Multi-parametric optimization of bifurcation points in nonlinear dynamical systems

Clément Grenat (1) , Sébastien Baguet (1) , Régis Dufour (1) , Claude-Henri Lamarque (2)

1 DCS - Dynamique et Contrôle des Structures
2 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

A frequency-domain method is proposed for tuning bifurcation points in nonlinear dy-namical systems by means of multi-parametric bifurcation tracking and optimization criteria. Introduction In the field of mechanical engineering, nonlinear phenomena introduced by large deflections, miniaturization, electro-mechanical couplings, nonlinear vibration absorbers,. .. , are often encountered. Nonlinear systems can have multiple solutions for one unique set of parameters or, on the opposite, no stable solution for a specific parameter range. These phenomena, characterized by bifurcation points such as limit points or Neimark-Sacker bifurcations, lead to jumps in the response or changes of dynamical regime. So, being able to optimize those bifurcation points is interesting for designing nonlinear systems. The literature on bifurcation points characterization and detection comprises numerous contributions. Since then, the obtained methods have been combined with arc-length continuation in order to follow bifurcation points with respect to one parameter. This work presents a multi-parametric analysis of bifurcation points combining multi-parametric continuation and a specific optimization criterion. The original contribution of this paper lies in the multi-parametric approach. The main target application is the design of Nonlinear Energy Sinks.

Domaines: Vibrations [physics.class-ph]

Clément Grenat, Sébastien Baguet, Régis Dufour, Claude-Henri Lamarque. Multi-parametric optimization of bifurcation points in nonlinear dynamical systems. NNM2016, 6th International Conference on Nonlinear Vibrations, Localization and Energy Transfer, Jul 2016, Liège, Belgium. ⟨hal-01369616⟩