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Acta Mechanica Sinica

, Volume 27, Issue 3, pp 426–437 | Cite as

Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams

  • Hu DingEmail author
  • Li-Qun Chen
Research Paper

Abstract

Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same, but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.

Keywords

Axially moving beam Nonlinearity Material time derivative Method of multiple scales Differential quadrature method 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH 2011

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.Department of MechanicsShanghai UniversityShanghaiChina

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