@article {TERRIEN2025119241, title = {Basins of attraction in a dynamical system with a time-varying control parameter: The case of attack transients in a simple model of reed musical instrument}, journal = {Journal of Sound and Vibration}, volume = {618}, year = {2025}, pages = {119241}, abstract = {

Multistability, a common phenomenon in dynamical systems in general and in musical instruments in particular, corresponds to the coexistence of several stable regimes for a given set of parameters. When a system is multistable, which regime is observed depends on the initial conditions on the state variables, and therefore relates to the basins of attraction. Here we consider a simple model of reed musical instrument. A bifurcation analysis shows that the system is bistable on a range of the blowing pressure, which is one of the main control parameters for the musician. In the bistability region, the boundary between basins of attraction is computed for the classical case of constant control parameters in the one hand, and for saturating ramps of the blowing pressure on the other hand. These profiles of the blowing pressure are chosen as prototypical representations of the so-called attack transients of the blowing pressure, during which the musician starts to blow in the instrument to create a musical note from silence. Attack transients are known to be of crucial importance in a musical context, yet mostly overlooked in physical models of the musician{\textendash}instrument system. The separatrix between basins of attraction is computed numerically by combining time-domain simulations with a machine learning technique relying on support vector machine. Our results demonstrate that attack transients of the blowing pressure significantly affect the practical observability of the different stable regimes, suggesting that they might be used by musicians to navigate between basins. From a more general point of view, these results relate to rate-induced tipping phenomena and might therefore be of interest beyond the particular case of musical instruments.

}, keywords = {Attack transients, Basins of attraction, Bifurcation analysis, Musical acoustics, Nonlinear dynamical systems, Physical modeling, Rate-induced tipping}, issn = {0022-460X}, doi = {https://doi.org/10.1016/j.jsv.2025.119241}, url = {https://www.sciencedirect.com/science/article/pii/S0022460X25003153}, author = {Soizic Terrien and Baptiste Bergeot and Christophe Vergez and Samy Missoum} } @article {, title = {Cartography of a Multistable System using Support Vector Machines Applied to a Clarinet Model}, journal = {Nonlinear Dynamics}, year = {2025}, month = {Apr-02-2025}, issn = {0924-090X}, doi = {10.1007/s11071-024-10842-1}, author = {Colinot, Tom and Szwarcberg, Nathan and Vergez, Christophe and Missoum, Samy} } @conference {gourc2022bifurcations, title = {Bifurcations d{\textquoteright}un Mod{\`e}le Simple de Corde Frott{\'e}e et Note du Loup}, booktitle = {16{\`e}me Congr{\`e}s Fran{\c c}ais d{\textquoteright}Acoustique, CFA2022}, year = {2022}, author = {Gourc, Etienne and Vergez, Christophe and Mattei, Pierre-Olivier and Missoum, Samy} } @article {, title = {Nonlinear dynamics of the wolf tone production}, journal = {Journal of Sound and Vibration}, volume = {516}, year = {2022}, pages = {116463}, doi = {10.1016/j.jsv.2021.116463}, url = {https://www.sciencedirect.com/science/article/pii/S0022460X21005010}, author = {Etienne Gourc and Christophe Vergez and Pierre-Olivier Mattei and Samy Missoum} } @article {, title = {Woodwind Instrument Design Optimization based on Impedance Characteristics with Geometric Constraints}, journal = {Journal of the Acoustical Society of America}, volume = {148}, year = {2020}, month = {11/2020}, chapter = {2864}, abstract = {

Computational optimization algorithms coupled with acoustic models of wind instruments provide instrument makers with an opportunity to explore new designs. Specifically, they enable the automatic discovery of geometries exhibiting desired resonance characteristics. In this paper, the design optimization of woodwind instruments with complex geometrical features (e.g., non-cylindrical bore profile and side holes with various radii and chimney heights) is investigated. Optimal geometric designs are searched so that their acoustic input impedance has peaks with specific target frequencies and amplitudes. However, woodwind instruments exhibit complex input impedance whose features, such as resonances, might have non-smooth evolution with respect to design variables, thus hampering gradient-based optimization. For this reason, this paper introduces new formulations of the impedance characteristics (resonance frequencies and amplitudes) using a regularized unwrapped angle of the reflection function. The approach is applied to an illustrative instrument subjected to geometric constraints similar to the ones encountered by manufacturers (a key-less pentatonic clarinet with two-registers). Three optimization problems are considered, demonstrating a strategy to simultaneously adjust several impedance characteristics on all fingerings.

}, doi = {10.1121/10.0002449}, url = {https://doi.org/10.1121/10.0002449}, author = {Augustin Ernoult and Christophe Vergez and Samy Missoum and Philippe Guillemain and Michael Jousserand} } @conference {, title = {Comment l{\textquoteright}optimisation peut-elle {\^e}tre une aide {\`a} la facture instrumentale ?}, booktitle = {Congr{\`e}s Fran{\c c}ais d{\textquoteright}Acoustique}, year = {2018}, address = {Le Havre, France}, author = {Ernoult, Augustin and Missoum, Samy and Jousserand, Michael and Guillemain, Phillipe and Vergez, Christophe and Sanchez, Patrick} } @conference {, title = {Mod{\`e}le minimal de la note du loup}, booktitle = {Congr{\`e}s Fran{\c c}ais d{\textquoteright}Acoustique}, year = {2018}, address = {Le Havre, France}, author = {Gourc, Etienne and Vergez, Christophe and Mattei, Pierre-Olivier and Missoum, Samy} } @article {boroson2017optimization, title = {Optimization Under Uncertainty of Parallel Nonlinear Energy Sinks}, journal = {Journal of Sound and Vibration}, volume = {394}, year = {2017}, month = {04/2017}, pages = {451-464}, abstract = {

Nonlinear Energy Sinks (NESs) are a promising technique for passively reducing the amplitude of vibrations. Through nonlinear stiffness properties, a NES is able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NESs do not require a specific tuning and absorb energy over a wider range of frequencies. Nevertheless, they are still only efficient over a limited range of excitations. In order to mitigate this limitation and maximize the efficiency range, this work investigates the optimization of multiple NESs configured in parallel. It is well known that the efficiency of a NES is extremely sensitive to small perturbations in loading conditions or design parameters. In fact, the efficiency of a NES has been shown to be nearly discontinuous in the neighborhood of its activation threshold. For this reason, uncertainties must be taken into account in the design optimization of NESs. In addition, the discontinuities require a specific treatment during the optimization process. In this work, the objective of the optimization is to maximize the expected value of the efficiency of NESs in parallel. The optimization algorithm is able to tackle design variables with uncertainty (e.g., nonlinear stiffness coefficients) as well as aleatory variables such as the initial velocity of the main system. The optimal design of several parallel NES configurations for maximum mean efficiency is investigated. Specifically, NES nonlinear stiffness properties, considered random design variables, are optimized for cases with 1, 2, 3, 4, 5, and 10 NESs in parallel. The distributions of efficiency for the optimal parallel configurations are compared to distributions of efficiencies of non-optimized NESs. It is observed that the optimization enables a sharp increase in the mean value of efficiency while reducing the corresponding variance, thus leading to more robust NES designs.

}, keywords = {Parallel nonlinear energy sinks; Optimization under uncertainty; Activation threshold}, doi = {http://dx.doi.org/10.1016/j.jsv.2016.12.043}, url = {http://www.sciencedirect.com/science/article/pii/S0022460X16308045}, author = {Ethan Boroson and Samy Missoum and Pierre-Olivier Mattei and Christophe Vergez} } @article {missoum2014explicit, title = {Explicit Mapping of Acoustic Regimes for Wind Instruments}, journal = {Journal of Sound and Vibration}, volume = {333}, year = {2014}, pages = {5018-5029}, doi = {10.1016/j.jsv.2014.05.017}, author = {Missoum, Samy and Vergez, Christophe and Doc, Jean-Baptiste} } @article {doc2014minimal, title = {A Minimal Model of a Single-Reed Instrument Producing Quasi-Periodic Sounds}, journal = {Acta Acustica United with Acustica}, volume = {100}, year = {2014}, pages = {543-554}, doi = {10.3813/AAA.918734}, author = {Doc, Jean-Baptiste and Vergez, Christophe and Missoum, Samy} } @conference {boroson2014optimization, title = {Optimization Under Uncertainty of Nonlinear Energy Sinks}, booktitle = {Proceedings of the ASME International Design and Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 8: 26th Conference on Mechanical Vibration and Noise}, year = {2014}, publisher = {American Society of Mechanical Engineers}, organization = {American Society of Mechanical Engineers}, address = {Buffalo, NY}, doi = {10.1115/DETC2014-34238}, url = {http://codes.arizona.edu/sites/default/files/pdf/Boroson2014.pdf}, author = {Boroson, Ethan and Missoum, Samy and Mattei, Pierre-Olivier and Vergez, Christophe} } @conference {missoum2013explicit, title = {Explicit Maps of Acoustic Regimes of a Wind Instrument}, booktitle = {Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 8: 22nd Reliability, Stress Analysis, and Failure Prevention Conference}, year = {2013}, publisher = {American Society of Mechanical Engineers}, organization = {American Society of Mechanical Engineers}, address = {Portland, OR}, doi = {10.1115/DETC2013-12644}, url = {https://asmedigitalcollection.asme.org/IDETC-CIE/proceedings-abstract/IDETC-CIE2013/55997/V008T13A097/256719}, author = {Missoum, Samy and Vergez, Christophe} }