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Journal Articles Physica D: Nonlinear Phenomena Year : 2024

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
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hal-04560135 , version 1 (26-04-2024)

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Filip Novkoski, Jules Fillette, Chi-tuong Pham, Eric Falcon. Nonlinear dynamics of a hanging string with a freely pivoting attached mass. Physica D: Nonlinear Phenomena, 2024, 463, pp.134164. ⟨10.1016/j.physd.2024.134164⟩. ⟨hal-04560135⟩
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