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Applied Mathematics and Mechanics

, Volume 22, Issue 3, pp 294–303 | Cite as

Dynamical stability of viscoelastic column with fractional derivative constitutive relation

  • Li Gen-guo
  • Zhu Zheng-you
  • Cheng Chang-jun
Article

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.

Key words

viscoelastic column fractional derivative constitutive relation averaging method weakly singular Volterra integro-differential equation dynamical stability 

CLC numbers

O165.6 O345 

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Li Gen-guo
    • 1
    • 2
  • Zhu Zheng-you
    • 1
    • 2
  • Cheng Chang-jun
    • 1
    • 3
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghaiP R China
  2. 2.Department of MathematicsShanghai UniversityShanghaiP R China
  3. 3.Department of mechanicsShanghai UniversityShanghaiP R China

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