Abstract
Impact oscillators demonstrate interesting dynamical features. In particular, new types of bifurcations take place as such systems evolve from a nonimpacting to an impacting state (or vice versa), as a system parameter varies smoothly. These bifurcations are called grazing bifurcations. In this paper we analyze the different types of grazing bifurcations that can occur in a simple sinusoidally forced oscillator system in the presence of friction and a hard wall with which the impacts take place. The general picture we obtain exemplifies universal features that are predicted to occur in a wide variety of impact oscillator systems.
Highlights
INTRODUCfiONWe say that a system is an impact oscillator if it has an oscillating object that impacts frequently with some other object [1,2)
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In this paper we analyze the different types of grazing bifurcations that can occur in a simple sinusoidally forced oscillator system in the presence of friction and a hard wall with which the impacts take place
Summary
We say that a system is an impact oscillator if it has an oscillating object that impacts frequently with some other object [1,2). Systems with ( ,a) in region I have grazing bifurcations from a period-1 attractor to a reversed infinite period adding cascade (case I). The analysis results in the division of (r, a) space into regions corresponding to the different types of grazing bifurcations in the system as explained above, as well as a scaling law for widths of the windows with high periods.
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