@misc{HDRBBergeot2024,
abstract = {The common thread of the research work presented in this thesis is the implementation of analytical and numerical methods to describe the dynamic behavior of nonlinear mechanical systems, which have several characteristic time scales and may be stochastic. I have developed these activities within the framework of two research areas in vibration and acoustics.
The first area concerns the passive attenuation of vibrations using nonlinear absorbers known as NESs (Nonlinear Energy Sinks). In this context, I am particularly interested in the control of self-sustained oscillations. The latter generally occur in dynamical systems whose equilibrium solution becomes unstable in favor of an oscillating solution, usually periodic. As the amplitude of these oscillations can be very large, it is desirable to be able to attenuate them. NESs are also oscillators with the particularity of possessing an essentially nonlinear stiffness, which gives them the ability to resonate at any frequency. When an NES is coupled to a self-sustaining oscillator, the resulting dynamic system has a number of solutions, some of which correspond to low-amplitude oscillations. The aim is to understand how to favor these solutions over others where the NES is almost inoperative.
The second area concerns the study of transient phenomena in single-reed musical instruments such as clarinets and saxophones. This work is situated within the general context of the study of strategies followed by musicians during transient phases: note attacks, transitions between two notes, extinction transients, etc. In particular, it aims to correlate gestures (or time evolutions of control parameters) with sound results. In this context, my work focuses on the study of attack transients. From the point of view of dynamical systems, this leads me to study the influence of the time variation of bifurcation parameters on the emergence of a periodic solution, but also on the basins of attraction when multistability occurs.
Although far apart in terms of application, it turns out that the systems studied in these two research areas (the self-oscillating mechanical system coupled to a NES on the one hand, and the instrument during attack transients on the other) have a common feature. Both are modeled by systems of differential equations, which reveal a small parameter highlighting their fast-slow nature. The time evolution of state variables in such fast-slow systems is characterized by a succession of fast and slow epochs. This common nature also enables these systems to be studied within a common mathematical framework. Within the mechanics and acoustics community, the originality of my approach lies above all in the appropriation of theoretical results known to mathematicians on singularly perturbed ordinary differential equations with the aim of understanding the complex behaviors of the concrete mechanical systems under consideration.
For each of the above-mentioned areas of research, my main contributions to the state of the art are presented, together with the prospects I envisage for the short- and medium- terms.},
author = {Bergeot, Baptiste},
date-added = {2024-02-19 14:25:06 +0100},
date-modified = {2024-02-19 14:44:41 +0100},
school = {Universit{\'e} de Tours},
tel = {https://hal.science/tel-04459911},
title = {Syst{\`e}mes rapides-lents en m{\'e}canique vibratoire (Fast-slow systems in vibratory mechanics)},
year = {Habilitation {\`a} Diriger des Recherche (HDR), Universit{\'e} de Tours, 2024},
bdsk-url-1 = {https://tel.archives-ouvertes.fr/tel-01149513}
}
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