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Item type:Publication, Access status: without files , Hyperchaos co-existing with periodic orbits in a frictional oscillator(2020-04-28); ; ; This work reports observations of complex dynamical behavior and chimera-alike dynamics in a self-excited frictional oscillator with a weak stiffness nonlinearity. Multi-stability in the form of several co-existing stable limit cycle solutions are identified for a wide range of system parameters. For a particular system configuration, an unstable periodic orbit is found that gives rise to irregular long-term behavior. Trajectories starting from this orbit turn out to be hyper-chaotic with multiple positive Lyapunov exponents. Trajectories starting from different regions in phase space converge to stable limit cycles. Hence, this numerical study reveals co-existing regular and irregular dynamics at a fixed system configuration. This sensitive dependence of the qualitative system dynamics on initial conditions adds new aspects to a better understanding of the rich dynamic behavior of structures subjected to friction-induced vibrations.Publicationtype: Journal Article156 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , The extended periodic motion concept for fast limit cycle detection of self-excited systems(2020-01-15); ; ; ; 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.Publicationtype: Journal Article134