Title | Investigation of transverse oscillations of a rope moving in longitudinal direction |
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Authors | V. N. Anisimov^{1}, V. L. Litvinov^{1}^{1}Syzran’ Branch of Samara State Technical University |

Annotation | The article researches the oscillations of a rope moving in the longitudinal direction. The model takes into account the tension of the rope and resistance of the external environment. The object of the study refers to a wide range of oscillating one-dimensional objects with moving boundaries. At a constant speed of longitudinal motion, the rope oscillations are characterized by a set of eigen frequencies. As a result, an equation is obtained in the form of series, which makes it possible to find the exact values of the eigen frequencies. The article analyzes how the speed of longitudinal rope motion affects the shape of natural oscillations. The solution is made in dimensionless variables, which allows us to use the obtained results to calculate the oscillations of a wide range of technical objects. |

Keywords | oscillations of objects with moving boundaries, boundary value problems, mathematical models, oscillation frequency |

Citation | Anisimov V. N., Litvinov V. L. ''Investigation of transverse oscillations of a rope moving in longitudinal direction'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 16-20, 2018). Saransk: SVMO Publ, 2018. - pp. 120-125. Available at: http://conf.svmo.ru/files/2018/papers/paper41.pdf. - Date of access: 24.08.2019. |

**© SVMO, National Research Mordovia State University, 2019**

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