The effects of damping on the amplitude and frequency response of a freely vibrating cylinder in cross-flow
We have studied the effects of controlled damping on the amplitude and frequency response profiles of an elastically mounted cylinder in cross-flow. The dimensionless damping parameter, b^*=2b/ρLDU, which is closely related to the traditional "mass-damping" parameter, m^*ζ, was varied over a wide range of values through the use of a variable magnetic eddy current damping system. For low damping and sufficiently high Reynolds number we observe the previously described large-amplitude, three-branch (initial, upper, lower) response profile, and for high damping or low Reynolds number we observe the small-amplitude, two-branch (initial and lower) response profile. However we find that, because of the influence of Reynolds number, the traditional labels of "high mass-damping" and "low mass-damping" are incomplete with regard to predicting a large or small-amplitude response profile. In our experiments, as damping is systematically increased, we observe a transition between these two profiles characterized by a gradual "erosion" and eventual disappearance of the large-amplitude section (upper branch) and the scaling down of the lower branch region. We find that jumps from the upper to the initial branch originate on the 2S/2P boundary in the Williamson–Roshko plane. Another new finding is a hysteresis between the lower branch and the desynchronized region, which only appears at low Reynolds numbers. We also explore changes in the frequency response profile, which are connected with the changes in the amplitude profile, for our upper branch cases. We observe that analogous to the three amplitude branches, there are three distinct branches for the frequency response.
© 2006 Elsevier Ltd. Received 10 October 2005; accepted 20 April 2006. Available online 31 July 2006. The application of magnetic damping described here was inspired by the theses of J. D. Smith and C. C. Feng who were students of Geoffrey V. Parkinson, recently deceased. We dedicate this paper to Geoff. We would like to thank Prof. Morteza Gharib for his continued involvement in this research effort and Prof. David Goodwin for his helpful suggestions regarding the damping system. We gratefully acknowledge the financial support provided by ONR Grant #N00014-94-1-0793. Scholarship support was provided by the National Science Foundation graduate fellowship program.