A Simple Discussion for Undamped Duffing Impact Oscillator

Most vibro-impact oscillators in engineering applications appear to include nonlinear stiffness or damping, but little attention has been paid to this kind of oscillator. Thus, in present paper, a physical model for an undamped and periodically forced Duffing oscillator with a constraint which leads to motions impacts was analyzed. Computational method was used to solve the nonlinear governing equations. Rich dynamical behaviors including periodic motion, chaotic motion, chattering and grazing were observed in this simple system. Influence of non-dimensional system parameters including the nonlinear stiffness coefficient β, the forced frequency Ω, the clearance Δ on motion character of the system were also discussed through corresponding bifurcation diagrams. It is supposed that: (a) chattering appears when Δ less than certain threshold. (b) chaotic motion arises when β larger than certain threshold. (c) grazing bifurcation occurs when r larger than certain threshold.