Journal of Jilin University(Engineering and Technology Edition) ›› 2024, Vol. 54 ›› Issue (4): 902-916.doi: 10.13229/j.cnki.jdxbgxb.20221637

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Periodic motion transition characteristics of a vibro-impact system with multiple impact constraints

Shi-jun WANG1,2(),Guan-wei LUO2   

  1. 1.School of Mechatronic Engineering，Lanzhou Jiaotong University，Lanzhou 730070，China
    2.Key Laboratory of System Dynamics and Reliability of Rail Transport Equipment of Gansu Province，Lanzhou 730070，China
  • Received:2022-12-29 Online:2024-04-01 Published:2024-05-17

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Abstract:

A type of two-degree-of-freedom forced vibro-impact system with rigid and elastic compound constraints was studied. Based on the numerical calculation method of two-parameter co-simulation， the mode types and existence regions of the periodic motions of the system were obtained on the parameter plane composed of the key parameters excitation force frequency and the gap value between two masses. The transition laws between impactless motion and adjacent fundamental period motion and between adjacent fundamental period motions were revealed. The effect of the change of the elastic constraint stiffness on the types of mode and the region of existence of the periodic motions of the system was analyzed. The results show that there are two main types of transition regions， including tongue-like regions and hysteresis regions， between impactless motion and adjacent fundamental period motion and between adjacent fundamental periodic motions. There are regular subharmonic motions in the tongue-like regions. These subharmonic motions and the adjacent fundamental period motions form a hysteresis region group near the boundary lines of the tongue-like regions. Increasing the stiffness value at the elastic constraint will significantly increase the existence regions of quasi-periodic motions and chaotic motions in the low frequency domain in the two-parameter plane， and divide the existence regions of periodic motions.

Key words: mechanical design, compound constraints, vibro-impact, co-simulation, hysteresis region group, bifurcation

CLC Number: 

  • O322

Fig.1

Mechanical model of a two-degree-of-freedomforced vibration system"

Fig.2

Schematic diagram of two-parameterco-simulation"

Fig.3

Pattern types and distribution regions of periodic motions of the system in the （ω，δ）-parameter plane associated with each constraint"

Fig.4

Global one-parameter bifurcation diagrams of the system at δ = 0.2"

Fig.5

Phase plane portraits of system periodic motion，δ=0.2，ω=1.2"

Fig.6

Time response diagram of displacement，δ=0.2，ω=0.25"

Fig.7

One-parameter bifurcation diagrams， δ = 1.0"

Fig.8

Phase plane portraits，δ=1.0，ω=1.7"

Fig.9

Partial description of Fig.4（b）"

Fig.10

One-parameter bifurcation diagrams for transversely traversing hysteretic region groups"

Fig.11

One-parameter bifurcation diagrams，δ=1.3"

Fig.12

Phase plane portraits"

Fig.13

Pattern types and distribution regions of periodic motions of system in （ω，δ）-parameter plane associated with constraint A12"

Fig.14

One-parameter bifurcation diagrams for transversely traversing hysteretic regions"

Fig.15

Phase plane portraits"

Fig.16

Phase plane portraits"

Fig.17

Pattern types and distribution regions of periodic motions of the system in （ω，δ）-parameter plane withdifferent constraint stiffness ratios μk0"

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