Technical Briefs

Dynamic Response of a Timoshenko Beam to a Moving Force

[+] Author and Article Information
Paweł Śniady

Institute of Civil Engineering, Wrocław University of Technology, WybrzeżeWyspiańskiego 27, 50-370 Wrocław, Polandpawel.sniady@pwr.wroc.pl

J. Appl. Mech 75(2), 024503 (Feb 26, 2008) (4 pages) doi:10.1115/1.2775500 History: Received October 27, 2006; Revised July 01, 2007; Published February 26, 2008

We consider the dynamical response of a finite, simply supported Timoshenko beam loaded by a force moving with a constant velocity. The classical solution for the transverse displacement and the rotation of the cross section of a Timoshenko beam has a form of a sum of two infinite series, one of which represents the force vibrations (aperiodic vibrations) and the other one free vibrations of the beam. We show that one of the series, which represents aperiodic (force) vibrations of the beam, can be presented in a closed form. The closed form solutions take different forms depending if the velocity of the moving force is smaller or larger than the velocities of certain shear and bar velocities.

Copyright © 2008 by American Society of Mechanical Engineers
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