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Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (3): 294-303.

• 论文 • 上一篇    下一篇

DYNAMICAL STABILITY OF VISCOELASTIC COLUMN WITH FRACTIONAL DERIVATIVE CONSTITUTIVE RELATION

根国1,2, 朱正佑1,2, 程昌钧1,3   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China;
    2. Departnent of Mathernatics, Shanghai University, Shanghai 201800, P. R. China;
    3. Department of mechanics, Shanghai University, Shanghai 200072, P. R. China
  • 收稿日期:2000-01-25 修回日期:2000-12-19 出版日期:2001-03-18 发布日期:2001-03-18
  • 基金资助:
    the National Natural Science Foundation of China( 19772027);the Science Foundation of Shanghai Municipal Commission of Sciences and Technology (98JC14032); the Science Foundation of Shanghai Municipal Comnission of Education (99A01)

DYNAMICAL STABILITY OF VISCOELASTIC COLUMN WITH FRACTIONAL DERIVATIVE CONSTITUTIVE RELATION

LI Gen-guo1,2, ZHU Zheng-you1,2, CHENG Chang-jun1,3   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China;
    2. Departnent of Mathernatics, Shanghai University, Shanghai 201800, P. R. China;
    3. Department of mechanics, Shanghai University, Shanghai 200072, P. R. China
  • Received:2000-01-25 Revised:2000-12-19 Online:2001-03-18 Published:2001-03-18
  • Supported by:
    the National Natural Science Foundation of China( 19772027);the Science Foundation of Shanghai Municipal Commission of Sciences and Technology (98JC14032); the Science Foundation of Shanghai Municipal Comnission of Education (99A01)

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摘要： The dynamic stability of simple supported viscoelastic column, subjected to a periodic axial force, is investigated. The viscoelastic material was assumed to obey the fractional derivative constitutive relation. The governing equation of motion was derived as a weakly singular Volterra integro-partial-differential equation, and it was simplified into a weakly singular Volterra integro-ordinary-differential equation by the Galerkin method. In terms of the averaging method, the dynamical stability was analyzed. A new numerical method is proposed to avoid storing all history data. Numerical examples are presented and the numerical results agree with the analytical ones.

Abstract: The dynamic stability of simple supported viscoelastic column, subjected to a periodic axial force, is investigated. The viscoelastic material was assumed to obey the fractional derivative constitutive relation. The governing equation of motion was derived as a weakly singular Volterra integro-partial-differential equation, and it was simplified into a weakly singular Volterra integro-ordinary-differential equation by the Galerkin method. In terms of the averaging method, the dynamical stability was analyzed. A new numerical method is proposed to avoid storing all history data. Numerical examples are presented and the numerical results agree with the analytical ones.

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