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Suppression of grazing-induced instability in single degree-of-freedom impact oscillators

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Abstract

As a typical non-smooth bifurcation, grazing bifurcation can induce instability of elementary near-grazing impact periodic motion in impact oscillators. In this paper, the stability for near-grazing period-one impact motion to suppress grazing-induced instabilities is analyzed, based on which, a control strategy is proposed. The commonly-used leading order zero time discontinuity mapping is extended to a higher order one to aid the perturbation analysis of the characteristic equation. It is shown that the degenerate grazing bifurcation can eliminate the singular term in the characteristic equation, leading to bounded eigenvalues. Based on such a precondition, the bounded eigenvalues are further restricted inside the unit circle, and a continuous transition between non-impact and controlled impact motion is observed. One discrete feedback controller that changes the velocity of the oscillator based on the selected Poincaré sections is adopted to demonstrate the control procedure.

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Author information

Authors and Affiliations

  1. School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou, 510006, China

    Shan Yin & Guilin Wen

  2. State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082, China

    Shan Yin & Guilin Wen

  3. School of Mechanical Engineering, Hunan Institute of Engineering, Xiangtan, 411104, Hunan Province, China

    Xin Wu

Authors
  1. Shan Yin
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  2. Guilin Wen
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  3. Xin Wu
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Correspondence to Guilin Wen.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11672104 and 11832009) and the Natural Science Foundation of Hunan Province of China (Nos.XJT2015408 and 2016JJ4027)

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Yin, S., Wen, G. & Wu, X. Suppression of grazing-induced instability in single degree-of-freedom impact oscillators. Appl. Math. Mech.-Engl. Ed. 40, 97–110 (2019). https://doi.org/10.1007/s10483-019-2403-6

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  • DOI: https://doi.org/10.1007/s10483-019-2403-6

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