Analytical solutions for a mass moving along a finite stretched string with random surface irregularities

• A mass moving along a string with random surface irregularities is considered.
• The analytical solutions are derived for the stochastic responses.
• A mass moving at subsonic, sonic or supersonic velocities are all considered.

This paper derives the analytical solution for the stochastic analysis of a concentrated mass moving at a constant velocity along a finite stretched string with random surface irregularities. Firstly, the problem of computing the spectral power density (PSD) of the random response is transformed into the problem of computing the transient response of a concentrated mass moving at a constant velocity along a stretched string with harmonic random surface irregularities. Next, the analytical solutions of the contact force between the string and the mass are derived for harmonically varying surface irregularities. Finally, the PSDs of contact force and the displacement of the string are determined in terms of the PSD of the random surface irregularities. The analytical solutions cover all three cases of subsonic, sonic or supersonic velocities. The proposed method was verified based on a comparison with the semi-analytical method.