Mathematical modeling of nonlinear vibrations of a rope with a moving boundary

Название	Mathematical modeling of nonlinear vibrations of a rope with a moving boundary
Авторы	Litvinov V. L.¹, Litvinova K. V.² ¹Syzran branch of Samara State Technical University ²Lomonosov Moscow State University
Аннотация	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.
Ключевые слова	nonlinear mathematical model, vibrations of a rope, moving boundaries.
Образец ссылки на статью	Litvinov V. L., Litvinova K. V. Mathematical modeling of nonlinear vibrations of a rope with a moving boundary [Электронный ресурс] // Математическое моделирование, численные методы и комплексы программ: XI Международная научная молодежная школа-семинар имени Е.В. Воскресенского (Саранск, 26-28 июля 2024 г.). - С. 229-231. Режим доступа: https://conf.svmo.ru/files/2024/papers/paper45.pdf. - Дата обращения: 16.10.2024.

МАТЕРИАЛЫ НАУЧНЫХ КОНФЕРЕНЦИЙ И ШКОЛ-СЕМИНАРОВ

Mathematical modeling of nonlinear vibrations of a rope with a moving boundary

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