A multi-parametric recursive continuation method for nonlinear dynamical systems
| Autor: | Claude-Henri Lamarque, Sébastien Baguet, Clément Grenat, Régis Dufour |
|---|---|
| Přispěvatelé: | Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Tribologie et Dynamique des Systèmes (LTDS), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-École Nationale des Travaux Publics de l'État (ENTPE)-Ecole Nationale d'Ingénieurs de Saint Etienne-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2019 |
| Předmět: |
Optimization
0209 industrial biotechnology Frequency response Aerospace Engineering 02 engineering and technology 01 natural sciences Isolated solutions Continuation Constraint algorithm 020901 industrial engineering & automation 0103 physical sciences Applied mathematics Limit (mathematics) 010301 acoustics Bifurcation Civil and Structural Engineering Mathematics Mechanical Engineering [SPI.MECA.VIBR]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph] Nonlinear vibration absorber Computer Science Applications Constraint (information theory) Continuation methods Nonlinear system Dynamic Vibration Absorber Control and Systems Engineering Signal Processing Harmonic Balance Method Stability and bifurcation analysis Bifurcation tracking |
| Zdroj: | Mechanical Systems and Signal Processing Mechanical Systems and Signal Processing, Elsevier, 2019, 127, pp.276-289. ⟨10.1016/j.ymssp.2019.03.011⟩ |
| ISSN: | 0888-3270 1096-1216 |
| DOI: | 10.1016/j.ymssp.2019.03.011 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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