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Publication Number: FHWA-HRT-05-083
Date: August 2007

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Chapter 5. Recommnedations for Future Research and Development

The design guidelines provide a concise approach to suppress wind-induced vibrations in cablestayed bridges, and are based on the existing knowledge base and further investigations performed through this project. While the design recommendations are empirical, the mitigation methods discussed (dampers, cable crossties, and surface modification) are proven to be effective through both past experience and research. Future research in the following areas clarifying some of the remaining key issues would strengthen the design guidelines.

This is the first time a set of design guidelines have been proposed for the mitigation of stay cable vibration. It is expected that future adjustments based on actual cable performance and advances in cable technology may require further refinements to the design guidelines.

WIND TUNNEL TESTING OF DRY INCLINED CABLES

Galloping of dry inclined cables was investigated using wind tunnel testing in the current study and was found to be less critical than previously believed. However, further research would be valuable to confirm the findings and to study the effects additional parameters. Future wind tunnel testing could include:

  • Adding data points to validate the first two phases.
  • Studying the effect of cable frequencies, which are potentially important for the aerodynamic behavior of the inclined dry cable.
  • Further studying the Reynolds number effect, resulting from the model surface condition and the orientation angle.

DECK-INDUCED VIBRATION OF STAY CABLES

Deck-induced vibration of stay cables has been observed in a few instances in the field-measured data, occurring in the fundamental mode of a stay with quite large amplitudes. Further investigation of this potential source of excitation would be beneficial, and may include comparison of analytical predictions and field measurements and analytical modeling of the influence of attached dampers. Effort needs to be made to identify more records in which interaction is evident between vibrations of the bridge deck and stays. As newer bridge superstructure sections are aerodynamically refined to mitigate vortex-induced oscillations of the roadway as a user comfort criteria, the deck-stay interaction may become primarily an issue for older bridges.

MECHANICS OF RAIN/WIND-INDUCED VIBRATIONS

Rain/wind-induced vibrations appear to be the most problematic of the measured vibrations, with their large amplitudes and relatively frequent occurrence, and are among the most significant considerations in the design of mitigation measures for stay cables. One of the primary components of future research could be to develop a more indepth understanding of the underlying mechanics of rain/wind-induced stay cable vibration. This effort would have a focus somewhat different from that adopted in this study, where the objective was simply to develop a sufficient understanding to be able to arrest the practical occurrence of objectionable levels of stay cable vibrations. It is believed that such an indepth study could build upon the findings from this and other recent projects, and include continued detailed analysis of the wealth of full-scale data collected (data on U.S. bridges as well as large-scale data from Japan as available) and a critical review of existing proposed mechanisms.

This effort may include the following two components: identification of key observed characteristics and evaluation of proposed mechanisms. Further analysis of the measured vibration records both before and after the damper installation could provide additional insight into the nature of the rain/wind excitation mechanism and clarify which types of proposed mechanisms are more appropriate. A good start on this task has already been made, but there are more data that need to be carefully analyzed that were outside the present project scope. Some of the more interesting observations need further detailed investigation using the diverse data sets.

Many of the proposed mechanisms were postulated based on wind tunnel investigations. While useful, some caution must be taken in interpretation of these data as field conditions may contain three-dimensionality of the flows that the wind tunnel testing cannot replicate.

DEVELOP A MECHANICS-BASED MODEL FOR STAY CABLE VIBRATION ENABLING THE PREDICTION OF ANTICIPATED VIBRATION CHARACTERISTICS

In designing effective and economical dampers for rain/wind-induced vibration suppression, it would be of great assistance to have a model with the capability to predict, for an arbitrary stay cable, the following characteristics of rain/wind-induced vibration:

  • Preferred mode: The full-scale measurements have indicated that rain/wind-induced vibrations tend to occur in a preferred mode over a fairly wide range of wind speeds; for a given stay, which mode(s) will be preferred?
  • Wind speed and direction: Over what range of wind speeds and wind directions will the problematic vibrations occur? (This question is actually not of significant concern in the design of dampers.)
  • Damping levels: How much damping is necessary to adequately suppress vibrations?
  • Amplitudes, forces, and power: What will be the steady-state amplitudes as a function of damping ratio? What levels of force may be expected in the damper, and what will be the power dissipation demands?

It is likely that rain/wind-induced vibrations can be modeled in a manner similar to vortexinduced vibrations: As a nonlinear oscillator characterized by a negative-damping type instability at small amplitudes, and a limit cycle at large amplitudes. Such a model could be developed using the following steps:

  • Obtain reliable estimates of inherent mechanical damping in the undamped stays, as inherent damping is expected to be a critically important parameter in estimating oscillation amplitudes.
  • Identify records from various stays corresponding to the onset of rain/wind-induced vibration, and characterize the energy input as a function of amplitude.
  • For each stay, from the records collected previously, identify an election of "worst-case" time histories corresponding to the maximum energy input under the ideal wind conditions for rain/wind-induced vibration.
  • Using parameters such as inherent mechanical damping; stay length, diameter, tension, and mass/length; wind speed and air density, obtain the best possible normalization of the "worstcase" energy-input versus amplitude curves so that the curves from various stays can collapse (almost) onto a single curve.
  • Identify a nonlinear oscillator model that can capture the measured energy input versus amplitude curves, and use the field-measured data to estimate the model parameters.
  • Investigate the dependence of the model parameters on wind speed and wind direction for the various stays, and identify appropriate normalizations of these parameters to allow comparison among stays.

There are strong indications that a nonlinear negative damping model may be a promising approach. This is based on observation of what appears to be a negative damping type of instability for small amplitudes, causing the amplitude to increase until a limit cycle is reached. Vibrations occur over a fairly narrow range of wind directions, and occur in one or two preferred modes over a fairly wide range of wind speeds. These observations and potential model can be used to carefully evaluate proposed mechanisms for consistency and reasonableness.

While ultimately the model resulting from the proposed work may take the form of an analytical formulation in which equations of motion for cable vibration are expressed mathematically, it may also be an empirical model which seeks to obtain a good fit to the field measurements from different stays, it may simply take the form of general conclusions achieved from a statistical analysis of the measured vibrations, or it may represent a combination of the three approaches.

Such a model will enable a much more comprehensive treatment of the problem both in terms of when such vibrations are likely to occur, and what (quantitatively) will be the effect of various mitigation approaches—dampers, crossties, and aerodynamic treatments. The ability to do such analysis presently does not exist.

PREDICT THE PERFORMANCE OF STAY CABLES AFTER MITIGATION USING THE MODEL

The most practical application of such a model would be to be able to predict the level of stay oscillations after the application of mitigation methods. This would also enable the combination of important observations from the modeling of the field-measured vibrations and from the analysis of the restrained system to predict performance after vibration mitigation efforts(specifically dampers and crossties). Special attention again could be devoted to a discussion of the mitigation of rain/wind-induced vibration. Mitigation of other types of vibration, such as vortex-induced vibrations (particularly in the higher modes) and deck-stay interaction, could also be evaluated. More indepth analysis of field measurements of damper performance can also be performed to compare measured and predicted oscillation amplitudes after mitigation.

PERFORM A DETAILED QUANTITATIVE ASSESSMENT OF VARIOUS ALTERNATIVE MITIGATION STRATEGIES

As has been demonstrated in this report, dampers are not the only method available for the mitigation of stay cable vibration. Other potentially suitable solutions include the provision of additional damping by other means, such as redesigned anchorages, crossties, and aerodynamic treatments. It is considered important to assess their relative performance using the model. There is data from stays with crossties from the Fred Hartman Bridge, and from stays with aerodynamic treatments (rings) from the Veterans Memorial Bridge. In addition, efficient analytical/numerical tools for the prediction of the dynamic response of two-dimensional cable "networks" (representing crosstied stay systems) have been developed using this project.

Using the results of the predictions, the performance of these approaches can be compared and this information used to evaluate the suitability of the various methods. Important economic assessments must also be considered.

IMPROVE UNDERSTANDING OF INHERENT DAMPING IN STAYS AND THAT PROVIDED BY EXTERNAL DEVICES

The inherent damping in a cable, generally accepted to be fairly low, is not readily quantifiable, and there are very few reported measurements. A better understanding of damping in cables(both with and without external dampers) could have some benefit in practical applications from extensive field measurements so as to facilitate more effective and rational mitigation of stay cable vibrations. Substantial progress has been made towards this goal by analyzing the full-scale measurement data collected at the Fred Hartman Bridge and by preliminarily estimating modal frequencies and damping ratios for two cables on the bridge as described in this report. By comparing the amplitudes of vibrations before and after damper installation, dampers were found to be generally successful in mitigating the vibrations. In a few cases, when the vibrations were primarily in the lateral direction and the dampers were oriented in the in-plane direction, there is evidence that the dampers were not effective at suppressing them.

Frequency shifts caused by the dampers were also clearly identified and the discovered relationship between modal frequency and vibration amplitude seems to be in agreement with the actual configuration of the cable-damper system in the field. Compared with frequency estimation, results from damping estimation are more complicated: Modal damping ratios estimated from different records are usually scattered, and the relationship between these estimated damping ratios and the characteristics of the vibrations is still not very clear. Nonetheless, the results do suggest that the level of inherent damping in the cables is indeed very low and that the rain/wind mechanism introduces some kind of negative damping into the system, consequently making the vibration amplitude large.

Relationships between the modal damping ratios and such quantities as modal displacement and modal damper force need to be investigated. Testing of an actual damper is also deemed as beneficial. The damper should be driven by either force or displacement with different periods. Numerical simulation can also be used for this purpose and force-displacement curves thus obtained can be compared to field measurement data. It will be helpful to separate the part of the vibration when the damper is evidently engaged from the rest of the vibration when it is not engaged (e.g., by using wavelet transforms). Energy methods can also be applied to the part of the vibration when the damper is engaged to estimate the effective damping during that period of time.

Research so far has been concentrated on full-scale measurement data from two cables of the Fred Hartman Bridge. Data from other instrumented cables of this bridge and some cables of the Veterans Memorial Bridge, which were instrumented during the same period of time, are also available for analysis. In addition, forced vibration tests and short-term ambient tests have been conducted on some cables of the Sunshine Skyway Bridge in Tampa, FL. Data collected from these tests are of special interest because cable damping can be estimated from the forced vibration tests using the logarithmic decrement method and compared with the values estimated from the ambient tests. No excessive cable vibration has been reported for the Sunshine Skyway Bridge so far, even though it is located in a region full of frequent wind and rain. More detailed analysis of the full-scale data from this bridge will help understand the reasons for these observations.

IMPROVE UNDERSTANDING OF CROSSTIE SOLUTIONS

As pointed out in the report, crossties combined with dampers seem to offer the possibility of enhanced performance over their component counterparts. Application of such a combined system has been discussed previously.(18) It is considered important to extend the modeling developed here to better study and understand these characteristics, and to provide a tool for designers. The ability to optimize crosstie configurations also seems to be an important area for future research.

REFINE RECOMMENDATIONS FOR EFFECTIVE AND ECONOMICAL DESIGN OF STAY CABLE VIBRATION MITIGATION STRATEGIES FOR FUTURE BRIDGES.

While the design recommendations proposed are believed to be sufficient as minimum criteria for practical mitigation of unacceptable levels of stay vibrations, these efforts could help by addressing the following issues quantitatively:

  • How much supplemental damping should be provided in each mode for vibration suppression?
  • Which type of nonlinear damper (including the case of linear) is most appropriate for cable vibration mitigation?
  • For which mode of vibration should the damper performance be optimized?
  • For what force levels and energy dissipation capacity should the damper be designed?

This project has been successful in producing a set of guidelines and recommendations for stay cable vibration mitigation based on information available at the time of its conclusion. While this does include information based on a review of the literature and a significant amount of research on the characterization of field measurements and damper performance, the guidelines may be improved through the future research items proposed.

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