Damping of Cables by a Transverse Force

A general asymptotic format is presented for the effect on the modal vibrations of a transverse damper close to the end of a cable. Complete locking of the damper leads to an increase of the natural frequencies, and it is demonstrated that the maximum attainable damping is a certain fraction of the relative frequency increase, depending on the type of damping device. The asymptotic format only includes a real and a complex nondimensional parameter, and it is demonstrated how these parameters can be determined from the frequency increase by locking and from an energy balance on the undamped natural vibration modes. It is shown how the asymptotic format can incorporate sag of the cable, and specific results are presented for viscous damping, the effect of stiffness and mass, fractional viscous damping, and a nonlinear viscous damper. The relation of the stiffness component to active and semiactive damping is discussed.     

Dynamic Behavior of Stay Cables with Rotational Dampers

Vibration reduction in stay cables by means of viscous dampers is of great interest in cable damage prevention and serviceability of structural system supported by such cables. The paper presents a study on the effectiveness, as well as the limits, of rotational viscous dampers and springs inserted at the two ends of a bending-stiff taut cable; influence of rotational stiffness of the springs is also investigated. After a nondimensional expression of the equation of motion has been obtained, as in other cases of nonproportionally damped continuous structures, complex modal analysis is pursued, obtaining complex eigenvalues and eigenfunctions. Comparison with intermediate dampers, widely used in bridge engineering, is performed showing the range of nondimensional parameters for which the proposed approach is of interest. Finally, a numerical technique based on complex mode superposition is presented in order to evaluate time domain responses for transversal distributed excitation. As an example, the procedure is applied to a wind-exposed cable.     

Damping of Taut-Cable Systems: Two Dampers on a Single Stay

The mitigation of in-plane stay oscillation in cable-stayed bridges is commonly addressed by placing an external mechanical damper, linear or nonlinear, on each stay or by introducing transverse cross-ties among cables. Although the problem of a cable with a single external damper has found significant attention in the past and different techniques have been proposed for the solution of the free-vibration problem, limitations are related to the fact that the location of the damper is usually very close to the cable end (on the bridge deck side) due to geometric constraints, leading to inherently low modal damping in the fundamental modes. In this paper the installation of more than one damper on an individual stay is considered to overcome such limitations and to increase the overall performance of the system. An existing procedure, based on the linearized taut-string theory, was modified to allow for the presence of multiple external discrete viscous dampers. The case of two devices with arbitrary location has been solved, identifying advantages and disadvantages of the proposed solution. In addition, extensions of the practical “universal curve” and the interpretation thereof are presented.     

Experimental Verification of Smart Cable Damping

Stay cables, such as are used in cable-stayed bridges, are prone to vibration due to their low inherent damping characteristics. Transversely attached passive viscous dampers have been implemented in many bridges to dampen such vibration. However, only minimal damping can be added if the attachment point is close to the bridge deck. For longer bridge cables, the relative attachment point becomes increasingly smaller, and passive damping may become insufficient. A recent analytical study by the authors demonstrated that “smart” semiactive damping can provide increased supplemental damping. This paper experimentally verifies a smart damping control strategy employing H2/linear quadratic Gaussian (LQG) clipped optimal control using only force and displacement measurements at the damper for an inclined flat-sag cable. A shear mode magnetorheological fluid damper is attached to a 12.65?m inclined flat-sag steel cable to reduce cable vibration. Cable response is seen to be substantially reduced by the smart damper.     

Analytical Study on Bending Effects in a Stay Cable with a Damper

The effects of bending on the modal properties of a stay cable with a transverse damper are analytically studied. Considering that the value of the flexural rigidity in the stay cable is small in practice, an explicit asymptotic formula for the modal damping of a cable with a general type of damper is derived. For a viscous damper, the asymptotic formula obtained is compact, accurate, and thus is very suitable for practical design. Furthermore, for the first few vibration modes of interest, the asymptotic solution is independent of the modal index. It is shown that flexure in the cable reduces the maximum attainable modal damping, possibly up to 20%, while it significantly increases the optimal damping coefficient of the damper.     

Damping of Vibration by Actively Controlled Initial Distortions

A concept for the artificial damping of free vibration by means of actively controlled initial distortions imposed on the structure is presented. Two formulations for active control are presented: The first simulates the natural damping properties of structures, while the second uses a more sophisticated modal strategy of control (but with a faster damping process). The general idea of damping by actively forced distortions is explained and followed by a simple example for a one‐degree‐of‐freedom system. Then, the simulation of natural damping (which is a particular case of active control) and the possibility of accelerating the damping process by the modal optimal strategy are discussed and demonstrated with some examples for a two‐degree‐of‐freedom system. Finally, the vibration control of a four‐degree‐of‐freedom system is presented to demonstrate the efficiency of the proposed method. The method of active damping is described for truss structures, but it can be easily generalized to include frame structures as well.     

Control Effect for 20-Story Benchmark Building Using Passive or Semiactive Device

In this paper, we study the control effect for a 20-story benchmark building and apply passive and semiactive control devices to the building. First, we take viscous damping walls as a passive control device which consists of two outer plates and one inner plate, facing each other with a small gap filled with viscous fluid. The damping force is related to the interstory velocity, temperature, and the shearing area. Next, we take a variable oil damper as a semiactive control device which can produce the control forces by little electrical power. We propose a damper model in which the damping coefficient changes according to the response of the damper and control forces calculated by the controller based on a linear quadratic Gaussian control theory. It is demonstrated from the results of some simulations that both passive device and semiactive device can effectively reduce the response of the structure in various earthquake motions.     

Damping of Taut-Cable Systems: Effects of Linear Elastic Spring Support

The influence of linear elastic support on the damper effectiveness of a cable-damper system was investigated by modeling the system as a taut string, an intermediate damper, and a spring in series. Two types of damper were analyzed in this study: (1)?the linear elastic damper; and (2)?the friction threshold. An exact formulation for the free vibration of the system was developed for the linear viscous damping system, and a complex eigenfrequencies equation was worked to obtain the explicit solution for the frequency shift. A damping ratio equation for different modes, which depicts the effect of the spring, was developed from the frequency shift. An effective flexibility coefficient was introduced to investigate the effect of different values of support stiffness on the effectiveness of the linear viscous damper. A universal curve family diagram was constructed, which indicated that linear elastic support reduces the effectiveness of the linear viscous damper. The universal curve obtained previously by Main and Jones was a special case of this universal curve family for the case in which the stiffness of the support approached infinity. The equation of maximum force introduced to the spring was also derived and was shown to be positively related to the cable tension force and the cable vibration amplitude at the damper attachment location. The influence of the linear elastic support on a cable-damper system with a friction threshold was also investigated by using the result of the linear viscous damper and the equivalent energy method. The result showed that the linear elastic support also reduces the effectiveness of the friction threshold. An equation showing how to select an optimal friction threshold for a stay cable was also proposed.     

Combined Damping Effect of Two Dampers on a Stay Cable

The combined effect of two dampers, either on the same end or opposite ends of a stay cable, is analytically studied in this paper. By considering small distances of the dampers from the anchorages, an asymptotic formula for the modal damping ratio of the cable is derived from which the total damping effect is presented in an explicit form. It is shown that when two dampers are installed at opposite ends of the cable, the total damping effect is asymptotically the sum of the contributions from single dampers. On the contrast, if two dampers are at the same end, there is no advantage of increasing the maximum modal damping in the cable over the use of a single damper.     

Free Vibrations of Taut Cable with Attached Damper. II: Nonlinear Damper

Free vibrations of a taut cable with a nonlinear power-law damper attached near the end are considered. An approximate analytical solution for the amplitude-dependent effective damping ratios in each mode is developed by assuming the same form of solution as for the linear damper and minimizing the mean-square error in the force equilibrium at the damper. An asymptotic approximate solution for small frequency shifts reveals a nondimensional grouping of parameters allowing the development of an amplitude-dependent “universal estimation curve” for the power-law damper. The shape of the universal curve is slightly different for each value of the damper exponent, but for a given exponent the curve is nearly invariant over the same range of parameters as the universal curve for the linear damper. This formulation yields insights into the dependence of nonlinear damper performance on mode number and amplitude of oscillation, suggesting potential advantages that may be offered by a nonlinear damper over a traditional linear damper.     

Semiactive Neurocontrol for Seismic Response Reduction Using Smart Damping Strategy

A new semiactive control strategy that combines a neurocontrol system with a smart damper is proposed to reduce seismic responses of structures. In the proposed semiactive control system, the improved neurocontroller, which was developed by employing a training algorithm based on a cost function and a sensitivity evaluation algorithm to replace an emulator neural network, produces the desired active control force, and then a bang-bang-type controller clips the control forces that cannot be achieved by a smart damper (e.g., a variable orifice damper, controllable fluid damper, etc.). Therefore, the proposed semiactive control strategy is fail-safe in that the bounded-input, bounded-output stability of the controlled structure is guaranteed. Numerical simulation results show that the proposed semiactive control system that employs a neural network-based control algorithm is quite effective in reducing seismic responses.     

Control of Wind-Induced Self-Excited Oscillations by Transfer of Internal Energy to Higher Modes of Vibration. II: Application to Taut Cables

In Part I of this paper, a theoretical basis is presented using a two-degrees-of-freedom model. In this second part of the study, the passive control and the two types of semiactive controls introduced in Part I are examined numerically for a taut cable experiencing wind-induced galloping motion. The passive and the semiactive control schemes for taut cables show a good similarity with the results obtained for the two-degrees-of-freedom model. The potential of using these control schemes in practical applications to flexible structures is demonstrated.     

Performance and Repair Design of Stay Cables with Rain/Wind-Induced Vibrations

The results of a multifaceted investigation into large-amplitude vibrations of bridge stay cables are presented. The vibration of the stay cables occurred under light rain and wind conditions, and resulted in low-frequency, large-amplitude oscillations having recorded displacements of over 24?in. (0.6?m). Due to concerns about the implications of the vibrations on the integrity and durability of the stay cables and observed damage to stay-cable anchorage components, an investigation and repair program was developed. The final repair program arose from an investigation that combined the talents of practicing engineers, the Texas Department of Transportation, and representatives from four universities. Ultimately, a combination of supplemental hydraulic dampers and cable restrainers were used to mitigate the vibrations. This paper describes the results of the investigation and presents the practice-based methodology used to develop the implemented repair program.     

Vibration Control of Stay Cables of the Shandong Binzhou Yellow River Highway Bridge Using Magnetorheological Fluid Dampers

The Shandong Binzhou Yellow River Highway Bridge is a three-tower, cable-stayed bridge in Shandong Province, China. Because the stay cables are prone to vibration, 40 magnetorheological (MR) fluid dampers were attached to the 20 longest cables of this bridge to suppress possible vibration. An innovative control algorithm for active and semiactive control of mass-distributed dynamic systems, e.g., stay cables, was proposed. The frequencies and modal damping ratios of the unimpeded tested cable were identified through an ambient vibration test and free vibration tests, respectively. Subsequently, a series of field tests were carried out to investigate the control efficacy of the free cable vibrations achieved by semiactive MR dampers, “Passive-off” MR dampers and “Passive-on” MR dampers. The first three modal damping ratios of the cable incorporated with the MR dampers were also identified from the in situ experiments. The field experiment results indicated that the semiactive MR dampers can provide significantly greater supplemental damping for the cable than either the Passive-off or the Passive-on MR dampers because of the pseudonegative stiffness generated by the semiactive MR dampers.     

Semiactive Control of the 20-Story Benchmark Building with Piezoelectric Friction Dampers

A new control algorithm is proposed in this paper to control the responses of a seismically excited, nonlinear 20-story building with piezoelectric friction dampers. The passive friction damping mechanism is used for low-amplitude vibration while the active counterpart takes over for high-amplitude vibration. Both the stick and sliding phases of dampers are taken into account. To effectively mitigate the peak story drift and floor acceleration of the 20-story building, multiple dampers are placed on the 20-story building based on a sequential procedure developed for optimal performance of the dampers. Extensive simulations indicate that the proposed semiactive dampers can effectively reduce the seismic responses of the uncontrolled building with substantially less external power than its associated active dampers, for instance, 67% less under the 1940 El Centro earthquake when the passive friction force is equal to 10% of the damper capacity.     

Free Vibrations of Taut Cable with Attached Damper. I: Linear Viscous Damper

Free vibrations of a taut cable with an attached linear viscous damper are investigated in detail using an analytical formulation of the complex eigenvalue problem. This problem is of considerable practical interest in the context of stay-cable vibration suppression in bridges. An expression for the eigenvalues is derived that is independent of the damper coefficient, giving the range of attainable modal damping ratios and corresponding oscillation frequencies in every mode for a given damper location without approximation. This formulation reveals the importance of damper-induced frequency shifts in characterizing the response of the system. New regimes of behavior are observed when these frequency shifts are large, as is the case in higher modes and for damper locations further from the end of the cable. For a damper located sufficiently near the antinode in a given mode, a regime of solutions is identified for which the damping approaches critical as the damper coefficient approaches a critical value. A regime diagram is developed to indicate the type of behavior in each mode for any given damper location.     

Isolation System for Vibration Control of Stay Cables

Rain-wind induced cable vibration can cause serious problems in cable-stayed bridges. Externally attached dampers have been used to provide an effective means to suppress the vibration of relatively short stay cables. For very long stay cables, however, such damper systems are rendered ineffective, as the dampers need be attached near the end of the cables for aesthetic reasons. This paper investigates a new stay-cable isolation system to mitigate the cable vibration. The proposed isolation system, which consists of a laminated rubber bearing and an internal damper, may be installed inside of the cable anchorage. A simple analytical model of the cable-damper system is developed first based on the taut string representation of the cable. The response of a cable with the proposed isolation system is obtained and then compared to those of the cable with and without an external passive damper. The proposed stay-cable isolation system is shown to perform better than the optimal passive viscous damper, thereby demonstrating its applicability in large cable-stayed bridges.     

Performance of Tuned Liquid Dampers

This paper investigates the performance of unidirectional and bidirectional tuned liquid dampers (TLDs) under random excitation. The performance of the tuned liquid dampers is measured in terms of efficiency and robustness. A series of experimental tests are conducted on model scale structure-tuned liquid damper systems to evaluate their performance, which is then compared to that of the well known tuned mass damper. The effective damping is calculated for each test conducted and the efficiency and robustness are subsequently examined. The performance of a mistuned TLD is experimentally investigated to highlight the robustness of these passive dynamic vibration absorbers. A nonlinear numerical model is used to conduct an extensive parametric study on the performance of a tuned liquid damper. This study has resulted in the development of performance charts for a tuned liquid damper. These charts allow the efficiency of a tuned liquid damper to be examined for a number of varying parameters, which include the excitation amplitude, water depth, and building frequency. These charts are particularly useful for the initial design of a tuned liquid damper when the precise frequency of the structure is not known.     

Vibration Control of Beams with Embedded Smart Composite Material

With an external electrical stimulus, a method of controlling the elastic/viscoelastic behavior of a cantilever beam embedded with a bulk viscoelastic material having ``smart' properties, is addressed. The test smart material used is constituted of a heteorogeneous mixture of barium titanate and ferrite (in powder forms) dispersed in a sol-gel phase of polyacrylamide with a specific aqueous content. The barium titanate content possesses the piezoelectric property that enables the material to exhibit electroelastic characteristics. The test beam made of plexiglass material keeps the smart material constrained in its core along its axis. When subjected to transient and static load conditions, and electrically stimulating the embedded smart material, the free-vibration damping characteristics of the test beam are elucidated. It is shown that the measured response of the cantilever beam excited to vibrate in its first natural mode can be controlled with the application of the voltage stimulation. Relevant experimental data are furnished.     

Optimal Nonlocal and Asymmetric Structural Damping Using Regenerative Force Actuation Networks

A regenerative force actuation (RFA) network consists of multiple electromechanical forcing devices distributed throughout a structural system and actuated in such a way as to reduce the response of the structure when it is subjected to an excitation. The associated electronics of the devices are connected together such that they are capable of sharing electrical power with each other. This makes it possible for some devices to extract mechanical energy from the structure while others reinject a portion of that energy back into the structure at other locations. The forcing capability of an RFA network is constrained by the requirement that the total network must always dissipate energy. As such, it differs from fully active control devices in that its operation requires only a small amount of external power. Furthermore, its power-sharing capability gives it a forcing versatility beyond that attainable with semiactive and traditional passive damping systems. In this paper, RFA networks are analyzed in the context of their ability to apply supplemental linear structural damping, taking into account dissipation due to electrical resistances and viscous damping associated with the actuators. It is shown that these systems can be used to produce nonlocal damping (i.e., damping forces between distant degrees of freedom) and asymmetric damping matrices. By comparison, semiactive and passive devices can only impose local damping forces. The more generalized linear damping capabilities of RFA networks are shown to yield significant improvements in linear-quadratic optimal performance in stationary response. Examples are given in which a RFA network is used in various configurations to reduce the stationary response of the three-story shear structure to stochastic base excitation.