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Mathematical Problems in Engineering
Volume 2013, Article ID 163970, 8 pages
http://dx.doi.org/10.1155/2013/163970
Research Article

Vibrations of String due to a Uniform Partially Distributed Moving Load: Closed Solutions

1Faculty of Environmental Engineering and Geodesy, Wrocław University of Environmental and Life Science, Plac Grunwaldzki 24, 50-363 Wrocław, Poland
2Instytut Matematyczny, Polska Akademia Nauk, Ulica Śniadeckich 8, 00-956 Warszawa, Poland
3Instytut Matematyczny, Uniwersytet Wrocławski, Plac Grunwaldzki 2/4, 50-384 Wrocław, Poland

Received 22 May 2013; Accepted 23 October 2013

Academic Editor: Xiaojun Wang

Copyright © 2013 Rafał Idzikowski et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the damping dynamical response of a finite string due to a uniformly distributed load and a point force moving with a constant velocity. The classical solution for the transverse displacement of a string has a form of a sum of two infinite series, one of which represents the forced vibrations (aperiodic vibrations) and the other one represents free vibrations of the beam. We show that the series which represents aperiodic (forced) vibrations of the string can be presented in a closed, analytical form.