Currently holding a post-doctoral position at the Structural Dynamics and Vibration Laboratory, McGill, Canada under the supervision of Prof. Mathias Legrand.

Two main topics of interest:

> non-linear modes for non-smooth systems (non-smooth modes)
> numerical schemes for a sound description of impacts

The presentation below is extremely succinct as most of the related work is under submission or in progress.

 Non-smooth modes

Non-linear modal analysis is now considered as a valuable and efficient tool for the dynamics analysis of non-linear mechanical systems. Related issues were investigated in the past decades among which:

  •      methods of analysis (analytical/numerical)
  •      reduced-order models
  •      stability and bifurcations of solutions

Currently, a major challenge is to consider non-smooth non-linearities in large-scale mechanical systems in the framework of non-linear modes. In this context, I study the behaviour of simple unforced structures subject to an elastic impact modelled by a Newton impact law.

The object below is an example of a non-smooth mode (NSM) of a 2-dof spring-mass system. The NSM is a surface which lives in the phase space -- here, the projection in a 3D space is represented. It is constituted by a continuum of periodic orbits. The green curve corresponds to the discontinuities in velocity. The red ellipse is the grazing linear mode.

non-smooth mode

Investigations on numerical schemes for a sound description of impacts

Classical FEM, because they intrinsically consider a finite number of nodes  do not account for high-frequency content, and therefore cannot soundly describe discontinuities: they either disperse or diffuse.

Additionally, discretised systems do not embed enough information about the wave which propagates after an impact: information must be added, by using an impact law. A commonly used impact law is that of Newton which introduces a coefficient of restitution. Both a contact phase and energy conservation cannot be ensured using such a law.

I am currently working on solutions to overcome such limitations.