Understanding Modal Interactions in Non-classically Damped Linear Oscillators with Closely Spaced Modes
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915501298417664 |
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| author | Pinto, Luis M. Baldelomar Mojahed, Alireza Mohammadi, Sobhan Moore, Keegan J. Bergman, Lawrence A. Vakakis, Alexander F. |
| author_facet | Pinto, Luis M. Baldelomar Mojahed, Alireza Mohammadi, Sobhan Moore, Keegan J. Bergman, Lawrence A. Vakakis, Alexander F. |
| contents | This work addresses non-classically damped coupled oscillators with closely spaced modes focusing on the physics of modal interactions. Considering the simplest representative example in the form of an impulsively excited two-degree-of-freedom (two-DOF) system, we show that there is a single parameter defined as a coupling versus damping non-proportionality ratio, that separates two different dynamical regimes. Based on complexification-averaging analysis, we show that, below the critical value of this parameter, the system response possesses two distinct dissipation rates but only one frequency of oscillation; as a result, energy is slowly exchanged between modes in a single beat phenomenon. However, above the critical parameter value, the response has a single dissipation rate but two distinct oscillation frequencies; this yields an infinity of beat phenomena as energy is interchanged at a faster rate between modes. Our analytical predictions are fully validated by experimental measurements. Our findings highlight the physics of modal interactions in coupled oscillators and provide a framework for system identification and reduced-order modeling of systems with closely spaced modes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Understanding Modal Interactions in Non-classically Damped Linear Oscillators with Closely Spaced Modes Pinto, Luis M. Baldelomar Mojahed, Alireza Mohammadi, Sobhan Moore, Keegan J. Bergman, Lawrence A. Vakakis, Alexander F. Classical Physics Mathematical Physics This work addresses non-classically damped coupled oscillators with closely spaced modes focusing on the physics of modal interactions. Considering the simplest representative example in the form of an impulsively excited two-degree-of-freedom (two-DOF) system, we show that there is a single parameter defined as a coupling versus damping non-proportionality ratio, that separates two different dynamical regimes. Based on complexification-averaging analysis, we show that, below the critical value of this parameter, the system response possesses two distinct dissipation rates but only one frequency of oscillation; as a result, energy is slowly exchanged between modes in a single beat phenomenon. However, above the critical parameter value, the response has a single dissipation rate but two distinct oscillation frequencies; this yields an infinity of beat phenomena as energy is interchanged at a faster rate between modes. Our analytical predictions are fully validated by experimental measurements. Our findings highlight the physics of modal interactions in coupled oscillators and provide a framework for system identification and reduced-order modeling of systems with closely spaced modes. |
| title | Understanding Modal Interactions in Non-classically Damped Linear Oscillators with Closely Spaced Modes |
| topic | Classical Physics Mathematical Physics |
| url | https://arxiv.org/abs/2509.14857 |