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Shock and Vibration
Volume 2014, Article ID 136149, 11 pages
Research Article

The Exact Solutions for a Point Mass Moving along a Stretched String on a Winkler Foundation

State Key Laboratory of Structural Analysis of Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116023, China

Received 5 December 2013; Revised 13 April 2014; Accepted 10 May 2014; Published 30 June 2014

Academic Editor: Dumitru I. Caruntu

Copyright © 2014 Q. Gao 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.


This paper derives the exact solutions for a point mass moving along a stretched infinite string on a Winkler foundation at a constant velocity. The solutions for the contact force between the string and the mass are derived and then the displacement responses of the string can be obtained easily. The solutions cover infinite string subjected to a moving mass at subsonic, sonic, or supersonic velocities. When time tends to infinity, the asymptotical solutions for the contact force between the mass and the string and for the displacement of the contact point are derived. The formulas derived are shown to be correct by comparison with the semianalytical method.