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Control of flutter of suspension bridge deck using TMD
Abstract
Passive control of the flutter condition of suspension bridges using a combined vertical and torsional tuned mass damper (TMD) system is presented. The proposed TMD system has two degrees of freedom, which are tuned close to the frequencies corresponding to vertical and torsional symmetric modes of the bridge which get coupled during flutter. The bridge-TMD system is analyzed for finding critical wind speed for flutter using a finite element approach. Thomas Suspension Bridge is analyzed as an illustrative example. The effectiveness of the TMD system in increasing the critical flutter speed of the bridge is investigated through a parametric study. The results of the parametric study led to the optimization of some important parameters such as mass ratio, TMD damping ratio, tuning frequency, and number of TMD systems which provide maximum critical flutter wind speed of the suspension bridge.
... The evaluation of flutter condition of suspension bridges is one of the most important phases in the design of these bridges. In recent years, many researchers123456789101112 have focused their attention on increasing the critical flutter wind speed of the cable-supported bridges using different types of control devices. Wilde et al. [10] proposed a passive aerodynamic control of flutter by adding two additional surfaces to generate stabilizing forces and by putting an additional pendulum to control the torsional motion. ...
... Other studies also have been carried out to control the critical flutter wind speed of long-span bridges using eccentric mass on the bridges131415. In 2002, the authors [12] proposed a passive control of critical flutter wind speed of suspension bridges using a combined vertical and torsional tuned mass damper (TMD) system. The proposed TMD system has two degrees of freedom, which are tuned close to the frequencies corresponding to vertical and torsional symmetric modes of the bridge, which get coupled during flutter. ...
... Since the values of H\ and A\ for this bridge are not available, they are assumed to be negligible. The flutter condition of this bridge is obtained by authors in another study [12]. It is observed that the 6th mode (i.e. the first symmetric torsional mode) is the predominant mode for the flutter condition. ...
The closed-loop state feedback control scheme by pole-placement technique, which is widely used in control literature, is applied to control the flutter instability of suspension bridges. When the mean wind speed U at the bridge site increases beyond the critical flutter wind speed, the real part of the dominant pole of the system is forced to a desired negative value by properly designing a state feed back gain matrix to control the flutter instability. The control force, which is expressed as a product of gain matrix and state vector in modal coordinates, is applied in the form of an active torsional moment in the middle of the bridge span. The values of the state variables are estimated by designing a full order observer system. The application of the control scheme for increasing the critical wind speed for flutter of suspension bridges is demonstrated by considering the Vincent Thomas Bridge as the numerical example. The efficiency of the method for controlling the bridge deck flutter is investigated under a set of parametric variations. The results of the numerical study show that the control scheme using pole-placement technique effectively brings down the divergent oscillation of the bridge at wind speeds greater than the critical wind speed for flutter, to almost zero value within few seconds.
... Therefore, it is necessary to suppress the adverse vibration of the bridge subjected to the actions of wind and passing traffic. Some research efforts have been made in mitigating excessive buffeting vibrations and improving flutter stabilities for long-span bridges during construction (Conti et al. 1996, Takeda et al. 1998, Chen and Wu 2008 and at service (Pourzeynali and Datta 2002, Omenzetter et al. 2002, Miyata and Yamada 1998. As a traditional control device, dynamic energy absorbers perform well in suppressing the excessive dynamic buffeting (Gu et al. 2001) or enhancing the flutter stability of bridges (Pourzeynali andDatta 2002, Gu et al. 1998). ...
... Some research efforts have been made in mitigating excessive buffeting vibrations and improving flutter stabilities for long-span bridges during construction (Conti et al. 1996, Takeda et al. 1998, Chen and Wu 2008 and at service (Pourzeynali and Datta 2002, Omenzetter et al. 2002, Miyata and Yamada 1998. As a traditional control device, dynamic energy absorbers perform well in suppressing the excessive dynamic buffeting (Gu et al. 2001) or enhancing the flutter stability of bridges (Pourzeynali andDatta 2002, Gu et al. 1998). Dynamic energy absorbers, such as tuned mass damper (TMD) and tuned liquid damper (TLD), are categorized into three types, namely, passive, active, and hybrid control devices. ...
The performance of bridges under strong wind and traffic is of great importance to set the traveling speed limit or to make operational decisions for severe weather, such as controlling traffic or even closing the bridge. Meanwhile, the vehicle's safety is highly concerned when it is running on bridges or highways under strong wind. During the past two decades, researchers have made significant contributions to the simulation of the wind-vehicle-bridge system and their interactive effects. This paper aims to provide a comprehensive review of the overall performance of the bridge and traffic system under strong wind, including bridge structures and vehicles, and the associated mitigation efforts.
... As the wind speed increases, aerodynamic instabilities such as flutter may occur at high wind speed [1]. Much research effort has been made in mitigating excessive buffeting vibrations and improving aerodynamic stabilities for long-span bridges during construction [2,3] and at service [4][5][6]. Among all of the control procedures, dynamic energy absorbers such as tuned mass dampers (TMDs) have been studied in suppressing the excessive dynamic buffeting [7] or enhancing the flutter stability of bridges [4,8]. ...
... Much research effort has been made in mitigating excessive buffeting vibrations and improving aerodynamic stabilities for long-span bridges during construction [2,3] and at service [4][5][6]. Among all of the control procedures, dynamic energy absorbers such as tuned mass dampers (TMDs) have been studied in suppressing the excessive dynamic buffeting [7] or enhancing the flutter stability of bridges [4,8]. As traditional control devices, the dynamic energy absorbers dissipate external energy through providing supplemental damping to the modes of concern [9][10][11]. ...
Tuned Mass Damper (TMD) is a well-known control device often used in dynamic vibration control of mechanical and civil structures. In the past decades, the control mechanism of TMD has been well studied for both Single Degree Of Freedom (SDOF) structures and Multiple Degree Of Freedom (MDOF) structures with weak modal coupling. With the increase of bridge span lengths and the tendency of bridge cross-section being more slender and streamlined, the vibration modes of bridges are more prone to couple together due to the interaction between the bridge and wind. The objective of this study is to develop a control mechanism that will be efficient not only for the control of resonant vibration, but also for controlling the vibration due to modal coupling. For this purpose, a theoretical derivation of coupled buffeting response of a bridge-TMD system is made. With the derived analytical formulation, control theory of TMD on coupled vibration is analytically and numerically investigated. It is found that TMD can suppress the coupled response through reducing the modal coupling effects, in addition to traditionally suppressing the resonant response. Such methodology is demonstrated and confirmed through an example.
... They attached a single mass to the beam structure by viscoelastic material. Pourzeynali and Datta [164] showed the efficiency of the TMD in control of the flutter in suspension bridge deck. They reported that the mass ratio, damping ratio, tuning frequency, and number of the TMDs create maximum critical flutter wind speed of the suspension bridge. ...
Given the burgeoning demand for construction of structures and high-rise buildings, controlling the structural vibrations under earthquake and other external dynamic forces seems more important than ever. Vibration control devices can be classified into passive, active and hybrid control systems. The technologies commonly adopted to control vibration, reduce damage, and generally improve the structural performance, include, but not limited to, damping, vibration isolation, control of excitation forces, vibration absorber. Tuned Mass Dampers (TMDs) have become a popular tool for protecting structures from unpredictable vibrations because of their relatively simple principles, their relatively easy performance optimization as shown in numerous recent successful applications. This paper presents a critical review of active, passive, semi-active and hybrid control systems of TMD used for preserving structures against forces induced by earthquake or wind, and provides a comparison of their efficiency, and comparative advantages and disadvantages. Despite the importance and recent advancement in this field, previous review studies have only focused on either passive or active TMDs. Hence this review covers the theoretical background of all types of TMDs and discusses the structural, analytical, practical differences and the economic aspects of their application in structural control. Moreover, this study identifies and highlights a range of knowledge gaps in the existing studies within this area of research. Among these research gaps, we identified that the current practices in determining the principle natural frequency of TMDs needs improvement. Furthermore, there is an increasing need for more complex methods of analysis for both TMD and structures that consider their nonlinear behavior as this can significantly improve the prediction of structural response and in turn, the optimization of TMDs.
... The result was a maximal critical flutter wind speed increment of approximately 14%. Pourzeynali and Datta [2] introduced an effective TMD control system with two degrees of freedom for a suspension bridge. considered three experimental variables: the suction slot position, suction interval, and suction rate. ...
The present wind tunnel study focuses on the effects of the steady-suction-based flow control method on the flutter performance of a 2DOF bridge deck section model. The suction applied to the bridge model was released from slots located at the girder bottom. The suction rates of all slots along the span were equal and constant. A series of test cases with different combinations of suction slot positions, suction intervals, and suction rates were studied in detail for the bridge deck model. The experimental results showed that the steady-suction-based flow control method could improve the flutter characteristics of the bridge deck with a maximal increase in the critical flutter speed of up to 10.5%. In addition, the flutter derivatives (FDs) of the bridge deck with or without control were compared to investigate the fundamental mechanisms of the steady-suction-based control method. According to the results, installing a suction control device helps to strengthen aerodynamic damping, which is the primary cause for enhanced flutter performance of bridge decks.
... Within this topic, a great attention was recently devoted to conceiving control strategies against bridge flutter. On this respect, many studies were focused on the use of single and multiple tuned mass dampers (Gu, et al. 1998, Lin, et al. 1999, Pourzeynali and Datta 2002, Kwon 2002, Chen and Kareem 2003, Kwon and Park 2004, Ubertini 2008b, although active control solution were also investigated (Preidikman andMook 1997, Kwon andChang 2000). Single tuned mass dampers (STMDs) are especially prone to mistuning effects (see for instance, Lin, et al. (2000)). ...
The aeroelastic stability of bridge decks equipped with multiple tuned mass dampers is studied. The problem is attacked in the time domain, by representing self-excited loads with the aid of aerodynamic indicial functions approximated by truncated series of exponential filters. This approach allows to reduce the aeroelastic stability analysis in the form of a direct eigenvalue problem, by introducing an additional state variable for each exponential term adopted in the approximation of indicial functions. A general probabilistic framework for the optimal robust design of multiple tuned mass dampers is proposed, in which all possible sources of uncertainties can be accounted for. For the purposes of this study, the method is also simplified in a form which requires a lower computational effort and it is then applied to a general case study in order to analyze the control effectiveness of regular and irregular multiple tuned mass dampers. A special care is devoted to mistuning effects caused by random variations of the target frequency. Regular multiple tuned mass dampers are seen to improve both control effectiveness and robustness with respect to single tuned mass dampers. However, those devices exhibit an asymmetric behavior with respect to frequency mistuning, which may weaken their feasibility for technical applications. In order to overcome this drawback, an irregular multiple tuned mass damper is conceived which is based on unequal mass distribution. The optimal design of this device is finally pursued via a full domain search, which evidences a remarkable robustness against frequency mistuning, in the sense of the simplified design approach.
... They attached a single mass to the beam structure by visco-elastic material. Pourzeynali and Datta (2002) showed the performance of the TMD in control of the flutter in suspension bridge deck. They reported that the mass ratio, damping ratio, tuning frequency, and number of the TMDs provide maximum critical flutter wind speed of the suspension bridge. ...
A state-of-the-art review on the response control of structures mainly using the passive tuned mass damper(s) (TMD/s) is presented. The review essentially focuses on the response control of wind- and earthquake-excited structures and covers theoretical backgrounds of the TMD and research developments therein. To put the TMD within a proper frame of reference, the study begins with a qualitative description and comparison of passive control systems for protecting structures subjected to wind-imparted forces and forces induced due to earthquake ground motions. A detailed literature review of the TMD is then provided with reference to both, the theoretical and experimental researches. Specifically, the review focuses on descriptions of the dynamic behavior and distinguishing features of various systems, viz. single TMD (STMD), multiple tuned mass dampers (MTMDs), and spatially distributed MTMDs (d-MTMD) which have been theoretically developed and experimentally tested both at the component level and through small-scale structural models. The review clearly demonstrates that the TMDs have a potential for improving the wind and seismic behaviors of prototype civil structures. In addition, the review shows that the MTMDs and d-MTMDs are relatively more effective and robust, as reported. The paper shows the scope of future research in development of time and frequency domain analyses of structures installed with the d-MTMDs duly considering uncertainties in the structural parameters and forcing functions. In addition, the consideration of nonlinearity in structural material and geometry is recommended for assessment of the performance of the STMD, MTMDs, or d-MTMDs.
... This research topic is relatively recent. Most efforts have been devoted to bridge deck passive control [7,8,9]. ...
The influence of a nonlinear tuned vibration absorber (NLTVA) on the airfoil flutter is investigated. In particular, its effect on the instability threshold and the potential subcriticality of the bifurcation is analyzed. For that purpose, the airfoil is modeled using the classical pitch and plunge aeroelastic model together with a linear approach for the aerodynamic loads. Large amplitude motions of the airfoil are taken into account with nonlinear restoring forces for the pitch and plunge degrees-of-freedom. The two cases of a hardening and a softening spring behavior are investigated. The influence of each NLTVA parameter is studied, and an optimum tuning of these parameters is found. The study reveals the ability of the NLTVA to shift the instability, avoid its possible subcriticality, and reduce the limit cycle oscillations (LCOs) amplitude.
... For mechanical facilities, passive approaches of TMD (tuned mass damper) types are widely studied. With the consideration of self-excited forces, the optimized TMD control system proves effective against flutter (Nobuto et al., 1988;Pourzeynali and Datta, 2002 ) at designed wind speed but does not perform well when system frequency deviates from expectation (Gu et al., 1998). To overcome this shortcoming, MTMD (multiple tuned mass dampers) is introduced to work in a wide range of frequencies (Igusa and Xu, 1990;Yamaguchi and Harnpornchai, 1993;Fujino and Abe, 1993;Kareem and Kline, 1995;Li, 2000) and shows good robustness and effectiveness when applied to flutter control (Kwon and Park, 2004). ...
An optimal control law is derived using a simple integral type quadratic functional. The resulting control scheme is applied
to seismically excited non-linear buildings modeled as lumped mass shear frame structures. The non-linearity is reflected
by the non-linear stiffness restoring force. Active tendon actuators are considered as control devices. The performance of
the proposed control is compared to those of the uncontrolled structure and the passive base isolation. It is shown by numerical
simulation results that the proposed control is capable of suppressing the uncontrolled seismic vibrations of the non-linear
structures.
A semiactive tuned mass damper (STMD) system with variable damping is used to control the flutter instability of long-span suspension bridges. For this purpose, a combined vertical and torsional model of a TMD system, which is placed at the middle of the center span, is used. This system has two degrees of freedom, which are tuned close to the frequencies corresponding to vertical and torsional symmetric modes of the bridge, that get coupled during flutter. The variable damping of the system is chosen through a fuzzy logic controller using the displacement and velocity at the center of the bridge as the inputs. The transient response of the bridge due to a given initial condition in presence of the wind self-excited forces is controlled so that critical flutter wind speed for the bridge is enhanced. The methodology is applied to increase the flutter wind speed of the Thomas Suspension Bridge. Also, a numerical study is conducted to investigate the effectiveness of the semiactive control scheme.
The effects of a class of nonlinear Tuned Mass Dampers on the aeroelastic behavior of SDOF systems are investigated. Unlike classical linear TMDs, nonlinear constitutive laws of the internal damping acting between the primary oscillator and the TMD are considered, while the elastic properties are keept linear. The perturbative Multiple Scale Method is applied to derive a set of bifurcation equations in the amplitude and phase and a parametric analysis is performed to describe the postcritical scenario of the system. Both cubic- and van der Pol-type dampings are considered and the dependence of the limit-cycle amplitudes on the system parameters is studied. These new results, compared with the previously obtained bifurcation scenario of a SDOF aeroelastic oscillator equipped with a linear TMD, show a detrimental effect on the maximum limit-cycle amplitude reduction of the nonlinear TMD. However, the analyses evidence that in the parameter region away from the perfect tuning condition the nonlinear connection can be used to tune the system with an enhancement of the limit-cycle amplitude reduction.
A fatigue reliability analysis of suspension bridges due to the gustiness of the wind velocity is presented by combining overall concepts of bridge aerodynamics, fatigue analysis, and reliability analysis. For this purpose, the fluctuating response of the bridge deck is obtained for buffeting force using a finite-element method and a spectral analysis in frequency domain. Annual cumulative fatigue damage is calculated using Palmgren - Miner's rule, stress-fatigue curve approach and different forms of distribution for stress range. In order to evaluate the reliability, both first-order second-moment (FOSM) method and full distribution procedure (assuming Weibull distribution for fatigue life) are used to evaluate the fatigue reliability. Probabilities of fatigue failure of the Thomas Bridge and the Golden Gate Bridge for a number of important parametric variations are obtained in order to make some general observations on the fatigue reliability of suspension bridges. The results of the study show that the FOSM method predicts a higher value of the probability of fatigue failure as compared to the full distribution method. Further, the distribution of stress range used in the analysis has a significant effect on the calculated probability of fatigue failure in suspension bridges.
A theoretical study of a slender engineering structure with lateral and angular deflections is investigated under the action of flow-induced vibrations. This aero-elastic instability excites and couples the system's bending and torsion modes. Semiactive means due to open-loop parametric excitation are introduced to stabilize this self-excitation mechanism. The parametric excitation mechanism is modeled by time-harmonic variation in the concentrated mass and/or moment of inertia. The conditions for full suppression of the self-excited vibrations are determined analytically and compared with numerical results of an example system. For the first time, example systems are presented for which parametric antiresonance is established at the parametric combination frequency of the sum type. [DOI:10.1115/1.3063631]
Techniques for stabilising slender bridges under wind loads are presented in this article. A mathematically consistent description of the acting aerodynamic forces is essential when investigating these ideas. Against this background, motion-induced aerodynamic forces are characterised using a linear time-invariant transfer element in terms of rational functions. With the help of these functions, the aeroelastic system can be described in the form of a linear, time-invariant state-space model. It is shown that the divergence wind speed constitutes an upper bound for the application of the selected mechanical actuators. Even active control with full state feedback cannot overcome this limitation. The results are derived and explained with methods of control theory.
With the rapid increase in scales of structures, research on controlling wind-induced vibration of large-scale structures,
such as long-span bridges and super-tall buildings, has been an issue of great concern. For wind-induced vibration of large-scale
structures, vibration frequencies and damping modes vary with wind speed. Passive, semiactive, and active control strategies
are developed to improve the wind-resistance performance of the structures in this paper. The multiple tuned mass damper (MTMD)
system is applied to control vertical bending buffeting response. A new semiactive lever-type tuned mass damper (TMD) with
an adjustable frequency is proposed to control vertical bending buffeting and torsional buffeting and flutter in the whole
velocity range of bridge decks. A control strategy named sinusoidal reference strategy is developed for adaptive control of
wind-induced vibration of super-tall buildings. Multiple degrees of freedom general building aeroelastic model with a square
cross-section is tested in a wind tunnel. The results demonstrate that the proposed strategies can reduce vibration effectively,
and can adapt to wind-induced vibration control of large-scale structures in the uncertain dynamic circumstance.
In this paper, wind-induced vibration control of a single column tower of a cable-stayed bridge with a multi-stage pendulum
mass damper (MSPMD) is investigated. Special attention is given to overcoming space limitations for installing the control
device in the tower and the effect of varying natural frequency of the towers during construction. First, the finite element
model of the bridge during its construction and the basic equation of motion of the MSPMD are introduced. The equation of
motion of the bridge with the MSPMD under along-wind excitation is then established. Finally, a numerical simulation and parametric
study are conducted to assess the effectiveness of the control system for reducing the wind-induced vibration of the bridge
towers during construction. The numerical simulation results show that the MSPMD is practical and effective for reducing the
along-wind response of the single column tower, can be installed in a small area of the tower, and complies with the time-variant
characteristics of the bridge during its entire construction stage.
Suspension bridges due to their long span are susceptible against dynamic events, like air flow which can cause considerable problems for them. Flutter, as an aerodynamic phenomenon, makes bridges vibrate, whereas their amplitude gradually diverges, needed the vibration control strategies. Tuned mass damper or in brief TMD, as the simplest passive device, can be used for this purpose. The performance of it can be enhanced when it’s parameters are adjusted to their optimum values. In this paper, the TMD was optimized by meta-heuristic optimization algorithms to control the flutter of long span suspension bridges. In this regard, the Golden Gate suspension bridge and Car tracking algorithm were selected for case study and optimization process, respectively. Firstly, the flutter analysis of bridge was done by multi-mode method in the time domain, and at second part, the TMD’s parameters were simultaneously optimized for maximum increase of flutter velocity of all the vulnerable modes. The results indicated that TMD was perfectly suitable device to control the flutter of long span bridges.
This article presents theoretical investigations on techniques for the improvement of the dynamic characteristics of slender bridges under wind action. Aerodynamically effective control shields are applied as controlled actuators. The first part of the article describes the modelling of the uncontrolled aeroelastic system. Acting aerodynamic forces are consistently characterised using linear time-invariant transfer elements in terms of rational functions. On this basis, two configuration levels of the uncontrolled system are represented with linear time-invariant state-space models and investigated. The second part of the article addresses controller design and the behaviour of the controlled aeroelastic system. Both fundamental limits for stabilisation and the efficiency for attenuating the influence of gusts are described for different actuator mechanisms. The results are derived and discussed with methods of control theory.
For a detailed investigation of the dynamic behaviour of slender bridges under wind action especially the motion-induced fluid forces should be available not only for harmonic motions but also for more general ones. If linear transfer behaviour is assumed, the force-displacement relation for almost arbitrary motions can be handled in the frequency domain using aerodynamic transfer functions. In aerospace engineering as well as in bridge engineering, these functions are usually approximated by special kinds of complex-valued rational functions which depend on complex frequencies. The quality of this approximation is evaluated for several bridge cross sections in this article. It is shown that rational functions are for some sections scarcely suitable to realistically represent the transfer behaviour of motion-induced aerodynamic forces for arbitrarily complex frequencies.
The main objective of this chapter is to find the optimal values of the parameters of the base isolation systems and that of the semi-active viscous dampers using genetic algorithms (GAs) and fuzzy logic in order to simultaneously minimize the buildings’ selected responses such as displacement of the top story, base shear, and so on. In this study, performance of base isolation systems, and semi-active viscous dampers are studied separately as different vibration control strategies. In order to simultaneously minimize the objective functions, a fast and elitist non-dominated sorting genetic algorithm (NSGA-II) approach is used to find a set of Pareto-optimal solution. To study the performance of semi-active viscous dampers, the torsional effects exist in the building due to irregularities, and unsymmetrical placement of the dampers is taken into account through 3D modeling of the building.
Applications of tuned mass damper (TMD) systems for bridge structures are observed for mitigation of problem related to excessive vibration induced by either wind loading or vehicle loading, where dominant modes usually in one direction (commonly vertical) are taken into account. Considering modes dominant in one direction may not be considered as a robust practice while any bridge structure is having dominant modes along both the transverse and vertical directions and the same bridge structure is subjected to loading along both the directions. In the present study, an approach for simultaneous control of major horizontal, vertical and torsional modes is presented targeting robust vibration control under general loading condition. A strategy using modal frequency response function (FRF) is proposed based on the traditional mode-wise control approach. The proposed modal FRF based approach is applied to an existing important large truss bridge (Saraighat Bridge) to carry out an analytical design of TMD system considering general loading conditions. The designed TMD system is found to demonstrate good performance under various white-noise based general loading conditions.
A control strategy for continuous, autonomous, linear mechanical systems, controlled via piezoelectric devices, and suffering Hopf bifurcations, triggered by positional nonconservative forces, is discussed. The strategy is based on the ‘principle of similarity’, proved in the literature to be successful in controlling externally excited systems. A continuous metamodel of Piezo-Electro-Mechanical system, loaded by position-dependent forces, is derived via the Extended Hamilton Principle. The similarity principle is introduced in the model, demanding for certain relations among mechanical and piezoelectric properties to be satisfied. A stability analysis is carried out via perturbation methods, also accounting for small deviations from similarity. It is shown that the similar control has always a detrimental effect in preventing the loss of stability of the mechanical systems and that this effect is robust under slight imperfections. As an example, a Generalized Beck beam is studied, internally and externally damped, under the simultaneous action of a follower and a dead load, for which the previous asymptotic results are corroborated by an exact analysis.
In this introductory chapter, the meteorology of wind storms is first introduced to provide information on the key features of wind storms. The basic configuration, structural systems and aerodynamic characteristics of both cable-stayed and suspension bridges are then described in order to facilitate understanding of aerodynamic phenomena and the performance of the bridges discussed in the subsequent chapters. Wind-induced excessive vibration and damage to long-span cable-supported bridges are discussed, focusing on the lessons learnt from them by the engineering profession. Finally, the history of bridge wind engineering, particularly for cable-supported bridges, is outlined in order to look back to the past and look forward to the future.
The main objective of this chapter is to find the optimal values of the parameters of the base isolation systems and that of the semi-active viscous dampers using genetic algorithms (GAs) and fuzzy logic in order to simultaneously minimize the buildings' selected responses such as displacement of the top story, base shear, and so on. In this study, performance of base isolation systems, and semi-active viscous dampers are studied separately as different vibration control strategies. In order to simultaneously minimize the objective functions, a fast and elitist non-dominated sorting genetic algorithm (NSGA-II) approach is used to find a set of Pareto-optimal solution. To study the performance of semi-active viscous dampers, the torsional effects exist in the building due to irregularities, and unsymmetrical placement of the dampers is taken into account through 3D modeling of the building.
The suppression of aerodynamic response of long-span suspension bridges during erection and after completion by using single TMD and multi TMD is presented in this paper. An advanced finite-element-based aerodynamic model that can be used to analyze both flutter instability and buffeting response in the time domain is also proposed. The frequency-dependent flutter derivatives are transferred into a time-dependent rational function, through which the coupling effects of three-dimensional aerodynamic motions under gusty winds can be accurately considered. The modal damping of a structure-TMD system is analyzed by the state-space approach. The numerical examples are performed on the Akashi Kaikyo Bridge with a main span of 1990 m. The bridge is idealized by a three-dimensional finite-element model consisting of 681 nodes. The results show that when the wind velocity is low, about 20m/s, the multi TMD type 1 (the vertical and horizontal TMD with 1% mass ratio in each direction together with the torsional TMD with ratio of 1% mass moment of inertia) can significantly reduce the buffeting response in vertical, horizontal and torsional directions by 8.6-13%. When the wind velocity increases to 40 m/s, the control efficiency of a multi TMD in reducing the torsional buffeting response increases greatly to 28%. However, its control efficiency in the vertical and horizontal directions reduces. The results also indicate that the critical wind velocity for flutter instability during erection is significantly lower than that of the completed bridge. By pylon-to-midspan configuration, the minimum critical wind velocity of 57.70 m/s occurs at stage of 85% deck completion.
Traveling crane is an important equipment of stereoscopic warehouse. The traveling crane is desired high efficiency for storing and retrieving by more and more consumer of warehouse. Thus, more higher velocity and acceleration of the traveling crane are all needed. However, they are restrained by many factors. The swing of mast is one of the most important factors. So, it is necessary to control the swing. In this paper, a scheme is presented to suppress the swing of the mast by TMD (tuned mass damper) but no extra mass is attached to the main structure. In this scheme, the upper beam is used as attached mass. So, the only necessary modify is that the juncture between the mast and the upper beam according to the desired dynamic parameter of TMD. The main principle of the scheme is introduced firstly in the paper. Then, the natural frequency and mode shape is calculated by means of FEM (finite element method) based on software AN SYS. After that, the dynamic response of the mast is simulated by means of the software SIMULINK of MATLAB. The result of measurement is introduced at last. The result shows that the scheme is feasible.
Control of wind-induced flutter of a bridge deck is studied using static output feedback. Servomotor-actuated winglets provide the control forces. Deck and winglets are modeled as flat plates and their aerodynamic interaction is neglected. Self-excited wind forces acting on deck and winglets are modeled using the Scanlan-Tomko model, with flat plate flutter derivatives (FDs) obtained from Theodorsen functions. Rogers rational function approximation (RFA) is used for time domain representation of wind forces in order to simplify the stability and control analyses. Control input to servomotors is based on direct feedback of vertical and torsional displacements of deck. Feedback gains that are constant, or varying with wind speed, are considered. Winglet rotations being restricted, flutter and divergence behavior is studied using system eigenvalues as well as responses. Results show that variable gain output feedback (VGOF) control using servomotor driven winglets is very effective. It provides the maximum increase in critical speed and maximum attenuation of response, followed by control with gain scheduling, with the former requiring less input power. Control with constant gain is least effective. Control of deck rotation generally appears to improve with wind speed.
Control of wind-induced flutter of a bridge deck section by using winglets is considered in this paper. The Scanlan-Tomko model was considered for self-excited wind forces acting on a deck and winglets. For this, the required flutter derivatives (FDs) of the deck were fitted using the Rogers rational function approximation. Vertical, lateral, and torsional degrees of freedom of the bluff body deck and their 18 corresponding experimental FDs were considered. Winglets were modeled as flat plates, for which FDs were obtained using Theodorsen's function. The time domain formulation involving aerodynamic states yields a divergence speed much lower than the correct divergence speed obtained by quasi-steady theory. Hence, a trial-and-error method involving sweeping through both speed and frequency was considered for the control study. Control inputs, that is, winglet rotations relative to the deck, were obtained using linear quadratic regulator (LQR) control with full state feedback. The state to be fed back was estimated by a full-order observer designed using pole placement. In order to prevent winglet stall, their absolute rotations were restricted within bounds. The flutter condition was verified using controlled responses and the results compared with those from closed-loop eigenvalue analysis. The control strategy appears to be quite effective in attenuating response and enhancing flutter speed.
This study addresses design methodologies of TMDs for control of bridge flutter, considering the uncertainty of aerodynamic data in order to enhance the robustness of tuned mass dampers (TMDs) against frequency drift caused by wind–bridge interaction. To evaluate the robust performance of a TMD system, the concept of minimum flutter velocity is introduced in the presence of perturbed unsteady aerodynamic forces. Two types of multiple tuned mass dampers (MTMD) are considered, i.e. the frequencies of each TMD are regularly or irregularly spaced. An optimization procedure for an irregular MTMD (IMTMD), which has an unequal frequency interval and different damping ratio of each individual TMD, is proposed based on genetic algorithms. The proposed TMDs are then applied to a cable stayed bridge and a suspension bridge to prove the validity of the methods. From the numerical results, the proposed IMTMD shows remarkable control efficiency compared with conventional single TMD (STMD) and MTMD.
The flutter phenomena of the suspension bridge and the airfoil are compared, employing a free- oscillation experimental method to measure model bridge flutter coefficients analogous to airfoil flutter coefficients. The airfoil is employed as a check on the experimental method, both as a theoretical backdrop and to test the nature of aerodynamic oscillatory forces under exponentially modified motion. A catalogue of bridge deck flutter coefficients is experimentally obtained which covers a range of bridge deck forms. Results are described to account for a number of phenomena observed in the wind tunnel and in the field.
A generalized theory of free torsional vibration for a wide class of suspension bridges with double lateral systems is developed, taking into account warping of the bridge deck cross section and the effect of torsional rigidity of the towers. The analysis is based on a linearized theory and on the use of the digital computer. A finite element approach is used to determine vibrational properties in torsion. Simplifying assumptions are made, and Hamilton's principle is used to derive the matrix equations of motion. The method is illustrated by numerical examples. The objective of the study is to clarify the torsional behavior of suspension bridges and to develop a method of determining a sufficient number of natural frequencies and mode shapes to enable an accurate practical analysis.
This technical note presents an analytical and experimental study on the effectiveness of a tuned mass damper (TMD) to suppress a wind-induced coupled flutter of a bridge deck. In the analysis, Theodorsen's aerodynamic forces are assumed to act on a bridge deck model. Parametric calculations indicate that critical velocity of the coupled flutter can be increased appreciably by TMD. A wind tunnel test is also performed, and confirms the effectiveness of TMD.
The multiple tuned liquid dampers (MTLDs), which consist of a number of TLDs whose first natural frequencies of sloshing are distributed over a certain range around the natural frequency of a structure, are studied. The simulations on the liquid motion in the MTLDs as well as the MTLDs-structure interaction are carried out by using a shallow water-wave theory. Then, two types of experiments, a forced-excitation experiment and an MTLDs-structure interaction experiment are conducted. The experiments and the simulation studies show that the MTLDs are efficient in the small amplitude range than the conventional TLDs, which have a single natural sloshing frequency, while the MTLDs efficiency is more or less the same level to that of the conventional TLDs in large amplitude range because of the damping nonlinearity of liquid motion. It is also shown that the control efficiency is not degraded, even though there is some offset in the tuning. This is the most significant point in actual engineering application. Finally, the application of the MTLDs to a high-rise building is presented as an example.
An active aerodynamic control method of suppressing flutter of a very-long-span bridge is presented in this paper. The control system consists of additional control surfaces attached to the bridge deck; their torsional movement, commanded via feedback control law, is used to generate stabilizing aerodynamic forces. The frequency independent formulation of unsteady aerodynamic forces acting on the bridge deck as well as the control surfaces is derived through rational function approximation. The high precision of approximation is ensured by multilevel linear and nonlinear constrained optimization. Although the proposed mathematical model of aeroservoelastic system is augmented by new aerodynamic states, it is in the form of a set of constant coefficient differential equations that are particularly convenient for control law synthesis. The obtained equations of motion are functions of mean wind speed so the efficiency of application of the conventional constant gain optimal feedback control is limited. To cope with the system dependence on wind speed, a variable-gain control is proposed. The static output variable-gain approach is formulated in terms of a mathematical optimization problem and the necessary conditions are derived. Application of the variable-gain control provides variation of control strategies in different wind velocities and is found to be efficient for the studied aerodynamic active control of bridge deck flutter.
A new kind of passive mechanical damper, tuned liquid damper (TLD). is studied that relies upon the motion of shallow liquid in a rigid tank for changing the dynamic characteristics of a structure and dissipating its vibration energy. A nonlinear model of two-dimensional liquid motion inside a rectangular TLD subjected to horizontal motion is developed on the basis of shallow-water wave theory, where the damping of the liquid motion is included semianalytically. Using the model, the response of a structure with TLD is also computed. The liquid motion inside the TLD under harmonic base excitation and, furthermore, the response of a single-degree-of-freedom structure with TLD, subjected to harmonic external force, are experimentally investigated. The agreement is good between the experiment and the prediction.
In this paper increasing the critical flutter wind speed of long-span bridges by using tuned mass dampers (TMDs) is theoretically and experimentally studied. Equations governing the motions of a bridge with TMDs are established. The Routh-Hurwitz stability criterion is used to study the aerodynamic instability of the bridge based on the characteristic equation of the system of the bridge and TMDs. A sectional model wind-tunnel test on the Tiger Gate Bridge, a suspension bridge with a steel box deck and a center span of 888 m, is carried out to confirm the numerical results. Some new findings from the test and the calculation are presented.
Tuned liquid column damper (TLCD) was developed mainly for the purpose of suppressing horizontal motion of structures. No relevant research has been found on the suppression of structural pitching vibration by using TLCD. This paper thus aims to investigate the possibility and effectiveness of applying TLCD to suppress pitching motion of structures. Both theoretical and experimental investigations are carried out. A mathematical model of tuned liquid column damper for suppressing structural pitching vibration is developed. The TLCD-structure interactive equations are derived and solved in both time domain and frequency domain. A series of free and forced vibration experiments with different TLCD configuration and parameters are performed. The influences of variable TLCD parameters on control effectiveness are determined. Numerical simulations corresponding to the experimental cases are carried out and compared with the experiments. A close agreement is obtained between the experimental results and theoretical simulation. This also verifies the developed theoretical model. Both theoretical and experimental studies show that TLCD can efficiently reduce structural pitching motion.
Analytical determination of the flutter and buffeting responses of long-span suspended bridges to wind excitation has predominantly been accomplished by single-mode-based methods. Proclivity towards design and construction of even longer span bridges has elevated the possibility of aerodynamic coupling of the flexural and torsional modes of vibration. A comprehensive, frequency-domain procedure developed to capture this multimode aeroelastic and aerodynamic response is presented in this paper. This new procedure is applied to evaluate the coupled response of a cable-stayed bridge. A quantitative assessment of the modal interactions at flutter and in the buffeting response is made to highlight the presence and effects of modal coupling. The multimode responses are then compared to single-mode and pseudomultimode results. As an extreme example, the bridge deck flutter derivatives were replaced with those of an airfoil to further investigate the ability of this approach to capture aeroelastic and aerodynamic coupling.
A procedure for the design of an active tuned mass damper for vibration control in tall buildings subject to wind loads is presented. The building motions are modeled by the first mode of the response, and it is assumed that the excitation is white noise. The controller is based on complete feedback (namely, feedback of displacement, velocity, and acceleration). The controller gains that minimize the variance of the rooftop displacement are derived in closed-form. Two examples, one of a 162 m tall planar frame and the other of a 400 m tall building in a city are studied to illustrate the active damper design and to evaluate the procedure and the results. The same examples are then studied as multiple-degree-of-freedom systems subject to nonwhite excitation that better simulates the wind. Results on the reduction of the dynamic response and control effectiveness of the active damper designs are presented and discussed.
An investigation is made of the possible application of tuned liquid column dampers and tuned liquid column/mass dampers in reducing the along-wind response of wind-sensitive structures. The structure is modeled as a lumped mass multi-degree-of-freedom system taking into account both bending and shear. The wind turbulence is modeled as a stochastic process that is stationary in time and nonhomogeneous in space. A random vibration analysis utilizing transfer matrix formulation is carried out to obtain response statistics. The nonlinear damping term in the fundamental equation of the tuned liquid damper is treated by an equivalent linearization technique. Numerical examples show that tuned liquid dampers, which have significant practical advantages, are as effective as the traditional tuned mass dampers if the parameters of the liquid dampers are properly selected. However, excess liquid motion in a tuned liquid column/mass damper may reduce the effectiveness of this damper. It is also shown that the wind-induced force- and acceleration-type responses of the structure with a damper, which is usually tuned to the fundamental frequency of the structure, should involve more than one vibration mode as higher-mode responses may become as large or even larger than the controlled-mode response.
Dynamic response behaviour of a simple torsionally coupled system with Multiple-Tuned Mass dampers (MTMDs) is investigated. The system is subjected to lateral excitation that is modelled as a broad-band stationary random process. MTMDs with uniformly distributed frequencies are considered for this purpose and they are arranged in a row covering the width of the system. A parametric study is conducted to investigate the effectiveness of MTMDs on reducing the response of torsionally coupled system. The parameters include the eccentricity of the main system, its uncoupled torsional to lateral frequency ratio and the damping of MTMDs. It is shown that the effectiveness of MTMDs in controlling the lateral response of the torsionally coupled system decreases with the increase in the degree of asymmetry. Further, the effectiveness of MTMDs, designed for an asymmetric system by ignoring the effect of the torsional coupling, is overestimated. © 1997 by John Wiley & Sons, Ltd.
Flutter suppression of a bridge deck by an active control method is tried. Bridge deck has control wings for suppressing flutter vibration. The aerodynamic forces acting on the control wings provide the additional aerodynamic force to the bridge deck. By providing the adequate phase and amplitude for the pitching motion of the control wings, the additional aerodynamic force produced by the control wings become positive aerodynamic damping. Thus the flutter is suppressed. Two dimensional theoretical analysis showed that the flutter speed of the bridge deck could be increased up to infinite high speed. From the model tests, the flutter speed was increased by a factor of two.
The purpose of this paper is to present a tuned mass damper which simultaneously reduces the vertical and torsional buffeting responses of long-span bridges. The proposed damper has two frequencies, which are tuned to the frequencies of the first flexural and torsional structural modes, to suppress the resonant effects. The aerodynamic coupling is taken into account for the formulation of the bridge-damper system, and this model is thus applicable to those bridges with significant mode coupling. The buffeting response reduction and the increase of the critical velocity are investigated through a parametric analysis. Based on this parametric study, the design procedures of the tuned mass damper for the wind-excited bridges are proposed. The results show that the proposed tuned mass damper is at least as effective as the usual tuned mass damper for suppressing buffeting response; furthermore it appreciably increases the stability of the bridge with either a single-degree-of-freedom flutter or a coupled flutter.
Multiple Tuned Mass Dampers (MTMD) consist of a large number of small oscillators with natural frequencies distributed around the natural frequency of a controlled mode of the structure. In the present paper, the modal characteristics and efficiency of the MTMD are studied analytically. Perturbation solutions for the modal properties of the MTMD–structure system are obtained and the modal characteristics are discussed. An explicit formula to estimate the effectiveness of the MTMD subjected to harmonic forces is also derived. It is shown that the MTMD is efficient when at least one of the oscillators is strongly coupled with the structure in any mode. Based on this observation, a critical bandwidth of the natural frequencies of the MTMD to make the system multiply tuned is derived in a simple form, and furthermore a robustness criterion for the frequency tuning under a given bandwidth is proposed. It is shown that, when properly designed, the MTMD can be much more stable (robust) than a conventional single TMD while maintaining more or less the same efficiency. Numerical studies verify the accuracy of the perturbation solutions and the proposed formulas.
Considerable attention has been paid to the research of passive and active structural control for wind-induced self-excited vibration of long-span bridges in recent years. In this paper a passive aerodynamic control of bridge flutter is proposed. The system consists of two additional surfaces to generate stabilizing forces. The torsional motion of the surfaces is governed by the additional pendulum attached to the bridge deck. The state-space equation of the flutter control system is derived through the rational function approximation of the unsteady aerodynamics of the bridge section. The performance of the control system is evaluated for various parameters of the pendulum and the potential improvement of flutter wind speed is demonstrated through numerical examples. The experimental study showed very good agreement with the theoretical prediction for small amplitude motion of the control surfaces.
Estimation of modal damping is always a critical first step in the analytical estimation of the flutter and buffeting reponses of long-span suspended bridges. The impact of under or over estimation of modal damping on the aerodynamic and aeroelastic behavior of suspended bridges is not clear. This issue surfaced when a seismic retrofit of the Golden Gate birdge using viscous dampers was proposed. The affect of these viscous dampers on the flutter and buffeting response of the Golden Gate bridge needed investigation. This paper considers the affect of additional damping imposed by these viscous dampers on the aeroelastic and aerodynamic response to wind-induced excitation. This mechanical damping was introduced into the aeroelastic system as additional modal damping. A multi-mode flutter and buffeting analysis was performed for several levels of modal damping. The results of the analysis revealed that additional damping decreased the buffeting response whereas the effect in flutter stability was more complex. At different levels of damping not only did the critical flutter velocity change but also the angle of attack at which it occurred.
The construction phase and its aerodynamic issues
- F Branceloni
- F Branceloni
Tuned mass damper to reduce building wind motion:, ASCE, Convention and Exposition
- K B Weisne
- K B Weisne
Application of robust control to the flutter in long span bridges
- N N Dung
- T Miyata
- H Yamada
- N N Dung
- T Miyata
- H Yamada