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Non-linear forced vibration of axially moving viscoelastic beams

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Abstract

The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Shenyang Institute of Aeronautical Engineering, Shenyang, 110034, China

    Xiaodong Yang

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

    Li-Qun Chen

Authors
  1. Xiaodong Yang
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  2. Li-Qun Chen
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Correspondence to Xiaodong Yang.

Additional information

Project supported by the National Natural Science Foundation of China (No. 10472060), Natural Science Foundation of Shanghai Municipality (No. 04ZR14058) and Doctor Start-up Foundation of Shenyang Institute of Aeronautical Engineering (No. 05YB04).

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Yang, X., Chen, LQ. Non-linear forced vibration of axially moving viscoelastic beams. Acta Mech. Solida Sin. 19, 365–373 (2006). https://doi.org/10.1007/s10338-006-0643-3

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  • DOI: https://doi.org/10.1007/s10338-006-0643-3

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