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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Mitigating Grazing Bifurcation and Vibro-Impact Instability in Time-Frequency Domain

Journal of Applied Nonlinear Dynamics 5(2) (2016) 169--184 | DOI:10.5890/JAND.2016.06.004

Chi-Wei Kuo; C. Steve Suh

Nonlinear Engineering and Control Lab, Mechanical Engineering Department, Texas A&M University College Station, Texas 77843-3123, U.S.A.

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Abstract

Impact oscillators are found in many applications. It is common for these applications to undergo the inadvertent state of grazing bifurcation. Vibro-impact incited grazing and route-to-chaos are difficult to control. The Newtonian model of a vibro-impact system rich of complex nonlinear behaviors is considered for the mitigation of impact induced instability and grazing. A novel concept capable of simultaneous control of vibration amplitude in the time-domain and spectral response in the frequency-domain is adopted to formulate a viable control solution. The concept has been demonstrated to be feasible for the control of dynamic instability including bifurcation and route-to-chaos in many nonlinear systems. The developed controller explores wavelet adaptive filters and filtered-x least mean square algorithm to the successful moderation of the grazing and dynamic instability of the non-smooth system. The qualitative behavior of the controlled impact oscillator follows a definitive fractal topology before settling into a stable manifold. The controlled response is categorically quasi-periodic and of the prescribed vibration amplitude and frequency spectrum.

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