Title | Mathematical modeling of nonlinear vibrations of a rope with a moving boundary |
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Authors | V. L. Litvinov^{1}, K. V. Litvinova^{2}^{1}Syzran branch of Samara State Technical University ^{2}Lomonosov Moscow State University |

Annotation | The problems of longitudinal – transverse vibrations of objects with moving boundaries were solved mainly in a linear setting, the energy exchange through the moving boundary and the interaction between longitudinal and transverse vibrations were not taken into account until now. The paper presents a new nonlinear mathematical model of transverse vibrations of an unbounded rope with a moving boundary, in which geometric nonlinearity is taken into account. The obtained mathematical model allows one to describe high-intensity vibrations of a rope with a moving boundary. The solution was made in the MATLAB environment of dimensionless variables, which allows one to use the obtained results to calculate oscillations of a wide range of technical objects. |

Keywords | nonlinear mathematical model, vibrations of a rope, moving boundaries. |

Citation | Litvinov V. L., Litvinova K. V. ''Mathematical modeling of nonlinear vibrations of a rope with a moving boundary'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 229-231. Available at: https://conf.svmo.ru/files/2024/papers/paper45.pdf. - Date of access: 12.11.2024. |

**© SVMO, National Research Mordovia State University, 2024**

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