Dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative
In this paper, the dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative is studied. First, a mathematical model of the single-degree-of-freedom system is established, and the approximate steady-state solution associated with the amplitude–freque...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2021-03-01
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| Series: | Journal of Low Frequency Noise, Vibration and Active Control |
| Online Access: | https://doi.org/10.1177/1461348419872372 |
| _version_ | 1818574287945072640 |
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| author | Jun Wang Yongjun Shen Shaopu Yang Yongjie Lu Xianghong Li Dawei Zuo |
| author_facet | Jun Wang Yongjun Shen Shaopu Yang Yongjie Lu Xianghong Li Dawei Zuo |
| author_sort | Jun Wang |
| collection | DOAJ |
| description | In this paper, the dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative is studied. First, a mathematical model of the single-degree-of-freedom system is established, and the approximate steady-state solution associated with the amplitude–frequency equation is obtained based on the averaging method. Then, the amplitude–frequency response equations are used for stability analysis, and the stability condition is founded. To validate the correctness and precision, the approximate solutions determined by the analytical method are compared with the solutions based on the numerical integration method. It is found that the approximate solutions and the numerical solutions are in excellent agreement. Finally, the effects of system parameters, such as fractional-order coefficient, order, clearance, and piecewise stiffness, on the complex dynamical behaviors of the piecewise linear single-degree-of-freedom oscillator are studied. The results show that the system parameters not only influence resonance amplitude and resonance frequency but also affect the size of the unstable region. |
| first_indexed | 2024-12-15T00:24:36Z |
| format | Article |
| id | doaj.art-26695c8eedf347d6971fe9c982496437 |
| institution | Directory Open Access Journal |
| issn | 1461-3484 2048-4046 |
| language | English |
| last_indexed | 2024-12-15T00:24:36Z |
| publishDate | 2021-03-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj.art-26695c8eedf347d6971fe9c9824964372022-12-21T22:42:11ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462021-03-014010.1177/1461348419872372Dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivativeJun WangYongjun ShenShaopu YangYongjie LuXianghong LiDawei ZuoIn this paper, the dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative is studied. First, a mathematical model of the single-degree-of-freedom system is established, and the approximate steady-state solution associated with the amplitude–frequency equation is obtained based on the averaging method. Then, the amplitude–frequency response equations are used for stability analysis, and the stability condition is founded. To validate the correctness and precision, the approximate solutions determined by the analytical method are compared with the solutions based on the numerical integration method. It is found that the approximate solutions and the numerical solutions are in excellent agreement. Finally, the effects of system parameters, such as fractional-order coefficient, order, clearance, and piecewise stiffness, on the complex dynamical behaviors of the piecewise linear single-degree-of-freedom oscillator are studied. The results show that the system parameters not only influence resonance amplitude and resonance frequency but also affect the size of the unstable region.https://doi.org/10.1177/1461348419872372 |
| spellingShingle | Jun Wang Yongjun Shen Shaopu Yang Yongjie Lu Xianghong Li Dawei Zuo Dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative Journal of Low Frequency Noise, Vibration and Active Control |
| title | Dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative |
| title_full | Dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative |
| title_fullStr | Dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative |
| title_full_unstemmed | Dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative |
| title_short | Dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative |
| title_sort | dynamic response of a piecewise linear single degree of freedom oscillator with fractional order derivative |
| url | https://doi.org/10.1177/1461348419872372 |
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