The analytical solutions for the wave propagation in a stretched string with a moving mass |
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| Affiliation: | 1. Department of Mathematics and Statistics, Arkansas State University, State University, AR 72464, United States;2. Department of Mathematical Sciences, University of Arkansas Fayetteville, AR 72701, United States;1. Professor of Structural Engineering, School of Civil and Building Engineering, Loughborough University, Leicestershire, LE 11 3TU, United Kingdom;2. Formerly, Research Student, School of Civil and Building Engineering, Loughborough University, Leicestershire, LE 11 3TU, United Kingdom |
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| Abstract: | 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. |
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| Keywords: | Analytical solution Moving mass Vibrations of string Subsonic Sonic or supersonic velocities |
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