Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (9): 987-994.

• Articles • Previous Articles     Next Articles

STABILITY AND CHAOTIC MOTION IN COLUMNS OF NONLINEAR VISCOELASTIC MATERIAL

CHEN Li-qun1,2, CHENG Chang-jun1,2   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China;
    2. Department of Mechanics, Shanghai University, Shanghai 201800, P. R. China
  • Received:1999-06-25 Revised:2000-05-25 Online:2000-09-18 Published:2000-09-18
  • Supported by:

    the National Natural Science Foundation of China(19727027);China Postdoctoral Science Foundation;Shanghai Municipal Development Foundation of Science and Technology(98JC14032,98 SHB1417)

Abstract: The dynamical stability of a homogeneous, simple supported column, subjected to a periodic axial force, is investigated. The viscoelastic material is assumed to obey the Leaderman nonlinear constitutive relation. The equation of motion was derived as a nonlinear integro-partial-differential equation, and was simplified into a nonlinear integro-differential equation by the Galerkin method. The averaging method was employed to carry out the stability analysis. Numerical results are presented to compare with the analytical ones. Numerical results also indicate that chaotic motion appears.

2010 MSC Number: 

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