Study on a Class of Piecewise Nonlinear Systems with Fractional Delay
In this paper, a dynamic model of piecewise nonlinear system with fractional-order time delay is simplified. The amplitude frequency response equation of the dynamic model of piecewise nonlinear system with fractional-order time delay under periodic excitation is obtained by using the average method...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2021/3411390 |
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| _version_ | 1832560658873319424 |
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| author | Meiqi Wang Wenli Ma Enli Chen Yujian Chang |
| author_facet | Meiqi Wang Wenli Ma Enli Chen Yujian Chang |
| author_sort | Meiqi Wang |
| collection | DOAJ |
| description | In this paper, a dynamic model of piecewise nonlinear system with fractional-order time delay is simplified. The amplitude frequency response equation of the dynamic model of piecewise nonlinear system with fractional-order time delay under periodic excitation is obtained by using the average method. It is found that the amplitude of the system changes when the external excitation frequency changes. At the same time, the amplitude frequency response characteristics of the system under different time delay parameters, different fractional-order parameters, and coefficient are studied. By analyzing the amplitude frequency response characteristics, the influence of time delay and fractional-order parameters on the stability of the system is analyzed in this paper, and the bifurcation equations of the system are studied by using the theory of continuity. The transition sets under different piecewise states and the constrained bifurcation behaviors under the corresponding unfolding parameters are obtained. The variation of the bifurcation topology of the system with the change of system parameters is given. |
| format | Article |
| id | doaj-art-3d52a9638d654ac4a211dfbcca85020d |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-3d52a9638d654ac4a211dfbcca85020d2025-02-03T01:27:00ZengWileyShock and Vibration1070-96221875-92032021-01-01202110.1155/2021/34113903411390Study on a Class of Piecewise Nonlinear Systems with Fractional DelayMeiqi Wang0Wenli Ma1Enli Chen2Yujian Chang3State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaState Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaState Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaState Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaIn this paper, a dynamic model of piecewise nonlinear system with fractional-order time delay is simplified. The amplitude frequency response equation of the dynamic model of piecewise nonlinear system with fractional-order time delay under periodic excitation is obtained by using the average method. It is found that the amplitude of the system changes when the external excitation frequency changes. At the same time, the amplitude frequency response characteristics of the system under different time delay parameters, different fractional-order parameters, and coefficient are studied. By analyzing the amplitude frequency response characteristics, the influence of time delay and fractional-order parameters on the stability of the system is analyzed in this paper, and the bifurcation equations of the system are studied by using the theory of continuity. The transition sets under different piecewise states and the constrained bifurcation behaviors under the corresponding unfolding parameters are obtained. The variation of the bifurcation topology of the system with the change of system parameters is given.http://dx.doi.org/10.1155/2021/3411390 |
| spellingShingle | Meiqi Wang Wenli Ma Enli Chen Yujian Chang Study on a Class of Piecewise Nonlinear Systems with Fractional Delay Shock and Vibration |
| title | Study on a Class of Piecewise Nonlinear Systems with Fractional Delay |
| title_full | Study on a Class of Piecewise Nonlinear Systems with Fractional Delay |
| title_fullStr | Study on a Class of Piecewise Nonlinear Systems with Fractional Delay |
| title_full_unstemmed | Study on a Class of Piecewise Nonlinear Systems with Fractional Delay |
| title_short | Study on a Class of Piecewise Nonlinear Systems with Fractional Delay |
| title_sort | study on a class of piecewise nonlinear systems with fractional delay |
| url | http://dx.doi.org/10.1155/2021/3411390 |
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