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Dynamic analysis of Duffing-van der Pol oscillators with fractional-order derivative and parametric excitation
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Tengda CUI1, Yongjun SHEN1, 2
Journal of Vibration Engineering | 2025, 38(4) : 715 - 721
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Journal of Vibration Engineering | 2025, 38(4): 715-721
Dynamic analysis of Duffing-van der Pol oscillators with fractional-order derivative and parametric excitation
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Tengda CUI1, Yongjun SHEN1, 2
Affiliations
  • 1.School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China
  • 2.State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China
Published: 2025-04-10 doi: 10.16385/j.cnki.issn.1004-4523.2025.04.006
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The dynamic behavior of the Duffing-van der Pol oscillator with fractional-order derivative and parametric excitation is studied in this paper. The effects of various parameters on the amplitude-frequency curves of the system under the combined action of viscous inertia(1≤p≤2)and parametric excitation are analyzed. The system is analyzed by the averaging method,and the fractional-order derivative is treated by the concepts of equivalent linear damping and equivalent mass. The approximate analytical solution of the system is obtained and compared with the numerical solution. The curves of the two solutions agree well with each other to a large extent,which proves the correctness of the analytical solution. The influences of system parameters on the amplitude-frequency curve are analyzed. It is found that the resonance peak value,resonance frequency,resonance region,the range and the number of multivalued solutions are all affected by the system parameters. Through analysis,it is found that the external excitation amplitude and the coefficient of fractional-order derivative can suppress the effect of parametric excitation to some extent.

nonlinear vibration  /  fractional-order derivative  /  viscous inertia  /  parametric excitation  /  averaging method
Tengda CUI, Yongjun SHEN. Dynamic analysis of Duffing-van der Pol oscillators with fractional-order derivative and parametric excitation[J]. Journal of Vibration Engineering, 2025 , 38 (4) : 715 -721 . DOI: 10.16385/j.cnki.issn.1004-4523.2025.04.006
Year 2025 volume 38 Issue 4
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Article Info
doi: 10.16385/j.cnki.issn.1004-4523.2025.04.006
  • Receive Date:2023-07-10
  • Online Date:2026-02-12
  • Published:2025-04-10
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History
  • Received:2023-07-10
  • Revised:2023-09-15
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Affiliations
    1.School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China
    2.State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China
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表12种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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