Geometrically non-linear vibrations of thin structures
The framework of my research is the large-amplitude vibrations of continuous thin structures such as beams, strings, plates and shells. The geometrical non-linearity give birth to a various and complex phenomenology : oscillation frequency dependence on amplitude, hysteretic behaviour, jump phenomena, mode coupling, instabilities, chaotic vibrations. Two main problems are of concern:
- Model reduction : In order to gain simulation time, a method base on the Non-linear Normal Modes (NNMs), have been developped.
- The numerical and experimental description of the rich variety of the geometrically non-linear behaviour. More particularly, the scenarios for the transition to chaos (via energy exchange, mode coupling and bifurcations) as well as the chaotic regime, are specifically studied. For large systems in the chaotic regime, the framework of wave turbulence is used. Gongs and cymbals is a nice applications of these typical chaotic vibrations in musical acoustics.
Non-linear Normal Modes (NNMs) in vibration theory
Thin plates and shells
Cymbals and gongs
Sound synthesis of gongs
Sound synthesis of cymbals with variable thickness
Wave Turbulence
