The complicated bifurcation of an archetypal self-excited SD oscillator with dry friction

作者：Li, Zhixin; Cao, Qingjie^*; Leger, Alain

来源：Nonlinear Dynamics, 2017, 89(1): 91-106.

DOI：10.1007/s11071-017-3438-9

• Self-excited SD oscillator
• Stick-slip limit cycle
• Tangent point
• Hopf bifurcation
• Grazing bifurcation

In this paper, we investigate the local and global bifurcation behaviors of an archetypal self-excited smooth and discontinuous oscillator driven by moving belt friction. The belt friction is described in the sense of Stribeck characteristic to formulate the mathematical model of the proposed system. For such a friction characteristic, the complicated bifurcation behaviors of the system are discussed. The bifurcation of the multiple sliding segments for this self-excited system is exhibited by analytically exploring the collision of tangent points. The Hopf bifurcation of this self-excited system with viscous damping is analyzed by making the examination of the eigenvalues at the steady state and discussing the stability of the limit cycles. The bifurcation diagrams and the corresponding phase portraits are depicted to demonstrate the complicated dynamical behaviors of double tangency bifurcation, the bifurcation of sliding homoclinic orbit to a saddle, subcritical Hopf bifurcation and grazing bifurcation for this system.

• 出版日期2017-7
• 单位哈尔滨工业大学