NON-SMOOTH BIFURCATION OF A PLASTIC IMPАCTING OSCILLATOR

Abstract

A single degree-of-freedom plastic impacting oscillator was considered under the conditions of grazing and codimension-1 bifurcations. Based on the two-and one-dimensional parameters bifurcation analysis、 the bifurcation characteristics of single-impact periodie motions was studied. The non-smooth bifurcations such as Crossing-sliding. Switching-sliding anc codimension-2 sliding bifurcations as well as the discontinuous bifureations such as grazing bifureation and uous boundary crisis were revealed. The non-sticking periodic motion and sticking periodic motion transit into each other via a crossing-sliding bifurcation. In the two-dimensional parameter region of the low frequency and small clearance, the periodic motions (1, 1, 1) and (1, 2, 1) are distributed alternately. The boundary between the two types of periodic motions is a switching-sliding bifurcation curve. The boundary crisis of chaos occurs leading the chaotic attractor and its basin to vanish.

Keywords

• Non-smooth system
• Plastic impact
• Sliding bifurcation
• Grazing bifurcation
• Boundary crisis