A multi-parametric recursive continuation method for nonlinear dynamical systems. (15th July 2019) - Grenat, C.; Baguet, S.; Lamarque, C.-H.; Dufour, R.
Highlights: Multi-parametric bifurcation tracking for nonlinear dynamical systems. Method based on extended systems, harmonic balance method, arc-length continuation. Recursive algorithm appending new constraints at each continuation level. The position and existence of bifurcations can be controlled by tuning parameters. Used to optimize the adverse dynamics of a nonlinear vibration absorber. Abstract: The aim of this paper is to provide an efficient multi-parametric recursive continuation method of specific solution points of a nonlinear dynamical system such as bifurcation points. The proposed method explores the topology of specific points found on the frequency response curves by tracking extremum points in the successive codimensions of the problem with respect to multiple system parameters. To do so, the characterization of extremum points by a constraint equation and its associated extended system are presented. As a result, a recursive algorithm is generated by successively appending new constraint equations to the extended system at each new level of continuation. Then, the methodology is applied to a nonlinear tuned vibration absorber (NLTVA). The limit of existence of isolated solutions and extremum points optimizing the region without isolated solution are found and used to improve the NLTVA.