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Bifurcation and stability of coexistence attractors in a time-varying stiffness impact vibration system
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Xin WANG1, Kai KANG1, 2, Hua JIN1
Journal of Mechanical Strength | 2025, 47(10) : 43 - 50
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Journal of Mechanical Strength | 2025, 47(10): 43-50
• Vibration·Noise·Monitoring·Diagnosis •
Bifurcation and stability of coexistence attractors in a time-varying stiffness impact vibration system
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Xin WANG1, Kai KANG1, 2, Hua JIN1
Affiliations
  • 1.School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
  • 2.Urumqi Locomotive Depot of China Railway Urumqi Bureau Group Co., Ltd., Urumqi 830023, China
Published: 2025-10-15 doi: 10.16579/j.issn.1001.9669.2025.10.005
Outline
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Considering the time-varying stiffness characteristics of mechanical systems, a single-degree-of-freedom time-varying impact vibration system model with clearance stiffness was studied. The dynamic model and Poincaré map were established, and numerical calculation methods were given. The influence of the ratio of time-varying stiffness amplitudes on the dynamic response and characteristics of the system was analyzed using numerical simulation and the maximum Lyapunov exponent. By combining multiple initial value bifurcation diagrams, attraction domains, phase diagrams, and Poincaré mapping diagrams, the evolution and bifurcation of coexisting attractors in the system were studied by applying the continuation shooting method. When the bifurcation parameter changes and the system exhibits the coexistence phenomenon,the reasons for the appearance and disappearance of local attractors and the distribution mechanism of unstable attractors in the attraction domain before and after bifurcation are revealed. The stability change rule of coexisting attractors is obtained.

Time-varying stiffness  /  Vibration system  /  Coexistence attractor  /  Stability  /  Bifurcation
Xin WANG, Kai KANG, Hua JIN. Bifurcation and stability of coexistence attractors in a time-varying stiffness impact vibration system[J]. Journal of Mechanical Strength, 2025 , 47 (10) : 43 -50 . DOI: 10.16579/j.issn.1001.9669.2025.10.005
Funding
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  • National Natural Science Foundation of China(12062008)
  • Science and Technology Plan of Gansu Province(21JR7RA314)
Appendix
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Year 2025 volume 47 Issue 10
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Article Info
doi: 10.16579/j.issn.1001.9669.2025.10.005
  • Receive Date：2024-01-02
  • Online Date：2026-02-11
  • Published：2025-10-15
Article Data
Affiliations
History
  • Received：2024-01-02
  • Revised：2024-02-29
Funding
National Natural Science Foundation of China(12062008)
Science and Technology Plan of Gansu Province(21JR7RA314)
Affiliations
    1.School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
    2.Urumqi Locomotive Depot of China Railway Urumqi Bureau Group Co., Ltd., Urumqi 830023, China

Corresponding:

JIN Hua, E-mail:
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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
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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