Two-parameter bifurcation analysis for an impact progressive vibration system

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (7) : 50-56.

L Xiaohong1,2, LUO Guanwei2

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Abstract

The mechanical model of an impact progressive vibration system was established. Impact types between a vibration exciter and a cushion,and progressive motion conditions of a slider were analyzed. Judgment conditions and dynamic equations for 4 possible motion states of the system were derived. Based on bifurcation analysis in a 2-D parametric plane,periodic vibration types of the system were obtained at all points in the parametric plane of (ω,l). The bifurcation characteristics of the fundamental impact motions of 1/1 and 2/1 were analyzed in detail. The relations among system parameters,impact velocity and slider’s progressive motion rate were studied. It was shown that the fundamental impact motion of 1/1 produces the periodic vibration of 2/2 through period-doubling bifurcation,and it produces the fundamental impact motion of 2/1 through virtual erasure bifurcation or multi-slip one; the fundamental impact motion of 2/1 produces the fundamental impact motion of 3/1 through real erasure bifurcation,virtual erasure one or multi-slip one; due to virtual erasure bifurcation of the fundamental impact motion of p/1(p=1,2),an intermediate transition region appears in the transition process from the fundamental impact motion of p/1 to the stable fundamental impact motion of (p+1)/1; the system exhibits a quasi-periodic motion and a periodic bubble phenomenon of the fundamental impact motion of 1/1 under certain parametric conditions.

Key words

non-smooth system / vibro-impact / progression / fundamental impact motion / bifurcation

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L Xiaohong1,2, LUO Guanwei2. Two-parameter bifurcation analysis for an impact progressive vibration system[J]. Journal of Vibration and Shock, 2019, 38(7): 50-56

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