Baptiste Bergeot - Academic Website

Research

The common thread of my research 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 focuses on the passive reduction of vibrations through nonlinear absorbers called Nonlinear Energy Sinks (NESs). The second area involves investigating transient phenomena in single-reed musical instruments, such as clarinets and saxophones.

Although these two research areas differ widely in their applications, the systems they examine—the self-oscillating mechanical system coupled to an NES on one side and the musical instrument during attack transients on the other-share an important common feature. Both can be modeled by differential equation systems that contain a small parameter, revealing their fast-slow dynamics. The evolution of their state variables therefore consists of alternating fast and slow phases. This shared structure allows both systems to be analyzed within a unified mathematical framework. Within the mechanics and acoustics community, the originality of my approach lies in drawing on theoretical results from the mathematics of singularly perturbed ordinary differential equations to gain insight into the complex behavior of these concrete mechanical systems.

A more detailed description of these research activities is provided in my Habilitation (HDR) manuscript.

Passive mitigation of unwanted vibrations by means nonlinear energy sink (NES)

This research focuses on the passive attenuation of vibrations using nonlinear absorbers known as Nonlinear Energy Sinks (NESs). In particular, I am interested in the control of self-sustained oscillations-phenomena that arise when the equilibrium state of a dynamical system becomes unstable and is replaced by an oscillatory, typically periodic, solution. Because these oscillations can reach large amplitudes, effective attenuation strategies are highly desirable. NESs are themselves oscillators characterized by an essentially nonlinear stiffness, which allows them to resonate over a broad frequency range. When an NES is coupled to a self-sustained oscillator, the combined system may exhibit several possible steady-state responses, including some associated with low-amplitude oscillations. The objective of this work is to understand how to promote these favorable, low-amplitude solutions over alternative states in which the NES remains largely ineffective.

Related publications

Baptiste Bergeot and Sébastien Berger. Fast--slow analysis of passive mitigation of self-sustained oscillations by means of a bistable nonlinear energy sink. Physica D: Nonlinear Phenomena, 460:134063, 2024.
Baptiste Bergeot. Effect of stochastic forcing on the dynamic behavior of a self-sustained oscillator coupled to a non-linear energy sink. International Journal of Non-Linear Mechanics, 150:104351, 2023.
Cherif Snoun, Baptiste Bergeot and Sébastien Berger. Robust optimization of nonlinear energy sinks used for mitigation of friction-induced limit cycle oscillations. European Journal of Mechanics - A/Solids, 93:104529, 2022.
Baptiste Bergeot, Sergio Bellizzi and Sébastien Berger. Dynamic behavior analysis of a mechanical system with two unstable modes coupled to a single nonlinear energy sink. Communications in Nonlinear Science and Numerical Simulation, 95:105623, 2021.
Baptiste Bergeot. Scaling law for the slow flow of an unstable mechanical system coupled to a nonlinear energy sink. Journal of Sound and Vibration, 503:116109, 2021.
Cherif Snoun, Baptiste Bergeot and Sébastien Berger. Prediction of the dynamic behavior of an uncertain friction system coupled to nonlinear energy sinks using a multi-element generalized polynomial chaos approach. European Journal of Mechanics - A/Solids, 80:103917, 2020.
Duc Thinh Kieu, Baptiste Bergeot, Marie-Laure Gobert and Sébastien Berger. Stability analysis of a clutch system with uncertain parameters using sparse polynomial chaos expansions. Mechanics & Industry, 20(1):104, 2019.
Baptiste Bergeot and Sergio Bellizzi. Steady-state regimes prediction of a multi-degree-of-freedom unstable dynamical system coupled to a set of nonlinear energy sinks. Mechanical Systems and Signal Processing, 131:728--750, 2019.
Baptiste Bergeot and Sergio Bellizzi. Asymptotic analysis of passive mitigation of dynamic instability using a nonlinear energy sink network. Nonlinear Dynamics, 94(2):1501--1522, 2018.
Baptiste Bergeot, Sébastien Berger and Sergio Bellizzi. Mode coupling instability mitigation in friction systems by means of nonlinear energy sinks : numerical highlighting and local stability analysis. Journal of Vibration and Control, 24(15):3487--3511, 2017.
Baptiste Bergeot, Sergio Bellizzi and Bruno Cochelin. Passive suppression of helicopter ground resonance using nonlinear energy sinks attached on the helicopter blades. Journal of Sound and Vibration, 392:41--55, 2017.
Baptiste Bergeot, Sergio Bellizzi and Bruno Cochelin. Analysis of steady-state response regimes of a helicopter ground resonance model including a non-linear energy sink attachment. International Journal of Non-Linear Mechanics, 78:72--89, 2016.
Baptiste Bergeot, Sergio Bellizzi and Bruno Cochelin. Passive suppression of helicopter ground resonance instability by means of a strongly nonlinear absorber. Advances in Aircraft and Spacecraft Science, 3(3):271--298, 2016.

Transient processes in clarinet-like musical instruments

This 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.

Related publication

Soizic Terrien, Baptiste Bergeot, Christophe Vergez and Samy Missoum. 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 of Sound and Vibration, 618(A):119241, 2025.
Baptiste Bergeot, Soizic Terrien and Christophe Vergez. Predicting transient dynamics in a model of reed musical instrument with slowly time-varying control parameter. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(7):073146, 2024. Selected as Editor's Pick.
Baptiste Bergeot and Christophe Vergez. Analytical prediction of delayed hopf bifurcations in a simplified stochastic model of reed musical instruments. Nonlinear Dynamics, 107:3291--3312, 2022.
André Almeida, Baptiste Bergeot, Christophe Vergez and Bruno Gazengel. Analytical Determination of the Attack Transient in a Clarinet With Time-Varying Blowing Pressure. Acta Acustica united with Acustica, 101(5):1026--1038, 2015.
Baptiste Bergeot andré Almeida, Bruno Gazengel, Christophe Vergez and Didier Ferrand. Response of an artificially blown clarinet to different blowing pressure profiles. The Journal of the Acoustical Society of America, 135(1):479, 2014.
Baptiste Bergeot andré Almeida, Christophe Vergez and Bruno Gazengel. Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure: influence of noise. Nonlinear Dynamics, 74(3):591--605, 2013.
Baptiste Bergeot andré Almeida, Christophe Vergez and Bruno Gazengel. Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure. Nonlinear Dynamics, 73(1-2):521--534, 2013.