A numerical study of an impact oscillator with the addition of dry friction

This paper presents an investigation into the non-linear behavior of an impact oscillator with the addition of dry friction. The equations that govern the relative motion of the impact oscillator, including the effects of dry friction, are formulated, resulting in a non-conservative, piecewise linear, ordinary differential equation of motion. The system is excited by a single component sinusoidal base motion. A computer model is used to numerically simulate the motion of the system, and to identify periodic solutions and the stability of these solutions. Trends of the periodic solutions are then interpreted using bifurcation theory to identify the non-linear behavior of this system as a function of both the excitation amplitude and the excitation frequency for two levels of the dry friction force. These results illustrate a rich behavior that includes turning point bifurcations, symmetry breaking pitchfork bifurcations, period-doubling bifurcation cascades and bifurcations that can be characterized as boundary grazing. The results also include the existence of a subharmonic resonance motion that encompasses three periods of the forcing during each period of the solution. Also presented are samples of time histories and phase portraits, and a plot of the stable response regions for clamping force as a function of excitation amplitude. (C) 1995 Academic Press Limited