Title | Transverse vibrations of a viscoelastic rope of variable length lying on an elastic base |
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Authors | V. L. Litvinov^{1}, V. N. Anisimov^{1}, I. V. Korpen^{1}, S. N. Kosinova^{1}^{1}Syzran’ Branch of Samara State Technical University |

Annotation | Using the Kantorovich-Galerkin method, an approximate solution of the problem of transverse vibrations of a viscoelastic rope with a moving boundary lying on an elastic base is found. The dependence of the drag force on the movement of the rope is assumed to be proportional to its speed. The flexural rigidity of the rope is taken into account. The results obtained for the amplitude of the oscillations corresponding to the n-th dynamical mode are presented. The phenomenon of steady resonance and passage through resonance is investigated. The solution is obtained for the most common case in practice, when external perturbations act on a moving boundary. |

Keywords | oscillations of systems with moving boundaries, flexural rigidity, viscoelasticity, elastic base, medium resistance, resonance properties, vibration amplitude |

Citation | Litvinov V. L., Anisimov V. N., Korpen I. V., Kosinova S. N. ''Transverse vibrations of a viscoelastic rope of variable length lying on an elastic base '' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 105-114. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper16.pdf. - Date of access: 15.10.2019. |

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

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