Abstract and Applied Analysis

Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops

Qunhong Li, Limei Wei, Jieyan Tan, and Jiezhen Xi

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Abstract

The double grazing periodic motions and bifurcations are investigated for a two-degree-of-freedom vibroimpact system with symmetrical rigid stops in this paper. From the initial condition and periodicity, existence of the double grazing periodic motion of the system is discussed. Using the existence condition derived, a set of parameter values is found that generates a double grazing periodic motion in the considered system. By extending the discontinuity mapping of one constraint surface to that of two constraint surfaces, the Poincaré map of the vibroimpact system is constructed in the proximity of the grazing point of a double grazing periodic orbit, which has a more complex form than that of the single grazing periodic orbit. The grazing bifurcation of the system is analyzed through the Poincaré map with clearance as a bifurcation parameter. Numerical simulations show that there is a continuous transition from the chaotic band to a period-1 periodic motion, which is confirmed by the numerical simulation of the original system.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 642589, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277080

Digital Object Identifier
doi:10.1155/2014/642589

Mathematical Reviews number (MathSciNet)
MR3228082

Zentralblatt MATH identifier
07022810

Citation

Li, Qunhong; Wei, Limei; Tan, Jieyan; Xi, Jiezhen. Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops. Abstr. Appl. Anal. 2014 (2014), Article ID 642589, 9 pages. doi:10.1155/2014/642589. https://projecteuclid.org/euclid.aaa/1412277080


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