Bifurcations in impact systems

“…Following the notation of Wagg and Bishop [17], we distinguish different periodic impacting motions by denoting the motion with p impacts occurring in q forcing periods of π/ω as P( p, q). A similar classification was used by Ivanov [18] and Peterka [19]. A period-q motion corresponds to q fixed points in Figure 6(a), which shows the difference between the maximum and minimum displacements x 2 of mass m 2 sampled per period of forcing.…”

Section: Bifurcation Schemesmentioning

confidence: 95%

Nonlinear Dynamics of an Electrically Driven Impact Microactuator

2005

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We study the dynamics of an electrostatically driven impact microactuator. Impact between moving elements of the microactuator is modeled using the coefficient of restitution. Friction between the microactuator and its supporting substrate is modeled using the Amonton-Coulomb law. We consider the bifurcations under changes in the driving voltage and frequency. Grazing bifurcations introduce discontinuous transitions between different motions. It is also found that impacts dramatically change the characteristics of the frequency-response curve. Finally, we discuss the evolution of incomplete chatter to complete chatter, that is, sticking.

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“…Pavlovskaia and Wiercigroch 11 presented a semi-analytical method which could be developed to compute periodic solutions for a new model of an impact oscillator with a drift. A linear oscillator with one or two stops and rigid block under periodic excitation was considered, 12 and the stability condition and bifurcation mechanism were investigated. A sinusoidally driven oscillator with linear stiffness and impacts at rigid stops was studied by S Foale, 13 and the analytical results revealed the transition mechanism of grazing bifurcation and codimension-two bifurcation.…”

Section: Dimentberg and Iourtchenkomentioning

confidence: 99%

Dynamical analysis of a single degree-of-freedom impact oscillator with impulse excitation

Wang

Shen

Yang

2017

Advances in Mechanical Engineering

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In this article, the dynamical behavior of a single degree-of-freedom impact oscillator with impulse excitation is studied, where the mass impacts at one stop and is shocked with impulse excitation at the other stop. The existing and stability conditions for periodic motion of the oscillator are established. The effects of system parameters on dynamical response are discussed under different initial velocities. It is found that smaller shock gap than impact gap could make the periodic motion more stable. The decrease in natural frequency would consume less impact energy, make the vibration frequency smaller, and reduce the vibration efficiency. Finally, the dynamical properties are further analyzed under a special case, that is, the shock gap approaches zero. It could be seen that the larger shock coefficient and impact restitution coefficient would make vibration period smaller. Based on the stability condition, there are an upper limit for the product of shock coefficient and impact restitution coefficient, so that a lower limit of corresponding vibration period exists.

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Bifurcations in impact systems

Cited by 75 publications

References 17 publications

Periodic Motions and Global Bifurcations of a Two-Degree-of-Freedom System With Plastic Vibro-Impact

Periodic Motions and Global Bifurcations of a Two-Degree-of-Freedom System With Plastic Vibro-Impact

Nonlinear Dynamics of an Electrically Driven Impact Microactuator

Dynamical analysis of a single degree-of-freedom impact oscillator with impulse excitation

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