Nonlinear dynamics of a hanging string with a freely pivoting attached mass
Abstract
We show that the natural resonant frequency of a suspended flexible string is significantly modified (by one order of magnitude) by adding a freely pivoting attached mass at its lower end. This articulated system then exhibits complex nonlinear dynamics such as bending oscillations, similar to those of a swing becoming slack, thereby strongly modifying the system resonance that is found to be controlled by the length of the pivoting mass. The dynamics is experimentally studied using a remote and noninvasive magnetic parametric forcing. To do so, a permanent magnet is suspended by a flexible string above a vertically oscillating conductive plate. Harmonic and period-doubling instabilities are experimentally reported and are modeled using the Hill equation, leading to analytical solutions that accurately describe the experimentally observed tonguelike instability curves.
Keywords
Cite
@article{arxiv.2404.16531,
title = {Nonlinear dynamics of a hanging string with a freely pivoting attached mass},
author = {Filip Novkoski and Jules Fillette and Chi-Tuong Pham and Eric Falcon},
journal= {arXiv preprint arXiv:2404.16531},
year = {2024}
}