Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (12): 120502-120502.doi: 10.1088/1674-1056/22/12/120502

• GENERAL • 上一篇    下一篇

Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

杨新伟a, 田瑞兰b, 李海涛b   

  1. a School of Traffic, Shijiazhuang Institute of Railway Technology, Shijiazhuang 050041, China;
    b Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
  • 收稿日期:2013-04-02 修回日期:2013-05-26 出版日期:2013-10-25 发布日期:2013-10-25
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11002093, 11172183, and 11202142) and the Science and Technology Fund of the Science and Technology Department of Hebei Province, China (Grant No. 11215643).

Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

Yang Xin-Wei (杨新伟)a, Tian Rui-Lan (田瑞兰)b, Li Hai-Tao (李海涛)b   

  1. a School of Traffic, Shijiazhuang Institute of Railway Technology, Shijiazhuang 050041, China;
    b Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
  • Received:2013-04-02 Revised:2013-05-26 Online:2013-10-25 Published:2013-10-25
  • Contact: Tian Rui-Lan E-mail:tianrl@stdu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11002093, 11172183, and 11202142) and the Science and Technology Fund of the Science and Technology Department of Hebei Province, China (Grant No. 11215643).

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摘要： A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.

关键词: mid-span deflection, beam bridge, infinite series of moving loads, codimension-two bifurcation

Abstract: A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.

Key words: mid-span deflection, beam bridge, infinite series of moving loads, codimension-two bifurcation

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
02.30.Oz (Bifurcation theory) 82.40.Bj (Oscillations, chaos, and bifurcations)