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Dynamic response of axially moving Timoshenko beams: integral transform solution

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Abstract

The generalized integral transform technique (GITT) is used to find a semianalytical numerical solution for dynamic response of an axially moving Timoshenko beam with clamped-clamped and simply-supported boundary conditions, respectively. The implementation of GITT approach for analyzing the forced vibration equation eliminates the space variable and leads to systems of second-order ordinary differential equations (ODEs) in time. The MATHEMATICA built-in function, NDSolve, is used to numerically solve the resulting transformed ODE system. The good convergence behavior of the suggested eigenfunction expansions is demonstrated for calculating the transverse deflection and the angle of rotation of the beam cross-section. Moreover, parametric studies are performed to analyze the effects of the axially moving speed, the axial tension, and the amplitude of external distributed force on the vibration amplitude of axially moving Timoshenko beams.

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Author information

Authors and Affiliations

  1. Offshore Oil/Gas Research Center, China University of Petroleum-Beijing, Beijing, 102249, P. R. China

    Chen An  (安 晨)

  2. Nuclear Engineering Program, COPPE, Universidade Federal do Rio de Janeiro, CP 68509, Rio de Janeiro, 21941-972, Brazil

    Jian Su  (苏 健)

Authors
  1. Chen An  (安 晨)
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  2. Jian Su  (苏 健)
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Corresponding author

Correspondence to Jian Su  (苏 健).

Additional information

Project supported by the Science Foundation of China University of Petroleum in Beijing (No. 2462013YJRC003)

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An, C., Su, J. Dynamic response of axially moving Timoshenko beams: integral transform solution. Appl. Math. Mech.-Engl. Ed. 35, 1421–1436 (2014). https://doi.org/10.1007/s10483-014-1879-7

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  • DOI: https://doi.org/10.1007/s10483-014-1879-7

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Chinese Library Classification

2010 Mathematics Subject Classification

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