On motions and switchability in a periodically forced, discontinuous system with a parabolic boundary

Luo, Albert C. J.; Rapp, Brandon M.

doi:10.1016/j.nonrwa.2009.09.010

Cited by 11 publications

(3 citation statements)

References 17 publications

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“…(69) (iv) The necessary and sufficient conditions for grazing motion on the boundary x ≡ ( , ) ∈ Ω 23 in domain Ω 2 or domain Ω 3 at time are (2) …”

Section: Theorem 9 For the Friction-induced Oscillator With An Ellipmentioning

confidence: 99%

“…Luo and Rapp [1,2] investigated different periodic motions in a periodic force discontinuous system. The switching boundary in the aforementioned papers was supposed to be an inclined line or a parabolic curve and the friction force acting on the oscillator was not considered.…”

Section: Introductionmentioning

confidence: 99%

“…In 2009, Luo and Rapp [1] investigated the flow switchability and periodic motions in a periodically forced, discontinuous dynamical system with switching control law of an inclined line. In the next year, Luo and Rapp [2] studied the motions and switchability of an oscillator in a periodically forced, discontinuous system with switching control law of a parabolic boundary. In 2015, Zheng and Fu [53] proposed the switched Van der Pol equation with impulsive effect as switched system and analyzed its features from a discontinuous point of view.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of Discontinuous Dynamical Behaviors of a Friction-Induced Oscillator with an Elliptic Control Law

Fan

Liu

et al. 2018

Mathematical Problems in Engineering

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This paper develops the passability conditions of flow to the discontinuous boundary and the sticking or sliding and grazing conditions to the separation boundary in the discontinuous dynamical system of a friction-induced oscillator with an elliptic control law and the friction force acting on the mass through the analysis of the corresponding vector fields and -functions. The periodic motions of such a discontinuous system are predicted analytically through the mapping structure. Finally, the numerical simulations are given to illustrate the analytical results of motion for a better understanding of physics of motion in the mass-spring-damper oscillator.

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“…(69) (iv) The necessary and sufficient conditions for grazing motion on the boundary x ≡ ( , ) ∈ Ω 23 in domain Ω 2 or domain Ω 3 at time are (2) …”

Section: Theorem 9 For the Friction-induced Oscillator With An Ellipmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%