Chaos in impact oscillators not in vain: Dynamics of new mass excited oscillator

Published on May 12, 2020in Nonlinear Dynamics5.022
· DOI :10.1007/S11071-020-05644-0
Dimitri Danulussi Alves Costa5
Estimated H-index: 5
(UFRJ: Federal University of Rio de Janeiro),
Vahid Vaziri9
Estimated H-index: 9
+ 4 AuthorsMarian Wiercigroch51
Estimated H-index: 51
Sources
Abstract
This work explores complex dynamics of a new mass excited impact oscillator reported in Wiercigroch et al. (Nonlinear Dyn 99:323–339, 2020) both experimentally and numerically in the context of development of chaos theory and its applications. The parameters of the rig were characterised and are presented in the paper. To improve quality of the recorded phase portraits, a new technique for processing of the experimental data allowing to reduce the influence of noise and to obtain clear orbits especially for higher periods is proposed. A comparison with the previous studies on the base excited impact oscillator confirms that the rig is much more accurate as well as it has capability to generate a wide range of excitation patterns. It is demonstrated that a precise control of the excitation is achieved by changing the coil current. It is also shown that the rig is able to capture co-existent attractors and multi-stability by reproducing various predicted numerical responses, which has not been possible before. The results obtained using a simple impact oscillator model are in a good agreement with the experimental results, which indicates that the rig can be used for further fundamental studies of impact phenomena including grazing. It can also serve as a tool to study nonlinear control including bifurcation control and control of co-existing orbits.
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Abstract Following the previous work on the degenerate grazing bifurcations of impact oscillators, this paper aims to explore novel two-parameter dynamics near the degenerate grazing points using GPU parallel computing technology. By using the technology, a further understanding of the near-grazing dynamics can be developed for impact oscillators. Three main indicators, i.e., the largest Lyapunov exponent, number of excitation periods and number of impacts, are calculated for each grid of the tw...
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