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为得到航天器上燃料晃动频率,针对Cassini贮箱内液体小幅晃动,将贮箱的柱段近似为非常扁长的椭球,建立了原点位于与箱内静液面接触线处相切的圆锥顶点的球坐标系,用高斯超几何级数解析表达速度势和波高的模态函数,采用伽辽金方法将变分方程转变为一个标准的特征值问题形式的频率方程,求解了不同尺寸比例的旋转椭球形贮箱和Cassini贮箱在不同的充液比和不同的Bond数情况下液体小幅晃动的基频,并与已有的理论和实验结果进行对照.结果表明,本文方法用于求解旋转椭球形贮箱和Cassini贮箱内液体小幅晃动频率是可行的.
In order to obtain the swaying frequency of the fuel on the spacecraft, aiming at the slight shaking of the liquid in the Cassini tank, the column of the tank is approximated as a very long ellipsoid, and a cone whose origin is tangent to the line of contact with the liquid in the tank is established The spherical coordinate system of the vertex is transformed into a standard frequency equation in the form of eigenvalue problem by using the Galerkin method to analyze and express the modal functions of velocity and wave height by Gaussian hypergeometric series. Of rotating ellipsoid tank and Cassini tank at different liquid filling ratio and different Bond number, and compared with the existing theoretical and experimental results.The results show that this method is used to solve Rotating the ellipsoidal tank and Cassini tank liquid sloshing frequency is feasible.