Analytical Threshold for Chaos of Piecewise Duffing Oscillator with Time-Delayed Displacement Feedback

In this paper, the bifurcation and chaotic motion of a piecewise Duffing oscillator with delayed displacement feedback under harmonic excitation are studied. Based on the Melnikov method, the necessary critical conditions for the chaotic motion in the system are obtained, and the chaos threshold cur...

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Main Authors: Zhang Ming-Xin, Wang Jun, Shen Yong-Jun, Zhang Jian-Chao
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Shock and Vibration
Online Access:http://dx.doi.org/10.1155/2022/9108004
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author Zhang Ming-Xin
Wang Jun
Shen Yong-Jun
Zhang Jian-Chao
author_facet Zhang Ming-Xin
Wang Jun
Shen Yong-Jun
Zhang Jian-Chao
author_sort Zhang Ming-Xin
collection DOAJ
description In this paper, the bifurcation and chaotic motion of a piecewise Duffing oscillator with delayed displacement feedback under harmonic excitation are studied. Based on the Melnikov method, the necessary critical conditions for the chaotic motion in the system are obtained, and the chaos threshold curve is obtained by calculation and numerical simulation. The accuracy of the analytical result is proved by some typical numerical simulation results, including the local bifurcation diagrams, phase portraits, Poincaré maps, and the largest Lyapunov exponents. The effects of excitation frequency and time delay of the displacement feedback are analytically discussed. It could be found that the critical excitation amplitude will increase obviously with the increase of the excitation frequency, and under the selection of certain parameters, the critical excitation amplitude takes the time delay of 0.58 as the inflection point, which decreases at first and then increases.
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institution Kabale University
issn 1875-9203
language English
publishDate 2022-01-01
publisher Wiley
record_format Article
series Shock and Vibration
spelling doaj-art-21b4ff4764dc4939a23298d8a12987992025-02-03T06:01:38ZengWileyShock and Vibration1875-92032022-01-01202210.1155/2022/9108004Analytical Threshold for Chaos of Piecewise Duffing Oscillator with Time-Delayed Displacement FeedbackZhang Ming-Xin0Wang Jun1Shen Yong-Jun2Zhang Jian-Chao3State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering StructuresState Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering StructuresState Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering StructuresState Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering StructuresIn this paper, the bifurcation and chaotic motion of a piecewise Duffing oscillator with delayed displacement feedback under harmonic excitation are studied. Based on the Melnikov method, the necessary critical conditions for the chaotic motion in the system are obtained, and the chaos threshold curve is obtained by calculation and numerical simulation. The accuracy of the analytical result is proved by some typical numerical simulation results, including the local bifurcation diagrams, phase portraits, Poincaré maps, and the largest Lyapunov exponents. The effects of excitation frequency and time delay of the displacement feedback are analytically discussed. It could be found that the critical excitation amplitude will increase obviously with the increase of the excitation frequency, and under the selection of certain parameters, the critical excitation amplitude takes the time delay of 0.58 as the inflection point, which decreases at first and then increases.http://dx.doi.org/10.1155/2022/9108004
spellingShingle Zhang Ming-Xin
Wang Jun
Shen Yong-Jun
Zhang Jian-Chao
Analytical Threshold for Chaos of Piecewise Duffing Oscillator with Time-Delayed Displacement Feedback
Shock and Vibration
title Analytical Threshold for Chaos of Piecewise Duffing Oscillator with Time-Delayed Displacement Feedback
title_full Analytical Threshold for Chaos of Piecewise Duffing Oscillator with Time-Delayed Displacement Feedback
title_fullStr Analytical Threshold for Chaos of Piecewise Duffing Oscillator with Time-Delayed Displacement Feedback
title_full_unstemmed Analytical Threshold for Chaos of Piecewise Duffing Oscillator with Time-Delayed Displacement Feedback
title_short Analytical Threshold for Chaos of Piecewise Duffing Oscillator with Time-Delayed Displacement Feedback
title_sort analytical threshold for chaos of piecewise duffing oscillator with time delayed displacement feedback
url http://dx.doi.org/10.1155/2022/9108004
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AT wangjun analyticalthresholdforchaosofpiecewiseduffingoscillatorwithtimedelayeddisplacementfeedback
AT shenyongjun analyticalthresholdforchaosofpiecewiseduffingoscillatorwithtimedelayeddisplacementfeedback
AT zhangjianchao analyticalthresholdforchaosofpiecewiseduffingoscillatorwithtimedelayeddisplacementfeedback