A multi-parametric recursive continuation method for nonlinear dynamical systems

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.
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Clément Grenat, Sébastien Baguet, Claude-Henri Lamarque, Régis Dufour. A multi-parametric recursive continuation method for nonlinear dynamical systems. Mechanical Systems and Signal Processing, Elsevier, 2019, 127, pp.276-289. ⟨10.1016/j.ymssp.2019.03.011⟩. ⟨hal-02067415⟩

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