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Estimates for frequencies of free vibrations of an arbitrary heavy barotropic fluid in closed reservoirsтезисы доклада Тезисы
- Авторы: Ryzhak E.I., Sinyukhina S.V.
- Сборник: APM 2018, Book of Abstracts, XLVI Int. Conf. "Advanced Problems in Mechanics", June 25–30, 2018, St. Petersburg, Russia
- Тезисы
- Год издания: 2018
- Место издания: Polytech-IPME RAS St. Petersburg
- Первая страница: 25
- Последняя страница: 30
- Аннотация: The free vibrations (FV) of a heavy barotropic fluid placed in a closed reservoir and undergoing the action of an arbitrary potential gravity field are investigated by variational methods. The functional whose extremals on the corresponding subspaces are the modes of FV and the extremal values are the squares of the frequencies of FV, is the ratio of the second variation of total potential energy (TPE) of the system to its doubled kinetic energy (where small displacements are substituted instead of velocities). Using the previously obtained [1, 2] canonical form of the second variation of TPE, we state and prove a comparison theorem for the frequencies of FV of different fluids in reservoirs of the same or similar shapes. In the case of reservoirs of special shapes (a rectangular parallelepiped (RP) with an arbitrary ratio of the edges lengths, a regular straight trihedral prism with an arbitrary ratio of the base side to the height, and some others), bilateral estimates for all the frequencies of FV depending on the density and elastic properties of the fluid and geometric parameters of the reservoir are obtained.
- Добавил в систему: Синюхина Светлана Владимировна