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Global dynamics for an impacting system of cantilever beam supported by oblique springs
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Yi-feng ZHANG1, Hui-dong XU2, Jian-wen ZHANG1
Journal of Vibration Engineering | 2024, 37(8) : 1308 - 1319
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Journal of Vibration Engineering | 2024, 37(8): 1308-1319
Global dynamics for an impacting system of cantilever beam supported by oblique springs
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Yi-feng ZHANG1, Hui-dong XU2, Jian-wen ZHANG1
Affiliations
  • 1College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
  • 2College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, China
Published: 2024-08-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.08.005
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In this paper，the global dynamics of chaos and subharmonic bifurcation of an impacting system of cantilever beam supported by oblique springs under bilateral asymmetric rigid constraints are studied. It is difficult to study analytically the chaos and subharmonic bifurcation of the system because the stiffness term of the oblique spring support structure is a transcendental function. To do this，the stiffness term of the system is fitted by the approximation method，and the homoclinic orbit and its internal orbits of the approximate system are compared with the orbits of the original system. The threshold conditions for homoclinic chaos and subharmonic bifurcation are presented by applying the Melnikov method to the non-smooth impacting cantilever beam system. Moreover，the stability of the impacting subharmonic orbit is analyzed by combining characteristic multipliers of smooth manifolds with impact function，and the relationship between subharmonic bifurcation and chaos is analyzed. The effects of damping，excitation frequency，excitation amplitude and impact coefficient of restitution on chaos and subharmonic bifurcation are studied based on threshold conditions，which further verify the theoretical analysis.

nonlinear vibration  /  cantilever beam with impact  /  homoclinic chaos  /  subharmonic bifurcation  /  Melnikov method
Yi-feng ZHANG, Hui-dong XU, Jian-wen ZHANG. Global dynamics for an impacting system of cantilever beam supported by oblique springs[J]. Journal of Vibration Engineering, 2024 , 37 (8) : 1308 -1319 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.08.005
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doi: 10.16385/j.cnki.issn.1004-4523.2024.08.005
  • Receive Date：2022-09-17
  • Online Date：2026-02-12
  • Published：2024-08-28
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  • Received：2022-09-17
  • Revised：2022-12-17
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    1College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
    2College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, China
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表12种不同金属材料的力学参数
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Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
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Genus		 种数
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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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