Complex-Mode Galerkin Approach in Transverse Vibration of an Axially Accelerating Viscoelastic String

ZHANG Neng-hui; WANG Jian-jun; CHENG Chang-jun

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(1): 1-8

ZHANG Neng-hui, WANG Jian-jun, CHENG Chang-jun. Complex-Mode Galerkin Approach in Transverse Vibration of an Axially Accelerating Viscoelastic String[J]. Applied Mathematics and Mechanics, 2007, 28(1): 1-8.

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Complex-Mode Galerkin Approach in Transverse Vibration of an Axially Accelerating Viscoelastic String

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

Received Date: 2005-10-21
Rev Recd Date: 2006-10-11
Publish Date: 2007-01-15

Abstract

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 was used to describe viscoelastic behaviors of the material. The basis function of the complex-mode Galerkin method for axially accelerating nonlinear strings was 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 was 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.
- axially accelerating string,
- viscoelasticity,
- transverse nonlinear vibration,
- complex-mode Galerkin method,
- geometry nonlinearity

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References(15)

References

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