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

Abstract

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.