非対称復元力を有する強制振動系の高分数調波振動の分岐現象とカオス : 第2報,1次共振点以上における周期解のfamilyと内部カタストロフィ

概要

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In this paper, a nonlinear oscillator derived from the gear meshing vibration is investigated, which exhibits successive different bifurcations ending in chaos above the first resonance. These bifurcations are examined in detail using bifurcation diagrams, Lyapunov exponents, winding numbers, invariant curves, and Poincare maps. In the bifurcation diagram, periodic subharmonic oscillations appearing nonsuccessively as a "window" belong to the same "families", which are divided into two kinds : type- I , in which fold bifurcation occurs iteratively (multifolding) in the family, and type- II , in which fold bifurcation occurs only at both ends of the family. Depending on whether both of the chaotic attractors before/after the bifurcation exist in the same area on the phase plane or not, the chaotic attractor bifurcates discontinuously according to "hysteresis" or "interior catastrophe". In the case that a 2^n-band attractor transforms into a 2^<n-1>-band attractor without fold bifurcated directly unstable fixed points, and a periodic directly unstable fixed point exists very close to an inset of a 2^<n-1>-periodic inversely unstable fixed point, the unstable 2^<n-1>-band attractor is suddenly transformed into a one-band attractor upon touching an inset of the periodic directly unstable fixed point.
一般社団法人日本機械学会の論文
1995-03-25