The analytical solutions for the wave propagation in a stretched string with a moving mass

• The analytical solutions are derived for a mass moving along a stretched string.
• The solutions cover the string of infinite, semi-finite and finite length.
• A mass moving at subsonic, sonic or supersonic velocities are all considered.

This paper derives the analytical solutions for a stretched string subjected to a concentrated mass moving at a constant velocity. From the derived analytical solutions of the contact force between the string and the mass, the displacement responses of the string can be easily obtained. The solutions cover an infinite, semi-infinite or finite string subjected to a moving mass at subsonic, sonic or supersonic velocities. For the semi-infinite or finite strings, the solutions for different types of boundary conditions are presented in both a unified form and in the form of a series of exponential and polynomial functions. The formula derived is shown to be correct by comparison with the semi-analytical method.