G.F.Zolotenko Nonlinear free oscillations of a fluid in a spherical tank after its speedup or braking |
Applied hydromechanics, Vol. 14 (86) ¹ 3, (2012) |
| The problem on nonlinear free oscillations of an ideal homogeneous incompressible heavy fluid that half fills a rigid spherical tank is considered. It is assumed that tank moves uniformly after its speedup (or braking). The vortex solution of this problem up to a singular component of pressure is suggested. The known condition of full mechanical energy conservation for fluid which is in motionless borders is generalized for the case of fluid with a free surface. On the base of the energy approach the hydrodynamic initial boundary-value problem is reduced to the classical equation for nonlinear oscillations of physical pendulum in the form of ball segment. The formula of the fluid oscillations frequency depending on initial position of a fluid free surface is deduced. The example is considered. |
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KEY WORDS: free oscillations, spherical tank, free surface |
| TEXT LANGUAGE: Russian |