Chaotic motion of a horizontal impact pair. (English) Zbl 1237.70028

Han, R. P. S.; Luo, A. C. J.; Deng, W.

J. Sound Vib. 181, No. 2, 231-250 (1995).

Summary: A theory for a system with discontinuities and applied to the impact analysis of a horizontal impact pair is presented. Mappings for four switch-planes are defined and from these several impact models are developed. As a case of special interest, the case of a steady state, periodic two-impacts/\(N\)-cycles motion is studied in greater detail. Numerical simulations of the various models are also given. The results show that the ensuing chaotic behavior can be eitherregularwith period-doubling bifurcation orrandomwith other types of bifurcation. The former refers to chaos, where its mathematical structure is regular, while the latter refers to one with a random mathematical structure.

MSC:

70F35	Collision of rigid or pseudo-rigid bodies
70K50	Bifurcations and instability for nonlinear problems in mechanics
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior