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Applied Mathematics and Mechanics

, Volume 28, Issue 1, pp 1–9 | Cite as

Complex-mode Galerkin approach in transverse vibration of an axially accelerating viscoelastic string

  • Zhang Neng-hui  (张能辉)Email author
  • Wang Jian-jun  (王建军)
  • Cheng Chang-jun  (程昌钧)
Article

Abstract

Under the consideration of harmonic fluctuations of initial tension and axially velocity, a nonlinear governing equation for transverse vibration of an axially accelerating string is set up by using the equation of motion for a 3-dimensional deformable body with initial stresses. The Kelvin model is used to describe viscoelastic behaviors of the material. The basis function of the complex-mode Galerkin method for axially accelerating nonlinear strings is constructed by using the modal function of linear moving strings with constant axially transport velocity. By the constructed basis functions, the application of the complex-mode Galerkin method in nonlinear vibration analysis of an axially accelerating viscoelastic string is investigated. Numerical results show that the convergence velocity of the complex-mode Galerkin method is higher than that of the real-mode Galerkin method for a variable coefficient gyroscopic system.

Key words

axially accelerating string viscoelasticity transverse nonlinear vibration complex-mode Galerkin method geometry nonlinearity 

Chinese Library Classification

O322 

2000 Mathematics Subject Classification

70K28 

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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Zhang Neng-hui  (张能辉)
    • 1
    • 2
    Email author
  • Wang Jian-jun  (王建军)
    • 1
  • Cheng Chang-jun  (程昌钧)
    • 1
    • 2
  1. 1.Department of MechanicsShanghai UniversityShanghaiP. R. China
  2. 2.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiP. R. China

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