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Self-similar vortex-induced vibrations of a hanging string

Published online by Cambridge University Press:  08 May 2013

C. Grouthier*
LadHyX, Department of Mechanics, Ecole Polytechnique, 91128 Palaiseau, France
S. Michelin
LadHyX, Department of Mechanics, Ecole Polytechnique, 91128 Palaiseau, France
Y. Modarres-Sadeghi
Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA
E. de Langre
LadHyX, Department of Mechanics, Ecole Polytechnique, 91128 Palaiseau, France
Email address for correspondence:


An experimental analysis of the vortex-induced vibrations of a hanging string with variable tension along its length is presented in this paper. It is shown that standing waves develop along the hanging string. First, the evolution of the Strouhal number $\mathit{St}$ with the Reynolds number $\mathit{Re}$ follows a trend similar to what is observed for a circular cylinder in a flow for relatively low Reynolds numbers ($32\lt \mathit{Re}\lt 700$). Second, the extracted mode shapes are self-similar: a rescaling of the spanwise coordinate by a self-similarity coefficient allows all of them to collapse onto a unique function. The self-similar behaviour of the spatial distribution of the vibrations along the hanging string is then explained theoretically by performing a linear stability analysis of an adapted wake-oscillator model. This linear stability analysis finally provides an accurate description of the mode shapes and of the evolution of the self-similarity coefficient with the flow speed.

©2013 Cambridge University Press 

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