An impact oscillator with a grazing cycle

AKHMET M., Kivilcim A.

Discontinuity, Nonlinearity, and Complexity, vol.6, no.2, pp.105-111, 2017 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.5890/dnc.2017.06.001
  • Journal Name: Discontinuity, Nonlinearity, and Complexity
  • Journal Indexes: Scopus
  • Page Numbers: pp.105-111
  • Keywords: Asymptotic stability, Grazing periodic solution, Grazing point, Linearization at a grazing point, Variable coefficient of restitution
  • Middle East Technical University Affiliated: Yes


© 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.