Nonlinear dynamics of a hanging string with a freely pivoting attached mass
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916222812028928 |
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| author | Novkoski, Filip Fillette, Jules Pham, Chi-Tuong Falcon, Eric |
| author_facet | Novkoski, Filip Fillette, Jules Pham, Chi-Tuong Falcon, Eric |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_16531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear dynamics of a hanging string with a freely pivoting attached mass Novkoski, Filip Fillette, Jules Pham, Chi-Tuong Falcon, Eric Pattern Formation and Solitons Soft Condensed Matter Classical Physics 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. |
| title | Nonlinear dynamics of a hanging string with a freely pivoting attached mass |
| topic | Pattern Formation and Solitons Soft Condensed Matter Classical Physics |
| url | https://arxiv.org/abs/2404.16531 |