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

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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.

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Authors and Affiliations

  1. Department of Mechanics, Shanghai University, Shanghai, 200444, P. R. China

    Zhang Neng-hui Doctor  (张能辉) (Associate Professor), Wang Jian-jun  (王建军) & Cheng Chang-jun  (程昌钧)

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

    Zhang Neng-hui Doctor  (张能辉) (Associate Professor) & Cheng Chang-jun  (程昌钧)

Authors
  1. Zhang Neng-hui Doctor  (张能辉)
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  2. Wang Jian-jun  (王建军)
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  3. Cheng Chang-jun  (程昌钧)
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Corresponding author

Correspondence to Zhang Neng-hui Doctor  (张能辉).

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Contributed by CHENG Chang-jun

Project supported by the National Natural Science Foundation of China (No.10472060), Shanghai Leading Academic Discipline Project (No.Y0103), the Natural Science Foundation of Shanghai (No.04ZR14058), the Outstanding Youth Program of Shanghai Municipal Commission of Education (No.04YQHB088)

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Zhang, Nh., Wang, Jj. & Cheng, Cj. Complex-mode Galerkin approach in transverse vibration of an axially accelerating viscoelastic string. Appl Math Mech 28, 1–9 (2007). https://doi.org/10.1007/s10483-007-0101-x

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  • DOI: https://doi.org/10.1007/s10483-007-0101-x

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