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An explicit solution for the dynamics of a taut string of finite length carrying a traveling mass: the subsonic case

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Abstract

The authors investigate the linear vibrations induced in an elastic string by a loading point-like mass constrained to moving on it with constant horizontal velocity. Exact solutions are shown in the case of subsonic regime. The displacement is explicitly provided in terms of a power series determined by iteration, which is shown to converge to the solution of the problem. The presence of a discontinuity in the right extremum of the considered space interval is also shown both analytically and numerically.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Rome La Sapienza, Rome, Italy

    Alberto Maria Bersani & Alessandro Della Corte

  2. Department of Civil, Chemical and Environmental Engineering, Polytechnic School, University of Genoa, Genova, Italy

    Giuseppe Piccardo

  3. Department of Architecture, Università di Roma Tre, Rome, Italy

    Nicola Luigi Rizzi

  4. International Research Center for the Mathematics and Mechanics of Complex Systems - MeMoCS, Università dell’Aquila, L’Aquila, Italy

    Nicola Luigi Rizzi

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  1. Alberto Maria Bersani
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  2. Alessandro Della Corte
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  3. Giuseppe Piccardo
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  4. Nicola Luigi Rizzi
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Correspondence to Alessandro Della Corte.

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Maria Bersani, A., Della Corte, A., Piccardo, G. et al. An explicit solution for the dynamics of a taut string of finite length carrying a traveling mass: the subsonic case. Z. Angew. Math. Phys. 67, 108 (2016). https://doi.org/10.1007/s00033-016-0703-6

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  • DOI: https://doi.org/10.1007/s00033-016-0703-6

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