Journal
NONLINEAR DYNAMICS
Volume 97, Issue 1, Pages 525-539Publisher
SPRINGER
DOI: 10.1007/s11071-019-04995-7
Keywords
Degenerate grazing bifurcation; Neimark-Sacker bifurcation; Perturbation of eigenvalue; Higher-order discontinuity mapping
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Funding
- CSC scholarship [201706130054]
- National Natural Science Foundation of China [11672104]
- Chair Professor of Lotus Scholars Program in Hunan province [XJT2015408]
- National Science Fund for Distinguished Young Scholars in China [11225212]
- Collaborative Innovation Center of Intelligent New Energy Vehicle
- Hunan Collaborative Innovation Center for Green Car
- Hunan Province Cooperative Innovation Center for the Construction & Development of Dongting Lake Ecological Economic Zone
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This paper presents the analysis of the degenerate grazing bifurcation in a three-degree-of-freedom impact oscillator by studying the bifurcations of near-grazing period-one impact motion near the degenerate grazing point. Actually, this paper extends the higher-order zero time discontinuity mapping to perform the perturbation analysis of characteristic equation of period-one impact motion and obtains feasible eigenvalue approximation to study the potential bifurcations. The shooting method is applied to verify the validity of the derived approximation and corresponding computation results. In addition to the known bifurcation scenarios of saddle-node and period-doubling, novel Neimark-Sacker bifurcation and related co-dimension two bifurcation points of near-grazing period-one impact motion are also found to arise near the degenerate grazing point in a three-degree-of-freedom impact oscillator. For the in-depth understanding of near-grazing dynamics, the obtained results are compared with the reported results in the single- and two-degree-of-freedom impact oscillators.
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