Specific features of application of perturbation techniques in problems of nonlinear oscillations of a liquid with free surface in cavities of noncylindrical shape
We consider the problem of nonlinear oscillations of an ideal incompressible liquid in a tank of a body-of-revolution shape. It is shown that the ordinary way of application of perturbation techniques results in the violation of solvability conditions of the problem. To avoid this contradiction we i...
Збережено в:
| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2007
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3291 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We consider the problem of nonlinear oscillations of an ideal incompressible liquid in a tank of a body-of-revolution shape. It is shown that the ordinary way of application of perturbation techniques results in the violation of solvability conditions of the problem. To avoid this contradiction we introduce some additional conditions and revise previously used approaches. We construct a discrete nonlinear model of the investigated problem on the basis of the Hamilton-Ostrogradskii variational formulation of the mechanical problem, preliminarily satisfying the kinematic boundary conditions and solvability conditions of the problem. Numerical examples testify to the efficiency of the constructed model. |
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