Analytical determination of bifurcations of periodic solution in three-degree-of-freedom vibro-impact systems with clearance

作者：Liu, Yongbao; Wang, Qiang; Xu, Huidong^*

来源：Chaos Solitons & Fractals, 2017, 99: 141-154.

DOI：10.1016/j.chaos.2017.04.002

• Vibro-impact system
• Explicit critical criteria
• Co-dimension-one and Co-dimension-two
• smooth bifurcations
• Grazing bifurcation

The smooth bifurcation and non-smooth grazing bifurcation of periodic solution of three-degree-of freedom vibro-impact systems with clearance are studied in this paper. Firstly, six-dimensional Poincare maps are established through choosing suitable Poincare section and solving periodic solutions of vibro-impact system. Then, as the analytic expressions of all eigenvalues of Jacobi matrix of six-dimensional map are unavailable, the numerical calculations to search for the critical bifurcation values point by point is a laborious job based on the classical critical criterion described by the properties of eigenvalues. To overcome the difficulty from the classical bifurcation criteria, the explicit critical criterion without using eigenvalues calculation of high-dimensional map is applied to determine bifurcation points of Co-dimension-one bifurcations and Co-dimension-two bifurcations, and then local dynamical behaviors of these bifurcations are further analyzed. Finally, the existence of the grazing periodic solution of the vibro-impact system and grazing bifurcation point are analyzed, the discontinuous grazing bifurcation behavior is studied based on the compound normal form map near the grazing point, the discontinuous jumping phenomenon and the co-existing multiple solutions near the grazing bifurcation point are revealed.

• 出版日期2017-6
• 单位中国人民解放军海军工程大学; 太原理工大学