Numerical bifurcation analysis of an impact oscillator with drift

Mechanical systems with impacting components have received considerable attention in the past due to their wide engineering applications. In this work, we study numerically a physical model that accounts for viscoelastic impacts and is able to reproduce the effect of the vertical progression (drift) observed e.g. in drilling applications (Pavlovskaia et al. 2001). The model is comprised of a harmonically excited mass simulating the penetrating part of the system and a viscoelastic slider, which represents the soil resistance. During operation, the system can move downwards in stick-slip phases, resulting in complex dynamical behaviour, which includes fold, period-doubling and grazing bifurcation of periodic orbits, as well as chaotic motion. The present work extends the previous investigations undertaken by theCADRwithinAberdeen University (Pavlovskaia et al. 2001, Pavlovskaia and Wiercigroch 2007) to gain an insight into the bifurcation structure of the underlying system. Specifically, the system is analyzed numerically by means of the software TC-HAT, a toolbox of AUTO 97 allowing numerical continuation and bifurcation detection of periodic orbits in non-smooth dynamical systems.