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

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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.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai, China

    Hu Ding & Li-Qun Chen

  2. Department of Mechanics, Shanghai University, 200436, Shanghai, China

    Li-Qun Chen

Authors
  1. Hu Ding
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  2. Li-Qun Chen
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Correspondence to Hu Ding.

Additional information

The project was supported by the National Natural Science Foundation of China (10902064 and 10932006), China National Funds for Distinguished Young Scientists (10725209), the Program of Shanghai Subject Chief Scientist (09XD1401700), Shanghai Leading Talent Program, Shanghai Leading Academic Discipline Project (S30106), the program for Cheung Kong Scholars Programme and Innovative Research Team in University (IRT0844).

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Ding, H., Chen, LQ. Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams. Acta Mech Sin 27, 426–437 (2011). https://doi.org/10.1007/s10409-011-0434-z

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  • DOI: https://doi.org/10.1007/s10409-011-0434-z

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