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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (6): 771-777.doi: https://doi.org/10.1007/s10483-009-0611-y

• Articles • 上一篇    下一篇

Nonlinear dynamic behaviors of viscoelastic shallow arches

易壮鹏1 王连华2 赵跃宇2   

  1. 1. School of Civil Engineering and Architecture, Changsha University of Science and Technology,Changsha 410076, P. R. China;
    2. College of Civil Engineering, Hunan University, Changsha 410114, P. R. China
  • 收稿日期:2008-08-22 修回日期:2009-02-25 出版日期:2009-06-01 发布日期:2009-06-01

Nonlinear dynamic behaviors of viscoelastic shallow arches

Zhuang-Peng YI1, Lian-Hua WANG2, Yue-Yu ZHAO2   

  1. 1. School of Civil Engineering and Architecture, Changsha University of Science and Technology,Changsha 410076, P. R. China;
    2. College of Civil Engineering, Hunan University, Changsha 410114, P. R. China
  • Received:2008-08-22 Revised:2009-02-25 Online:2009-06-01 Published:2009-06-01

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摘要： The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches subjected to external excitation are investigated. Based on the d’Alembert principle and the Euler-Bernoulli assumption, the governing equation of a shallow arch is obtained, where the Leaderman constitutive relation is applied. The Galerkin method and numerical integration are used to study the nonlinear dynamic properties of the viscoelastic shallow arches. Moreover, the effects of the rise, the material parameter and excitation on the nonlinear dynamic behaviors of the shallow arch are investigated. The results show that viscoelastic shallow arches may appear to have a chaotic motion for certain conditions.

关键词: viscoelastic shallow arch, Leaderman constitutive relation, Galerkin method, bifurcation, chaos

Abstract: The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches subjected to external excitation are investigated. Based on the d’Alembert principle and the Euler-Bernoulli assumption, the governing equation of a shallow arch is obtained, where the Leaderman constitutive relation is applied. The Galerkin method and numerical integration are used to study the nonlinear dynamic properties of the viscoelastic shallow arches. Moreover, the effects of the rise, the material parameter and excitation on the nonlinear dynamic behaviors of the shallow arch are investigated. The results show that viscoelastic shallow arches may appear to have a chaotic motion for certain conditions.

Key words: viscoelastic shallow arch, Leaderman constitutive relation, Galerkin method, bifurcation, chaos

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