An impact oscillator with a grazing cycle

Date

2017-01-01

Author

Akhmet, Marat
Kivilcim, A.

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© 2017 L&H Scientific Publishing, LLC.An oscillator which impacts against a rigid barrier is taken into account. A cycle with zero impact velocity is discussed. The main result of this article concerns stability of the grazing cycle. A significant attention to a model with the variable coefficient of restitution depending on velocity is paid. The mechanical reasons for that are provided as well as new theo- retical advantages have been discovered for the investigation of dynamics near a grazing cycle. The W-map which reduces the system with variable moments of impacts to that with fixed moments and simplifies the analy- sis, is defined. A new type of linearization system with two compounds is applied to investigate the stability of the grazing cycle whose existence is easily examined. A new approach to suppress a singularity, caused by the tangency, in linearization has been developed. Simulations are provided to visualize the stability of the grazing cycle.

Subject Keywords

Asymptotic stability, Grazing periodic solution, Grazing point, Linearization at a grazing point, Variable coefficient of restitution

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85020833172&origin=inward
https://hdl.handle.net/11511/99282

Journal

Discontinuity, Nonlinearity, and Complexity

DOI

https://doi.org/10.5890/dnc.2017.06.001

Collections

Department of Mathematics, Article

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Citation Formats

M. Akhmet and A. Kivilcim, “An impact oscillator with a grazing cycle,” Discontinuity, Nonlinearity, and Complexity, vol. 6, no. 2, pp. 105–111, 2017, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85020833172&origin=inward.