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arXiv · 2404.16531

Nonlinear dynamics of a hanging string with a freely pivoting attached mass

Filip Novkoski·Jules Fillette·Chi-Tuong Pham·Eric Falcon
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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.

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Filip Novkoski, Jules Fillette, Chi-Tuong Pham, Eric Falcon. 2024-04-25. Nonlinear dynamics of a hanging string with a freely pivoting attached mass. https://doi.org/10.1016/j.physd.2024.134164

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