Sticking motions of impact oscillators

Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator

“…We have shown numerical simulations of typical sticking solutions, and a rising event which occurs as the forcing frequency parameter is varied. From these numerical simulations we have observed similar results to [14] regarding the significant reduction in sticking time as a rising bifurcation occurs. In fact we have shown how the sticking time first separates into two distinct parts, one of which rapidly reduces to zero as the system parameter is increased.…”

“…The multi-sliding bifurcation can also be related to the rising phenomena observed in vibro-impact systems -a connection which was first reported by [20]. In this paper, we examine the rising phenomena found in a two-degree of freedom vibroimpact system as a system parameter is varied, and find similar results to [14] regarding the drop in sticking time. We demonstrate using numerical simulations that rising and multi-sliding are qualitatively equivalent bifurcations events by observing that the sticking solutions become tangent to the boundary of the sticking region at a rising eventanalogous to results for sliding orbits shown by [18].…”

“…Studies of chatter and sticking have been carried out for both single degree of freedom impact oscillators in [12] and for two degree of freedom systems by [13]. The behaviour of periodic sticking motions in both single and multi degree of freedom systems is considered by Toulemonde and Gontier [14], and the authors make reference to the "rising bifurcation" which they demonstrate occurs for a two degree of freedom system. It is this so called rising behaviour which forms the focus for the current study.…”

Multiple Non-Smooth Events in Multi-Degree-of-Freedom Vibro-Impact Systems

“…The behaviour of periodic sticking motions in both single and multi-degree-of-freedom systems has also been studied [19]. The sticking phenomena observed here is analogous to the sliding in other systems [20], as discussed in [21].…”

Dynamics of a Two Degree of Freedom Vibro-Impact System With Multiple Motion Limiting Constraints

“…The behavior of periodic sticking motions in both single and multi degree of freedom systems is considered by Toulemonde & Gontier [1998]. In addition the sticking phenomena discussed here have similar properties to the sliding orbits in relay feedback systems described by Di Benardo et al [2001].…”