  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.
