| People | Locations | Statistics |
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| Seuring, Stefan |
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| Nor Azizi, S. |
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| Pato, Margarida Vaz |
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| Kölker, Katrin |
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| Huber, Oliver |
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| Király, Tamás |
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| Spengler, Thomas Stefan |
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| Al-Ammar, Essam A. |
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| Dargahi, Fatemeh |
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| Mota, Rui |
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| Mazalan, Nurul Aliah Amirah |
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| Macharis, Cathy | Brussels |
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| Arunasari, Yova Tri |
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| Nunez, Alfredo | Delft |
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| Bouhorma, Mohammed |
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| Bonato, Matteo |
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| Fitriani, Ira |
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| Autor Correspondente Coelho, Sílvia. |
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| Pond, Stephen |
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| Okwara, Ukoha Kalu |
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| Toufigh, Vahid |
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| Campisi, Tiziana | Enna |
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| Ermolieva, Tatiana |
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| Sánchez-Cambronero, Santos |
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| Agzamov, Akhror |
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Vakakis, Alexander F.
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Publications (11/11 displayed)
- 2023Machine learning extreme acoustic non-reciprocity in a linear waveguide with multiple nonlinear asymmetric gatescitations
- 2022Exceeding the classical time-bandwidth product in nonlinear time-invariant systemscitations
- 2022Nonlinear targeted energy transfer: state of the art and new perspectivescitations
- 2021Modal energy exchanges in an impulsively loaded beam with a geometrically nonlinear boundary condition: computation and experimentcitations
- 2021Analysis of the non-periodic oscillations of a self-excited friction-damped system with closely spaced modescitations
- 2020Broadband non-reciprocity with robust signal integrity in a triangle-shaped nonlinear 1D metamaterialcitations
- 2020Energy transmission by impact in a system of two discrete oscillatorscitations
- 2017Numerical and experimental investigations of a rotating nonlinear energy sinkcitations
- 2014Interactions of propagating waves in a one-dimensional chain of linear oscillators with a strongly nonlinear local attachmentcitations
- 2011A time-domain nonlinear system identification method based on multiscale dynamic partitionscitations
- 2003Designing a Linear Structure with a Local Nonlinear Attachment for Enhanced Energy Pumpingcitations
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document
Analysis of the non-periodic oscillations of a self-excited friction-damped system with closely spaced modes
Abstract
It is widely known that dry friction damping can bound the self-excited vibrations induced by negative damping. The vibrations typically take the form of (periodic) limit cycle oscillations. However, when the intensity of the self-excitation reaches a condition of maximum friction damping, the limit cycle loses stability via a fold bifurcation. The behavior may become even more complicated in the presence of any internal resonance conditions. In this work, we consider a two-degree-of-freedom system with an elastic dry friction element (Jenkins element) having closely spaced natural frequencies. The symmetric in-phase motion is subjected to self-excitation by negative (viscous) damping, while the symmetric out-of-phase motion is positively damped. In a previous work, we showed that the limit cycle loses stability via a secondary Hopf bifurcation, giving rise to quasi-periodic oscillations. A further increase in the self-excitation intensity may lead to chaos and finally divergence, long before reaching the fold bifurcation point of the limit cycle. In this work, we use the method of complexification-averaging to obtain the slow flow in the neighborhood of the limit cycle. This way, we show that chaos is reached via a cascade of period-doubling bifurcations on invariant tori. Using perturbation calculus, we establish analytical conditions for the emergence of the secondary Hopf bifurcation and approximate analytically its location. In particular, we show that non-periodic oscillations are the typical case for prominent nonlinearity, mild coupling (controlling the proximity of the modes), and sufficiently light damping. The range of validity of the analytical results presented herein is thoroughly assessed numerically. To the authors’ knowledge, this is the first work that shows how the challenging Jenkins element can be treated formally within a consistent perturbation approach in order to derive closed-form analytical results for limit cycles and their bifurcations.
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