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: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2022/9108004 |
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| _version_ | 1832551381493350400 |
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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. |
| format | Article |
| id | doaj-art-21b4ff4764dc4939a23298d8a1298799 |
| 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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