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

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 solution...

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Bibliographic Details
Published in:Wave motion 2015-12, Vol.59, p.1-28
Main Authors: Gao, Q., Zhang, J., Zhang, H.W., Zhong, W.X.
Format: Article
Language:English
Subjects:
Analytical solution
Constants
Functions (mathematics)
Mathematical analysis
Moving mass
Polynomials
Series (mathematics)
Sonic or supersonic velocities
Strings
Subsonic
Vibrations of string
Wave motion
Wave propagation
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Summary: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. •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.
ISSN:0165-2125
1878-433X
DOI:10.1016/j.wavemoti.2015.07.004