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Dynamic response of axially moving Timoshenko beams: integral transform solution

Chen AN
Organization: China University of Petroleum-Beijing
Department: Offshore Oil/Gas Research Center
Jian Su
Organization: Universidade Federal do Rio de Janeiro
Journal / Anthology

Applied Mathematics and Mechanics. English Edition
Year: 2014
Volume: 35
Issue: 11
Page range: 14211436

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.

*Applied Mathematics