Self-similar vortex-induced vibrations of a hanging string

TL;DR

This paper investigates vortex-induced vibrations of a hanging string, revealing self-similar mode shapes and their theoretical explanation through a linear stability analysis, with results aligning with flow behavior similar to circular cylinders at low Reynolds numbers.

Contribution

It introduces the concept of self-similar mode shapes in vortex-induced vibrations of a hanging string and provides a theoretical framework for their behavior.

Findings

Self-similar mode shapes can be collapsed onto a single function using a rescaling coefficient.

The Strouhal number's evolution with Reynolds number mirrors that of a circular cylinder at low Re.

Linear stability analysis accurately predicts mode shapes and self-similarity evolution.

Abstract

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. The evolution of the Strouhal number St with the Reynolds number Re first follows a trend similar to what is observed for a circular cylinder in a flow for relatively low Reynolds numbers (32<Re<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 on 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.