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

doi:10.1088/1674-1056/22/12/120502

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.

Keywords: mid-span deflection beam bridge infinite series of moving loads codimension-two bifurcation

Received: 02 April 2013
Revised: 26 May 2013
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	02.30.Oz	(Bifurcation theory)
	82.40.Bj	(Oscillations, chaos, and bifurcations)

Fund: 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).

Corresponding Authors: Tian Rui-Lan
E-mail: tianrl@stdu.edu.cn

Cite this article:

Yang Xin-Wei (杨新伟), Tian Rui-Lan (田瑞兰), Li Hai-Tao (李海涛) Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads 2013 Chin. Phys. B 22 120502

[1]	Song Y F 2000 Dynamics of Highway Bridge (Beijing: China Communication Press) (in Chinese)
[2]	Li G H 1996 Steady and Vibraton of Bridge Structure (Beijing: China Railroad Press) (in Chinese)
[3]	Fryba L 1996 Dynamics of Railway Bridge (London: Thomas Telford)
[4]	Fryba L 1999 Vibration of Solids and Structures under Moving Loads (London: Thomas Telford)
[5]	Yang Y B and Lin C W 2005 J. Sound Vib. 284 205
[6]	Rao R G 2000 J. Vib. Acoust. 122 281
[7]	Ouyang H J 2011 Mechanical Systems and Signal Processing 25 2039
[8]	Azizi N 2011 Appl. Math. Model 36 3580
[9]	Nayfeh A H and Mook D T 1979 Nonlinear Oscillations (New York: Wiley-Interscience)
[10]	Yanmeni Wayou A N, Tchoukuegno R and Woafo P 2004 J. Sound Vib. 273 1101
[11]	Ansari M, Esmailzadeh E and Younesian D 2010 Nonlinear Dyn. 61 163
[12]	Ding H, Chen L Q and Yang S P 2012 J. Sound Vib. 331 2426
[13]	Moon F C 1992 Chaotic and Fractal Dynamics (New York: Wiley)
[14]	Yagasaki K 1999 Nonlinear Mech. 34 983
[15]	Duan L X and Lu Q S 2005 Chin. Phys. Lett. 22 1325
[16]	Zhang Q C, Wang W and Liu F H 2008 Chin. Phys. B 17 4123
[17]	Zhang Q C and Tian R L 2009 Eng. Mech. 26 216 (in Chinese)
[18]	Liu F H, Zhang Q C and Tan Y 2010 Chin. Phys. Lett. 27 044702
[19]	Tian R L, Cao Q J and Yang S P 2010 Nonlinear Dyn. 59 19
[20]	Liu X L and Liu S Q 2012 Nonlinear Dyn. 67 847
[21]	Linaro D, Alan C and Desroches M, et al. 2012 J. Appl. Dyn. Sys. 11 939
[22]	Chen Q L, Teng Z D and Wang L, et al. 2013 Nonlinear Dyn. 71 55
[23]	Tian R L, Yang X W, Cao Q J and Han Y W 2012 Int. J. Bifur. Chaos 22 12501081
[24]	Kim S M 2004 Eng. Struct. 26 95

[1]	An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. Chin. Phys. B, 2023, 32(3): 030203.
[2]	A color image encryption algorithm based on hyperchaotic map and DNA mutation Xinyu Gao(高昕瑜), Bo Sun(孙博), Yinghong Cao(曹颖鸿), Santo Banerjee, and Jun Mou(牟俊). Chin. Phys. B, 2023, 32(3): 030501.
[3]	Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system Huamei Yang(杨华美) and Yuangen Yao(姚元根). Chin. Phys. B, 2023, 32(2): 020501.
[4]	Epilepsy dynamics of an astrocyte-neuron model with ammonia intoxication Zhixuan Yuan(袁治轩), Mengmeng Du(独盟盟), Yangyang Yu(于羊羊), and Ying Wu(吴莹). Chin. Phys. B, 2023, 32(2): 020502.
[5]	Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[6]	Resonance and antiresonance characteristics in linearly delayed Maryland model Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Chin. Phys. B, 2022, 31(12): 120502.
[7]	A novel hyperchaotic map with sine chaotification and discrete memristor Qiankun Sun(孙乾坤), Shaobo He(贺少波), Kehui Sun(孙克辉), and Huihai Wang(王会海). Chin. Phys. B, 2022, 31(12): 120501.
[8]	Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control Hongwei Zhang(张红伟), Ran Cheng(程然), and Dawei Ding(丁大为). Chin. Phys. B, 2022, 31(10): 100504.
[9]	Periodic and chaotic oscillations in mutual-coupled mid-infrared quantum cascade lasers Zhi-Wei Jia(贾志伟), Li Li(李丽), Yi-Yan Guo(郭一岩), An-Bang Wang(王安帮), Hong Han(韩红), Jin-Chuan Zhang(张锦川), Pu Li(李璞), Shen-Qiang Zhai(翟慎强), and Feng-Qi Liu(刘峰奇). Chin. Phys. B, 2022, 31(10): 100505.
[10]	Exponential sine chaotification model for enhancing chaos and its hardware implementation Rui Wang(王蕊), Meng-Yang Li(李孟洋), and Hai-Jun Luo(罗海军). Chin. Phys. B, 2022, 31(8): 080508.
[11]	Characteristics of piecewise linear symmetric tri-stable stochastic resonance system and its application under different noises Gang Zhang(张刚), Yu-Jie Zeng(曾玉洁), and Zhong-Jun Jiang(蒋忠均). Chin. Phys. B, 2022, 31(8): 080502.
[12]	Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Chin. Phys. B, 2022, 31(8): 080504.
[13]	Effect of astrocyte on synchronization of thermosensitive neuron-astrocyte minimum system Yi-Xuan Shan(单仪萱), Hui-Lan Yang(杨惠兰), Hong-Bin Wang(王宏斌), Shuai Zhang(张帅), Ying Li(李颖), and Gui-Zhi Xu(徐桂芝). Chin. Phys. B, 2022, 31(8): 080507.
[14]	Research and application of stochastic resonance in quad-stable potential system Li-Fang He(贺利芳), Qiu-Ling Liu(刘秋玲), and Tian-Qi Zhang(张天骐). Chin. Phys. B, 2022, 31(7): 070503.
[15]	Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system Sheng-Hao Jia(贾生浩), Yu-Xia Li(李玉霞), Qing-Yu Shi(石擎宇), and Xia Huang(黄霞). Chin. Phys. B, 2022, 31(7): 070505.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention