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Dynamical stability of viscoelastic column with fractional derivative constitutive relation

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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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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, 200072, Shanghai, P R China

    Li Gen-guo Doctor, Zhu Zheng-you Professor (Supervisor of Ph D candidates) & Cheng Chang-jun

  2. Department of Mathematics, Shanghai University, 201800, Shanghai, P R China

    Li Gen-guo Doctor & Zhu Zheng-you Professor (Supervisor of Ph D candidates)

  3. Department of mechanics, Shanghai University, 200072, Shanghai, P R China

    Cheng Chang-jun

Authors
  1. Li Gen-guo Doctor
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  2. Zhu Zheng-you Professor
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  3. Cheng Chang-jun
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Additional information

Paper from CHENG Chang-jun, Member of Editorial Committee, AMM

Foundation item: 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 Commission of Education (99A01)

Biographies: LI Gen-guo (1969-) ZHU Zheng-you (1937-)

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Gen-guo, L., Zheng-you, Z. & Chang-jun, C. Dynamical stability of viscoelastic column with fractional derivative constitutive relation. Appl Math Mech 22, 294–303 (2001). https://doi.org/10.1007/BF02437967

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  • DOI: https://doi.org/10.1007/BF02437967

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