This study concerns the derivation of optimum tuning formulas for a passive Tuned Mass Damper (TMD) device, for the case of benchmark ideal excitations acting on a single-degree-of-freedom (SDOF) damped primary structure. The free TMD parameters are tuned first through a non-linear gradient-based optimisation algorithm, for the case of harmonic or white noise excitations, acting either as force on the SDOF primary structure or as base acceleration. The achieved optimum TMD parameters are successively interpolated according to appropriate analytical fitting proposals, by non-linear least squares, in order to produce simple and effective TMD tuning formulas. In particular, two fitting models are presented. The main proposal is composed of a simple polynomial relationship, refined within the fitting process, and constitutes the optimum choice. A second model refers to proper modifications of literature formulas for the case of an undamped primary structure. The results in terms of final (interpolated) optimum TMD parameters and of device effectiveness in reducing the structural dynamic response are finally displayed and discussed in detail, showing the wide and ready-to-use validity of the proposed optimisation procedure and achieved tuning formulas. Several post-tuning trials have been carried out as well on SDOF and MDOF shear-type frame buildings, by confirming the effective benefit provided by the proposed optimum TMD.

OPTIMAL TMDS FOR IMPROVING THE SEISMIC PERFORMANCE OF HISTORICAL BUILDINGS

In this paper, optimal design and assessment of the capability of tuned mass dampers (TMDs) in improving the seismic behavior of confined masonry walls as the main element of historical buildings has been studied. For this purpose, the design parameters of TMDs have been determined through the minimization of wall response using Genetic algorithms (GAs). For simulation the behavior of confined masonry wall under earthquake, the triple linear shear beam model has been used. For illustration, the method has been tested on confined masonry walls equipped with linear TMDs. To study the effects of frequency content and peak ground acceleration (PGA) of earthquake records on the performance of TMDs, the controlled walls have been subjected to different earthquake records. Results have shown that the proposed method has been effective in designing optimal TMDs regarding the convergence and simplicity behavior of GA in solving the optimization problem. It has also been shown that using TMD enhances the seismic behavior of confined masonry walls which its efficiency depends on the earthquake characteristics and the mass ratio. Finally, it can be concluded that the results of this research could be used as guides to design TMDs for historical and heritage buildings

Extracting parameters of TMD and primary structure from the combined system responses

Tuned mass dampers (TMDs) have been a prevalent vibration control device for suppressing excessive vibration because of environmental loadings in contemporary tall buildings since the mid-1970s. A TMD must be tuned to the natural frequency of the primary structure to be effective. In practice, a TMD may be assembled in situ, simultaneously with the building construction. In such a situation, the respective dynamic properties of the TMD device and building cannot be identified to determine the tuning status of the TMD. For this purpose, a methodology was developed to obtain the parameters of the TMD and primary building on the basis of the eigenparameters of any two complex modes of the combined building–TMD system. The theory was derived in state-space to characterize the nonclassical damping feature of the system, and combined with a system identification technique to obtain the system eigenparameters using the acceleration measurements. The proposed procedure was first demonstrated using a numerical verification and then applied to real, experimental data of a large-scale building–TMD system. The results showed that the procedure is capable of identifying the respective parameters of the TMD and primary structure and is applicable in real implementations by using only the acceleration response measurements of the TMD and its located floor.

An improvement of the step-by-step analysis method for study on passive flutter control of a bridge deck

The present study investigated the problem of increasing the critical flutter wind speed of long-span bridges by using tuned mass dampers (TMDs) on both theoretical and experimental aspect. The governing equations of motion of a bridge deck with TMD are analytically formulated. The method of step-by-step flutter analysis is improved and extended from the 2-DOF model to the 4-DOF model to calculate the critical flutter wind speed and parameters of TMD. A sectional model wind tunnel test is carried out to examine and validate the numerical results, and some new findings from the obtained results are included.

New approaches in reliability based optimization of tuned mass damper in presence of uncertain bounded parameters

This work deals with control of vibrating structures using tuned mass damper (TMD) in presence of uncertain bounded structural parameters. The adopted optimization strategy of the TMD parameters is the reliability based optimization (RBO) where the failure probability, approximated with the classical Rice’s formula, is related to the primary structure displacement. In presence of uncertain bounded structural parameters it is convenient to describe them using intervals. Consequently, the optimized failure probability is also defined over an interval.In this paper a continuous-optimization nested loop method (CONLM) is presented to provide the exact range of the optimum TMD parameters and their corresponding failure probabilities. The CONLM is time consuming; in this context an approximation method using the monotonicity-based extension method (MBEM) with box splitting is also proposed. Therefore, the initial non-deterministic optimization problem can be transformed into two independent deterministic sub-problems involving discrete-optimization nested loop rather than the continuous-optimization nested loop used in the CONLM. The effectiveness and robustness of the presented optimum bounds of the TMD parameters are investigated and a performance index is introduced. The numerical results obtained with a one degree of freedom and a multi-degree of freedom systems subject to different seismic motions have shown the efficiency of the proposed methods, even with high level of uncertainties. Besides, the good robustness of the TMD device when it is exactly tuned on the optimum TMD parameters corresponding to the deterministic structural parameters has been proven.

Optimum Parameters for Tuned Mass Damper Using Shuffled Complex Evolution (SCE) Algorithm

This study is investigated the optimum parameters for a tuned mass damper (TMD) under the seismic excitation. Shuffled complex evolution (SCE) is a meta-heuristic optimization method which is used to find the optimum damping and tuning frequency ratio for a TMD. The efficiency of the TMD is evaluated by decreasing the structural displacement dynamic magnification factor (DDMF) and acceleration dynamic magnification factor (ADMF) for a specific vibration mode of the structure. The optimum TMD parameters and the corresponding optimized DDMF and ADMF are achieved for two control levels (displacement control and acceleration control), different structural damping ratio and mass ratio of the TMD system. The optimum TMD parameters are checked for a 10-storey building under earthquake excitations. The maximum storey displacement and acceleration obtained by SCE method are compared with the results of other existing approaches. The results show that the peak building response decreased with decreases of about 20% for displacement and 30% for acceleration of the top floor. To show the efficiency of the adopted algorithm (SCE), a comparison is also made between SCE and other meta-heuristic optimization methods such as genetic algorithm (GA), particle swarm optimization (PSO) method and harmony search (HS) algorithm in terms of success rate and computational processing time. The results show that the proposed algorithm outperforms other meta-heuristic optimization methods.

Optimum tuned mass damper approaches for adjacent structures

Pounding of adjacent structures are always a notable reason for damages after strong ground motions, but it is already unforeseen detail in newly constructed structures. Thus, several approaches have been proposed in order to prevent the pounding of structures. By using optimally tuned mass dampers, it is possible to decrease the displacement vibrations of structures. But in adjacent structures, the response of both structures must be considered in the objective function of optimization process. In this paper, two different designs of Tuned Mass Dampers (TMD) are investigated. The first design covers independent TMDs on both structures. In the second design, adjacent structures are coupled by a TMD on the top of the structures. Optimum TMD parameters are found by using the developed optimization methodology employing harmony search algorithm. The proposed method is presented with single degree of freedom and multiple degree of freedom structures. Results show that the coupled design is not effective on multiple degree of freedom adjacent structures. The coupled design is only effective for rigid structures with a single degree of freedom while the use of independent TMDs are effective on both rigid and flexural structures.

Optimum tuning of Tuned Mass Dampers for frame structures under earthquake excitation

Tuned Mass Damper (TMD) devices are one of the oldest vibration control means and are widely used in different engineering contexts. Despite the bulk of literature on various TMD-related issues, the effectiveness of TMDs in reducing the earthquake response of civil engineering structures is still debated. This paper deals with the optimum tuning of the free parameters of a passive TMD applied to sample frame structures subjected to selected seismic excitations. A tuning procedure consisting of a numerical Minimax optimization algorithm is implemented within MATLAB. The so-conceived TMD turns out to be optimum with respect to the specific seismic event, hence allowing for optimum reduction in primary seismic response. Both optimization process and seismic analysis are carried out in the time domain, through direct integration of the equations of motion. The method is tested on benchmark single-DOF and multi-DOF shear-type prototype structures from the literature by assuming first the Imperial Valley 1940 seismic input, as a sort of benchmark excitation, and then additional recent strong motion earthquakes. In essence, this paper shows that, in principle, with present reference to frame structures, the optimum tuning of TMD parameters at given seismic input is theoretically possible.

OPTIMUM TUNING PARAMETERS OF TUNED MASS DAMPERS FOR VIBRATION CONTROL OF IRREGULAR HIGHRISE BUILDING STRUCTURES

Tall buildings have become increasingly one-of-a-kind signature structures that are often irregular in plan and elevation with complicated dynamic behavior. Vibration control of irregular highrise building structures using a recently developed tuned mass dampers (TMD), the bidirectional TMD (BTMD), is investigated. A key issue for effective implementation of a TMD is the determination of their tuning parameters. Eight different sets of equations for tuning the parameters of TMDs are investigated using a 5-story building with plan and elevation irregularity, and a 15-story and a 20-story building with plan irregularity subjected to seismic loading. Appropriate equations are recommended for building structures with a fundamental period of vibrations of greater than one second.

Tuned Mass Damper optimization for the mitigation of human-induced vibrations of pedestrian bridges

The design of Tuned Mass Dampers (TMD) to satisfy serviceability requirements is becoming more and more usual in the current design of footbridges. This paper analyzes the TMD design for the mitigation of pedestrian-induced vibrations with three main objectives: the introduction of a specific TMD optimization criterion for pedestrian-induced vibrations of footbridges, a critical analysis of the applicability to this specific loading scenario of classic literature optimization criteria, and a quantification of the TMD efficiency in the reduction of the footbridge acceleration. A numerical optimization criterion is proposed, based on the maximization of an efficiency factor, defined as the ratio between the uncontrolled acceleration standard deviation and the controlled one. Optimum TMD parameters are compared with classic criteria given by the literature. A possible modification of TMD parameters that permits to keep the TMD relative displacement within prescribed limits (aspect that is often a technical requirement in the TMD design) is also discussed. Monte Carlo simulations are carried out in order to confirm the validity of the standard deviation-based optimization for the reduction of the maximum dynamic response of the bridge. An application to a real footbridge is finally presented.

Hybrid damping systems in offshore jacket platforms with float-over deck

Employing dampers to control wave-induced and seismic vibrations of offshore jacket platforms is an attractive method in order to mitigate fatigue and seismic damage. However, adjustable parameters of a damper are designed by considering only one type of environmental loads; either normal-condition load or extreme-condition load. So, it is important to investigate effectiveness of damping system, for both of two main categories of environmental loads. Also it is ideal for the system to have an acceptable performance in both normal and extreme conditions. The idea investigated in the current study is to use a friction damper device (FDD) and a tuned mass damper (TMD) simultaneously in offshore jacket platforms with float-over deck to control both fatigue damage as well as seismic vibration. To develop the idea, adjustable parameters of FDD and TMD have been adjusted for wave loading. Afterward, they are combined with those designed for earthquake, so the hybrid damping system (HDS) is introduced. By introducing HDS, it is intended to make damping system have a high seismic performance while being effective in fatigue damage mitigation. Moreover, HDS can have different combinations. So, certain variants of HDS are determined which have much higher performance than the other variants.

Modelling and optimization of a passive structural control design for a spar-type floating wind turbine

Compared with fixed-bottom installation, deep water floating wind turbine has to undergo more severe structural loads due to extra degrees of freedom. Aiming for effective load reduction, this paper deals with the evaluation of a passive structural control design for a spar-type floating wind turbine, and the proposed strategy is to install a tuned mass damper (TMD) into the spar platform. Firstly, a mathematical model for wind turbine surge-heave-pitch motion is established based on the D’Alembert’s principle of inertial forces. Then, parameter estimation is performed by comparing the outputs from the proposed model and the state-of-the-art simulator. Further, different optimization methods are adopted to optimize TMD parameters when considering different performance indices. Finally, high fidelity nonlinear simulations with previous optimized TMD designs are conducted under different wind and wave conditions. Simulation results demonstrate both the effectiveness and limitation of different TMD parameter choices, providing parametric analysis and design basis for future improvement on floating wind turbine load reduction with structural control methods.

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.

ABC optimization of TMD parameters for tall buildings with soil structure interaction

This paper investigates the optimized parameters of Tuned Mass Dampers (TMDs) for vibration control of high-rise structures including Soil Structure Interaction (SSI). The Artificial Bee Colony (ABC) method is employed for optimization. The TMD Mass, damping coefficient and spring stiffness are assumed as the design variables of the controller; and the objective is set as the reduction of both the maximum displacement and acceleration of the building. The time domain analysis based on Newmark method is employed to obtain the displacement, velocity and acceleration of different stories and TMD in response to 6 types of far field earthquakes. The optimized mass, frequency and damping ratio are then formulated for different soil types; and employed for the design of TMD for the 40 and 15 story buildings and 10 different earthquakes, and well results are achieved. This study leads the researchers to the better understanding and designing of TMDs as passive controllers for the mitigation of earthquake oscillations.