Control of Wind-Induced Self-Excited Oscillations by Transfer of Internal Energy to Higher Modes of Vibration. I: Analysis in Two Degrees of Freedom

This paper and its companion paper present a new remedy to control wind-induced self-excited oscillation of long and flexible structures with low-internal damping, such as stay cables in cable-stayed bridges. A simple magnetic or mechanical device is used to disturb the cable motion in the lower modes of vibration and thus to transfer a portion of the internal energy of the system from the lower modes to higher modes. Because higher modes generally have high-positive aerodynamic damping when lower modes are excited by wind, the transferred energy is dissipated during the decay of high-frequency vibration. The present paper aims at capturing the fundamentals of energy transfer and dissipation through a detailed theoretical analysis based on a simplified model: A two-degree-of-freedom system with galloping-type self-exciting wind forces. The efficiency to reduce the amplitude of oscillation with a passive device and two types of semiactive devices is demonstrated using energy considerations. Results of numerical simulations are also presented.     

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.     

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.     

Vibration Control of the Wind-Excited 76-Story Benchmark Building by Liquid Column Vibration Absorbers

A study has been undertaken on the effectiveness of using liquid column vibration absorbers (LCVAs), in the suppression of wind-induced motion of the 76-story benchmark building. Much work has been undertaken on the behavior of the LCVA on an experimental level and its benefits have been demonstrated for wind-induced vibration control on a full-scale communications tower in Sydney, Australia, with a further installation being made on the “One Wall Center Building” Vancouver, Canada. The behavior of the LCVA has also been investigated numerically by use of computational fluid dynamics, and its potential has been illustrated in controlling a five-story building model. In this study, the LCVA adopted is composed of four identical columns of water. Initially, the performance of the LCVA is assessed without the inclusion of additional damping enhancing mechanisms. Subsequently, the same LCVA is considered with the inclusion of orifice plates, allowing a direct comparison of the two strategies. In order to address the issue of robustness, the sensitivity of the LCVA (with and without orifice) to mistuning is examined by perturbing the structural stiffness of the building by +15% and ?15%, respectively. From this, an indication of the system performance under conditions of mistuning has been assessed. The performance of the adopted LCVA has also been compared to that of the sample tuned mass damper (TMD) control device. The overall response reductions of the LCVA are shown to be comparable to the TMD. Furthermore, it is shown that the LCVA has several inherent features that make it more attractive than the classical TMD.     

Vibration of Tensioned Beams with Intermediate Damper. II: Damper near a Support

Analytical solutions are used to investigate the free vibrations of tensioned beams with a viscous damper attached transversely near a support. This problem is of particular relevance for stay-cable vibration suppression, but no restrictions on the level of axial load are introduced, and the results are quite broadly applicable. Characteristic equations for both clamped and pinned supports are rearranged into forms suitable for numerical solution by fixed-point iteration, whereby the complex eigenfrequencies and corresponding damping ratios can be accurately computed within a few iterations. Explicit asymptotic approximations for the complex eigenfrequencies are also obtained, subject to restrictions on the closeness of the eigenfrequencies to their undamped values. These asymptotic approximations are expressed in the same “universal” form identified in previous studies. It is observed that the maximum attainable modal damping ratios and the corresponding optimal values of the damper coefficient can be significantly affected by bending stiffness and by the nature of the support conditions, and a nondimensional parameter grouping is identified that enables an assessment of when bending stiffness should be considered.     

Effects of False Floors on Vibration Serviceability of Building Floors. II: Response to Pedestrian Excitation

This is the second of two papers that present the results of a comprehensive and systematic study into the effects of false flooring on the vibration serviceability of long-span concrete floors. In this paper, controlled pedestrian response measurements were utilized to determine the effects of the installation of false flooring on the vibration serviceability of long-span concrete floors. It was found that, in most cases, the installation of false flooring tended to reduce the measured vibration response of the floor under controlled pedestrian excitation. This was more significant for false floors with a relatively high finished floor height (FFH) than for floors with a lower finished floor height. It is tentatively proposed that the effects of false flooring be incorporated into existing design procedures by multiplying calculated responses by a vibration response reduction factor. This factor would be 0.9 for false flooring with FFH less than 500 mm or 0.8 for false flooring with FFH of 500 mm or greater.