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

Wagg, DJ

doi:10.1016/j.chaos.2004.03.003

Cited by 61 publications

(29 citation statements)

References 21 publications

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“…The behavior of chatter, sticking and chaotic impacting motion in a two degree of freedom system has been studied by Wagg and Bishop in [19]. Wagg described rising phenomena and periodic sticking motion in [20,21], respectively. Sticking motions of a two degree of freedom system with multiple motion limiting constrains were considered in [22].…”

Section: Introductionmentioning

confidence: 98%

Impulsive control of sticking motion in van der Pol one-sided constraint system

Wang

et al. 2014

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 98%

Impulsive control of sticking motion in van der Pol one-sided constraint system

Wang

et al. 2014

Applied Mathematics and Computation

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“…[39][40][41][42][43][44][45][46][47][48]. Wagg [42,43] studied rising phenomena and multiple non-smooth events of impacting chatter with stick in multi-degree-of-freedom vibro-impact systems. Souza and Caldas [44] numerically investigated the basins of attraction of coexisting periodic and chaotic attractors in a gear-rattling impact model.…”

Section: Introductionmentioning

confidence: 99%

Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

et al. 2014

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A two-degree-of-freedom periodically forced system with a clearance is considered. The correlative relationship and matching law between dynamics and system parameters are analyzed by the co-simulation analysis of multi-parameter and multiperformance. Key parameters of the system, such as the exciting frequency, clearance value and constraint stiffness, are emphasized to analyze the influence of the main factors on its soft impact characteristics and reveal diversity, evolution and distribution regions of periodic-impact motions. The quantity of the fundamental group of p/1 impact motions, which have the excitation period and differ by the number p of impacts, is basically determined by the constraint stiffness. A series of grazing bifurcations occur with decreasing the exciting frequency so that the number p of impacts of the fundamental group of motions correspondingly increases one by one. As the constraint stiffness is very large, the impact number p of the fundamental group of motions becomes also big enough in low exciting frequency range. Consequently, the system possibly exhibits chattering-impact characteristics and the relative impact velocities successively attenuate in an excitation period. There exist a series of singular points between any two adjacent ones of the fundamental group of motions as the damping ratio or the damping constant of the viscous dashpot connecting two masses is very small, i.e., real-grazing and baregrazing bifurcation boundaries of one of them, saddlenode and period-doubling bifurcation boundaries of the other mutually cross themselves at the point of intersection and create two types of transition regions: hysteresis and tongue-shaped regions. A series of zones of regular and complex subharmonic impact motions are found to dominate in the tongue-shaped regions. The dimensionless parameters have been designed technically, under which large mass ratio or small supporting stiffness ratio leads to diversity and complexity of periodic-impact motions of the system. Based on the sampling ranges of parameters, the influence of system parameters on relative impact velocities, existence regions and correlative distribution of different types of periodic-impact motions of the system is emphatically studied.

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“…The occurrence of the multi-sliding bifurcation in vibro-impact systems was first highlighted by [19] (referred to as a rising bifurcation) and has been studied for two degree-of-freedom systems by [21]. Multi-sliding occurs when a sliding orbit in the region S becomes tangent (in a similar way to grazing) to the exit boundary ∂S as a system parameter is varied.…”

Section: Multiple Nonsmooth Eventsmentioning

confidence: 99%

“…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]. In this paper we consider the same two degree-of-freedom example studied in [1], but examine the multi-dimensional nonsmooth events which can occur in the chatter and sticking region.…”

Section: Introductionmentioning

confidence: 99%

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

Wagg

2006

Nonlinear Dyn

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Abstract.The behaviour of a multi-degree-of-freedom vibro-impact system is studied using a two degree-of-freedom impact oscillator as a motivating example. A multi-modal model is used to simulate the behaviour of the system, and examine the complex dynamics which occurs when both degrees of freedom are subjected to a motion limiting constraint. In particular the chattering and sticking behaviour which occurs for low forcing frequencies is discussed. In this region a variety of nonsmooth events can occur, including newly studied phenomena such as sliding bifurcations. In this paper the multiple nonsmooth events which can occur in the two degree-of-freedom system are categorised, and demonstrated using numerical simulations.

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

Cited by 61 publications

References 21 publications

Impulsive control of sticking motion in van der Pol one-sided constraint system

Impulsive control of sticking motion in van der Pol one-sided constraint system

Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

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

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