Adrien Melot, Postdoctoral Researcher at I4S Inria Team.
Title: Computational methods for bifurcation analysis and control.
The ever-increasing demand for lighter structures and more efficient systems requires that the effects of nonlinearities be evaluated at the design stage. One of the most notable characteristics that sets apart nonlinear systems from their linear counterparts is bifurcation phenomena. When a parameter is varied, e.g. the forcing frequency, a bifurcation may occur, resulting in qualitatively different responses such as quasi-periodic or chaotic oscillations.
Bifurcation analysis, which aims at predicting and studying such phenomena, is a thriving research field. Recent research investigated the computation of the stability of periodic solutions or the parametric analysis of bifurcation points. However, very few studies attempted optimizing the structural parameters of a mechanical system for it to exhibit bifurcations at desired locations and never in the context of nonlinear vibrations. After a brief introduction to nonlinear vibrations, we will discuss state-of-the-art methods for carrying out efficient parametric bifurcation analyses and introduce a computational optimization framework based on the harmonic balance method (HBM) to enforce the appearance of bifurcation points at targeted locations.
