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Shock and Vibration
Volume 18 (2011), Issue 1-2, Pages 281-287

Nonlinear Models for Transverse Forced Vibration of Axially Moving Viscoelastic Beams

Hu Ding1 and Li-Qun Chen1,2

1Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200077, China
2Department of Mechanics, Shanghai University, Shanghai, 200444, China

Received 2 February 2010; Revised 17 May 2010

Copyright © 2011 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nonlinear models of transverse vibration of axially moving viscoelastic beams subjected external transverse loads via steady-state periodical response are numerically investigated. An integro-partial-differential equation and a partial-differential equation of transverse motion can be derived respectively from a model of the coupled planar vibration for an axially moving beam. The finite difference scheme is developed to calculate steady-state response for the model of coupled planar and the two models of transverse motion under the simple support boundary. Numerical results indicate that the amplitude of the steady-state response for the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters and the integro-partial-differential equation gives results more closely to the coupled planar vibration.