Journal of Jilin University(Engineering and Technology Edition) ›› 2023, Vol. 53 ›› Issue (2): 364-375.doi: 10.13229/j.cnki.jdxbgxb20220644

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Dynamic stability analysis of a amplitude⁃limited vibration system with multiple rigid constraints

Yan YANG1,2(),Yu-qing SHI1,2,Xiao-rong ZHANG2,Guan-wei LUO2   

  1. 1.School of Mechatronic Engineering，Lanzhou Jiaotong University，Lanzhou 730070，China
    2.Gansu Provincial Key Laboratory of System Dynamics and Reliability of Rail Transport Equipment，Lanzhou 730070，China
  • Received:2022-05-25 Online:2023-02-01 Published:2023-02-28

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Abstract:

The mechanical model of a two-degree-of-freedom amplitude-limited vibration system with multiple rigid constraints is established. Combined with the periodic and impact Poincaré mapping， the pattern types of periodic impact motions and their occurrence domains are identified in a two-parameter system. With the irreversible mutual transition of adjacent one-periodic impact motions， there are a series of singularities， hysteresis and tongue-shaped transition domains on the critical line of the distribution domains. Based on the sampling range of dynamic parameter， the dynamic response of the vibration system under extreme mass distribution conditions is analyzed. The simulation results show that the non-smooth bifurcation behaviors such as Grazing bifurcation and Sliding bifurcation leads to the one-periodic impact motion sequence transits to incomplete and complete chattering-impact motions. Excessive energy loss in instantaneous impact leads to sticking phenomenon， which changes the original structure of the vibration system and reduces the degree of freedom of the system. Due to the simultaneous action of complete chattering-impact at multiple rigid constraints， the transient static state appears in extreme control parameter domain.

Key words: mechanical design, amplitude-limited vibration, bifurcation, transition domain, chattering-impact

CLC Number: 

  • TH113.1

Fig.1

Limiting vibration system with multiple rigid constraints"

Fig.2

Modes and distribution domains of periodic-impact motions in the （ω，δ）parameter system"

Fig.3

Descriptions about transition domains between adjacent p/1 and （p+1）/1 period 1 motions"

Fig.4

One-parameter bifurcations of the tongue-shaped domain between adjacent 4/1 and 3/1 motions， δ=0.3"

Fig.5

Phase plane portraits and Poincaré mapping diagrams of mass blocks M1， δ=0.3"

Fig.6

Modes and distribution domains of periodic motions in the （ω，δ） parameter system when μm =0.05"

Fig.7

Chattering impact bifurcation at constraint A2A3， μm =0.05， ω=1.5"

Fig.8

Time trajectories of chattering impact motions， μm =0.05， ω=1.5"

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