微重力下圆柱形贮箱内液体晃动的分岔现象

为了得到微重力下液体晃动的特性,晃动模态用具有水平静液面的液体晃动模态近似. 液体晃动取前5 个重要模态,用Lagrange 方程推导了横向力作用下液体晃动和航天器结构的无量纲的耦合动力学方程并进行数值模拟. 模拟了液体晃动模态随外力振幅和频率变化产生的分岔现象,并分析了系统参数,如Bond数、接触角、接触角迟滞、充液高度、频率比、质量比以及外力的周期形式和方向等对晃动模态的分岔的影响.

BIFURCATIONS OF LIQUID SLOSHING IN CYLINDRICAL CONTAINERS IN MICROGRAVITY CONDITION

The analytical velocity potential and the wave height of the sloshing liquid with horizontal hydro-static surface are obtained from Laplace equations. It is observed experimentally that the mode shapes of a curved hydrostatic surface in a microgravity condition do not appreciably differ from the mode shapes of a flat hydrostatic surface. To obtain sloshing characteristics in cylindrical containers in microgravity conditions, the mode shapes of a flat hydrostatic surface are used to approximate the curved hydrostatic surface. After truncating the first five modes of sloshing, the dimensionless coupling dynamics equations for the sloshing liquid and the main rigid body are derived by the Lagrange equation. The bifurcations of the sloshing modes are simulated for the amplitude and the frequency of the force variations. The effects of the system parameters, such as the Bond number, the contact angle, the contact angle hysteresis, the liquid height, the frequency ratio, and the mass ratio, and of the periodic form and the direction of the force, on the bifurcations of sloshing modes are studied.