Sound production induced by FRICTion: Investigating non-smOoth dynamics with Numerical and experimental bifurcation AnaLysis – FRICTIONAL

The project FRICTIONAL aims to characterize, analyze, model and control the nonlinear mechanisms involved in friction-induced vibrations and sound production. Frictional systems are non-smooth dynamical systems. They display a wealth of dynamics, from the sound produced by insects (e.g. crickets) to the sound of a violin to the diversity of brake noises in transports. The existence, stability, observability and acoustic characteristics of these regimes can depend sensitively on the design and control parameters of the system. Although frictional systems are very common, and frequently encountered in various industrial contexts, the prediction of their oscillatory dynamics remains a major challenge.

This project relies on an interdisciplinary approach, at the crossroad of engineering sciences and applied mathematics, to investigate friction-induced sound and vibration production. It aims at accessing an exhaustive, global cartography of the oscillation regimes in the space of design and control parameters of frictional systems. In particular, advanced numerical methods will be adapted to perform a complete bifurcation analysis of physical models written in the form of piecewise smooth differential equations. In parallel, an experimental continuation procedure will be developed to perform the first model-free (and therefore approximation-free) bifurcation analysis of a self-oscillating system. This dual approach will unveil new information that remain inaccessible with existing techniques, and which will provide an in-depth understanding of the nonlinear mechanisms involved in sound production. Overall, this will allow to improve the physical models of sound production, in order to go towards the accurate prediction of the qualitative and quantitative oscillating dynamics. This will pave the way to virtual prototyping of frictional systems (with applications, for example, in the automotive industry) and to the optimisation of their dynamics, for example to suppress a particular sound regime.