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Suppressing Homoclinic Chaos for Vibro-Impact Oscillators

Shuangbao Li

https://orcid.org/0000-0002-4947-6435

Research Institute of Science and Technology, Civil Aviation University of China, Tianjin 300300, P. R. China

E-mail Address: shuangbaoli@yeah.net

Corresponding author.

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Jinzhuo Chen

College of Science, Civil Aviation University of China, Tianjin 300300, P. R. China

E-mail Address: jinzhuochen00@163.com

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, and

Liying Kou

College of Science, Civil Aviation University of China, Tianjin 300300, P. R. China

E-mail Address: liykou@163.com

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https://doi.org/10.1142/S0218127422502273Cited by:2 (Source: Crossref)

Abstract

In this paper, theoretical framework and numerical verification for suppressing homoclinic chaos of a class of vibro-impact oscillators are discussed by adding parametric excitations in the form of $x f cos (ω τ + φ)$ $x f cos (ω τ + φ)$ as the control item. The analytical Melnikov method for planar vibro-impact systems is employed to obtain the corresponding thresholds of parameters as sufficient conditions for suppressing chaos. Two typical oscillators are presented to show the effectiveness of theoretical analysis for suppressing homoclinic chaos by tuning the amplitudes, frequencies and phases of the parametric excitations.

Keywords:

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