Publisher DOI: 10.1016/j.compstruc.2019.106139
Title: The extended periodic motion concept for fast limit cycle detection of self-excited systems
Language: English
Authors: Jahn, Martin 
Stender, Merten  
Tatzko, Sebastian 
Hoffmann, Norbert  
Grolet, Aurélien 
Wallaschek, Jörg 
Keywords: Bifurcations; Chaos; Nonlinear modes; Self-excited vibrations; Stability; Unstable periodic orbits
Issue Date: 15-Jan-2020
Source: Computers and Structures (227): 106139 (2020-01-15)
Abstract (english): 
Limit cycle solutions of self-excited dynamic systems can be determined by continuation of solutions along a system parameter variation or by brute-force testing. While the brute-force search for basins of attraction is computationally intractable, continuation methods compute only those branches that are connected to others, thus neglecting a-priori unknown solutions and detached branches, such as isolas. In this work, a method is proposed for finding limit cycles of self-excited dynamic systems. The method is based on the continuation of nonlinear modes for non-conservative systems, for which the Extended Periodic Motion Concept (E-PMC) is applied. The E-PMC allows for finding stable and unstable periodic solutions along the nonlinear mode and is especially helpful for determining solutions that are detached from other solution branches. Hence, the a-priori selection of proper initial conditions for the limit cycle computation is no longer necessary. A self-excited frictional oscillator with cubic stiffness terms is studied. The proposed technique proves to be robust and finds all isolated periodic solutions that were published previously by other authors. In an extended model configuration, the E-PMC finds co-existing stable limit cycles and unstable periodic orbits, one of which gives rise to hyper-chaotic motion with multiple positive Lyapunov exponents.
ISSN: 0045-7949
Journal: Computers & structures 
Institute: Strukturdynamik M-14 
Document Type: Article
Project: SPP 1897: Calm, Smooth and Smart - Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation: Teilprojekt Simulationsbasierter Entwurf hybrider Partikeldämpfer mit Anwendung auf flexible Mehrkörpersysteme 
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