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Dynamics of a driven oscillator carrying a freely sliding mass

MPG-Autoren
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Parlitz,  Ulrich
Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Zitation

Többens, A., Mettin, R., & Parlitz, U. (2012). Dynamics of a driven oscillator carrying a freely sliding mass. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 22(06): 1250132. doi:10.1142/S0218127412501325.


Zitierlink: https://hdl.handle.net/11858/00-001M-0000-002A-360E-E
Zusammenfassung
A mathematical model for a nonlinear oscillator, which is composed of an oscillating mass interacting with a freely sliding friction damper, is introduced and investigated. This oscillator is a strongly simplified model for a damping principle applied to turbine blades to suppress oscillations induced by inhomogeneous flow fields. It exhibits periodic, quasi-periodic, as well as chaotic dynamics occuring suddenly due to adding sliding bifurcations. Mathematically, the oscillator is given as a piecewise smooth (Filippov) system with a switching manifold corresponding to the sticking phase of the damper mass. The rich dynamics of this system is analyzed and illustrated by means of resonance curves, Lyapunov diagrams, Poincaré sections and reductions to iterated one-dimensional maps.