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

L. Q. Chen, J. W. Zu, J. Wu

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Abstract

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.

Original languageEnglish
Pages (from-to)143-155
Number of pages13
JournalActa Mechanica
Volume162
Issue number1-4
DOIs
StatePublished - May 2003

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