Stabilization of a heavy particle on a vibrating soft ribbon

When sand is sprinkled on a vibrated plate, it accumulates near the vibration nodes of the plate forming the famous "Chladni patterns" [1]. These patterns, which vary with the forcing frequency, provide an easy visualization of a musical instrument when it needs to be tuned, for example. However, if the plate is soft enough, as an elastic membrane, grains can deform it and then change in turn the modes’ pattern and frequency.

Here, as a first step towards the modelisation of this coupling, we propose a 1D-version of the system, where a bead is bouncing on a narrow elastic ribbon. As expected, the presence of the bead shifts the first modes of resonance, but it also excites new modes. Specifically, the ribbon can twist to stabilize the bead at a precise frequency. We suggest that this mode results from the combination between the bead size and the ribbon’s elastic properties.

[1] M. Faraday, Philos. Trans. Roy. Soc. London 52, 299 (1831)