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Steady-state response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle

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Summary.

 The steady-state transverse vibration of a parametrically excited axially moving string with geometric nonlinearity is investigated in this paper. The Boltzmann superposition principle is employed to characterize the material property of the string. The method of multiple scales is applied directly to the governing equation, which is a nonlinear partial-differential-integral equation. The solvability condition of eliminating the secular terms is established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the summation resonance are obtained. Some numerical examples showing effects of the viscoelastic parameter, the amplitude of excitation, the frequency of excitation, and the transport speed are presented.

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Authors and Affiliations

  1. Department of Mechanics, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200436, , , , , , CN

    L.-Q. Chen

  2. Department of Mechanical and Industrial Engineering, University of Toronto, Ontario, M5S 3G8 Canada, , , , , , CA

    J. W. Zu

  3. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China, , , , , , CN

    J. Wu

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  1. L.-Q. Chen
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  2. J. W. Zu
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  3. J. Wu
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Received February 12, 2002; revised October 25, 2002 Published online: May 8, 2003

The research was supported by the National Natural Science Foundation of China (Project No. 10172056).

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Chen, LQ., Zu, J. & Wu, J. Steady-state response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle. Acta Mechanica 162, 143–155 (2003). https://doi.org/10.1007/s00707-002-1000-3

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  • DOI: https://doi.org/10.1007/s00707-002-1000-3

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