Dynamic analysis of a self-excited hysteretic system
Author(s)
Author(s)
Ding, Q.
Cooper, J. E.
Date Issued
2001
Publisher
Elsevier
Journal
Journal of Sound and Vibration
Volume
245
Issue
1
Start page
151
End page
164
Abstract
The dynamic behaviour of a self-excited system with hysteretic non-linearity is investigated in this paper. The averaging method is applied to the autonomous system and the resulting bifurcation equation of the self-excited response is analyzed using the singularity theory. The study of the bifurcation diagrams reveals the multivalued and jumping phenomena due to the effect of the hysteretic non-linearity. Secondly, the steady state response of the averaged system of the non-autonomous oscillator in primary resonance is investigated. Due to the effect of the hysteretic non-linearity, the system exhibits softening spring behaviour. A stability analysis shows that the steady state periodic response exists over a limited excitation frequency range. It loses its stability outside the frequency range through Hopf bifurcation and then the system undergoes quasi-periodic motion. Finally, by using circle maps to get winding numbers, various orders of super- and subharmonic resonance and mode-locking are investigated. The mode-locking, alternating with the quasi-periodic responses, takes place according to the Farey number tree as revealed in many other systems. The increase of the hystereticity can improve the stability of subharmonic resonance.
SFU Affiliated Publication
No
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