V. I. Tsurkov ,   A. A. Gourchenkov International conference on optimization: techniques and application, UK University of Swansea , 06.1993 , language: английский  Аннотация We consider the oscillation problem of the coupled solid and uniform viscous ideal incompressible fluid by the overturning moment of a force. The solid has a symmetric cavity which is filled partially. The equations of disturbed motion about the uniform rotation are offered. This hydro-mechanical problem is solved for the following cavities: cylinder, ellipsoid, paraboloid, hyperboloid, cone. The stability of the system is investigated. In particular the stability or instability of the ellipsoid depends only on the quotient of main semi-axises. In other cases the eigen frequencies are obtained, which realize the stability* The velocity field of viscous fluid has a thin boundary layer near walls if the Ekman's number is great. The rest of fluid motion is similar this one of ideal fluid. The equations of the weakly disturbed solid motion containing viscous fluid are introduced. The motion equations are linearized about the uniform rotation. The influence of the fluid on the solid motion is carried out by means of connection inertances which are determined by the Zhukovsky's potentials. These ones are the solution of a linear boundary eigen value problem which depends on the geometry of the cavity. The viscosity of the fluid is taken into account by means of generalized dissipative forces according to Landau's method. The motion equations are a infinite integral differential system. The first three equations describe the equivalent solid motion by inter moments of forces. The rest of ones determines fluid oscillation. The fluid velocity field is written as series. The coefficients of these ones are amplitudes of fluid oscillations. The integral differential system is solved by means of- Landau's transformations. Afterwards the types of fluid oscillations are determined. In the viscosity case we investigate the stability about axis with most moment of inertia and instability with least one. The characteristic equation is offered which generalizes this one of ideal fluid. Computational tests show that the eigen frequences displace in proportion to the root of viscosity. Moreover the viscosity bring about a new stability criterion. Thus the viscosity involve either the stability of uniform rotation or a loss of this one.  Ключевые слова viscous fluid, stability, oscillation

	Наш адрес: 119991 ГСП-1 Москва В-71, Ленинский просп., 14 Телефон: 938-0309 (Справ. бюро) Факс: (495)954-3320 (Лен.пр.,14), (495)938-1844 (Лен.пр.,32а)	Назад