Variational statement of the problem of vibrations of a beam with a moving boundary

Название	Variational statement of the problem of vibrations of a beam with a moving boundary
Авторы	Litvinov V. L.^{1, 2}, Litvinova K. V.^{1, 2} ¹Moscow State University ²Syzran’ Branch of Samara State Technical University
Аннотация	The statement of the problem of vibrations of a beam with a moving spring–loaded support carrying an attached mass is obtained. When the support is not absolutely rigid, energy exchange occurs through the moving boundary. In this regard, there is a difficulty in writing the boundary conditions. To formulate the problem, we used the variational principle of Hamilton. In this case, the viscoelastic properties of the beam material are taken into account. The problem posed includes the differential equation of vibrations, initial conditions for the bent axis of the beam and for the added mass, boundary conditions. The conditions on the moving boundary are written as ratios between the values of the function and its derivatives to the left and right of the boundary.
Ключевые слова	oscillations of a beam, boundary conditions, variational principles, moving spring support
Образец ссылки на статью	Litvinov V. L., Litvinova K. V. Variational statement of the problem of vibrations of a beam with a moving boundary [Электронный ресурс] // Дифференциальные уравнения и их приложения в математическом моделировании: сборник материалов XVI Международной научной конференции. (Саранск, 17-20 августа 2023 г.). - Саранск: СВМО, 2023. - С. 283-285. Режим доступа: https://conf.svmo.ru/files/2023/papers/paper46.pdf. - Дата обращения: 12.05.2024.

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Variational statement of the problem of vibrations of a beam with a moving boundary

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