Experimental validation of the analytical modelling of a digitally created duffing acoustic nonlinear oscillator at low amplitudes
Nonlinear dynamics have long been exploited in order to damp vibrations in solid mechanics. The phenomenon of irreversible energy transfer from a linear primary system to a nonlinear absorber has driven great attention to the optimal design of vibration absorbers both for stationary and transient re...
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EDP Sciences
2025-01-01
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| Series: | Mechanics & Industry |
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| Online Access: | https://www.mechanics-industry.org/articles/meca/full_html/2025/01/mi240011/mi240011.html |
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| author | Morell Maxime Collet Manuel Gourdon Emmanuel Ture Savadkoohi Alireza De Bono Emanuele |
| author_facet | Morell Maxime Collet Manuel Gourdon Emmanuel Ture Savadkoohi Alireza De Bono Emanuele |
| author_sort | Morell Maxime |
| collection | DOAJ |
| description | Nonlinear dynamics have long been exploited in order to damp vibrations in solid mechanics. The phenomenon of irreversible energy transfer from a linear primary system to a nonlinear absorber has driven great attention to the optimal design of vibration absorbers both for stationary and transient regimes. Recently, the same principle has also been targeted in acoustics for the absorption of sound waves at high excitation amplitudes. Meanwhile, acoustic absorption by electro-active means has found great success for noise reduction in the linear regime. This study uses a method allowing the design of nonlinear resonators at amplitudes that typically induce linear behaviors. This research proposes an analytical study of the implementation of the duffing equation as a nonlinear electroacoustic resonator coupled to an acoustic mode of a tube. Experiments are carried out and compared to the analytical results. The experimental implementation is done using a real-time-based algorithm retrieving the measured pressure from a microphone and giving the electrical current to send to a loudspeaker as an output thanks to a Runge-Kutta-like algorithm. Despite the several assumptions of the model, the analytical modelling is validated by the experiment, showing that the model is able to predict the two-degree-of-freedom system. |
| format | Article |
| id | doaj-art-509f9b8ca5564dac9ed17c4dd3925f6e |
| institution | Kabale University |
| issn | 2257-7777 2257-7750 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | Mechanics & Industry |
| spelling | doaj-art-509f9b8ca5564dac9ed17c4dd3925f6e2025-02-07T08:25:41ZengEDP SciencesMechanics & Industry2257-77772257-77502025-01-0126210.1051/meca/2024036mi240011Experimental validation of the analytical modelling of a digitally created duffing acoustic nonlinear oscillator at low amplitudesMorell Maxime0https://orcid.org/0000-0003-3940-7548Collet Manuel1Gourdon Emmanuel2Ture Savadkoohi Alireza3De Bono Emanuele4ENTPE, Ecole Centrale de Lyon, CNRS, LTDS, UMR5513CNRS, Ecole Centrale de Lyon, ENTPE, LTDS, UMR5513ENTPE, Ecole Centrale de Lyon, CNRS, LTDS, UMR5513ENTPE, Ecole Centrale de Lyon, CNRS, LTDS, UMR5513Ecole Centrale de Lyon, CNRS, ENTPE, LTDS, UMR5513Nonlinear dynamics have long been exploited in order to damp vibrations in solid mechanics. The phenomenon of irreversible energy transfer from a linear primary system to a nonlinear absorber has driven great attention to the optimal design of vibration absorbers both for stationary and transient regimes. Recently, the same principle has also been targeted in acoustics for the absorption of sound waves at high excitation amplitudes. Meanwhile, acoustic absorption by electro-active means has found great success for noise reduction in the linear regime. This study uses a method allowing the design of nonlinear resonators at amplitudes that typically induce linear behaviors. This research proposes an analytical study of the implementation of the duffing equation as a nonlinear electroacoustic resonator coupled to an acoustic mode of a tube. Experiments are carried out and compared to the analytical results. The experimental implementation is done using a real-time-based algorithm retrieving the measured pressure from a microphone and giving the electrical current to send to a loudspeaker as an output thanks to a Runge-Kutta-like algorithm. Despite the several assumptions of the model, the analytical modelling is validated by the experiment, showing that the model is able to predict the two-degree-of-freedom system.https://www.mechanics-industry.org/articles/meca/full_html/2025/01/mi240011/mi240011.htmlprogrammableduffing oscillatormultiple scaleselectroacoustic resonatortransient regime |
| spellingShingle | Morell Maxime Collet Manuel Gourdon Emmanuel Ture Savadkoohi Alireza De Bono Emanuele Experimental validation of the analytical modelling of a digitally created duffing acoustic nonlinear oscillator at low amplitudes Mechanics & Industry programmable duffing oscillator multiple scales electroacoustic resonator transient regime |
| title | Experimental validation of the analytical modelling of a digitally created duffing acoustic nonlinear oscillator at low amplitudes |
| title_full | Experimental validation of the analytical modelling of a digitally created duffing acoustic nonlinear oscillator at low amplitudes |
| title_fullStr | Experimental validation of the analytical modelling of a digitally created duffing acoustic nonlinear oscillator at low amplitudes |
| title_full_unstemmed | Experimental validation of the analytical modelling of a digitally created duffing acoustic nonlinear oscillator at low amplitudes |
| title_short | Experimental validation of the analytical modelling of a digitally created duffing acoustic nonlinear oscillator at low amplitudes |
| title_sort | experimental validation of the analytical modelling of a digitally created duffing acoustic nonlinear oscillator at low amplitudes |
| topic | programmable duffing oscillator multiple scales electroacoustic resonator transient regime |
| url | https://www.mechanics-industry.org/articles/meca/full_html/2025/01/mi240011/mi240011.html |
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