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Symmetry 2019, 11(1), 4; https://doi.org/10.3390/sym11010004

Stochastic Bifurcation of a Strongly Non-Linear Vibro-Impact System with Coulomb Friction under Real Noise

1
Department of Applied Mathematics, Northwestern Polytechnic University, Xi’an 710072, China
2
School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
*
Author to whom correspondence should be addressed.
Received: 18 November 2018 / Revised: 11 December 2018 / Accepted: 20 December 2018 / Published: 21 December 2018
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Abstract

This manuscript investigated the response of a strongly non-linear vibro-impact (VI) system with Coulomb friction. The impact model is used with classical impact. The excitation is modelled by real noise. First, the VI system is converted into a simplified system without any barrier by non-smooth transformation (symmetric transformation). The stochastic averaging method is adopted to obtain the theoretical stationary probability function of the VI system. Next, the Duffing Van der Pol VI system with Coulomb friction is used to verify the validity of the proposed theoretical method compared with numerical simulations. Moreover, the influence of bandwidth, noise intensity, and friction amplitude are further analyzed in detail on the probability density function (PDF) of distribution of the VI system. The P-bifurcation is studied by a qualitative change of friction amplitude and restitution coefficient on the stationary probability distribution, which indicated that these parameters can arouse the emergence of stochastic P-bifurcation. View Full-Text
Keywords: vibro-impact system; Coulomb friction; stochastic response; stochastic P-bifurcation vibro-impact system; Coulomb friction; stochastic response; stochastic P-bifurcation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Liu, L.; Xu, W.; Yue, X.; Huang, D. Stochastic Bifurcation of a Strongly Non-Linear Vibro-Impact System with Coulomb Friction under Real Noise. Symmetry 2019, 11, 4.

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