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针对旋转椭球形贮箱内液体小幅晃动,建立了原点位于与箱于箱内静液面接触线处相切的圆锥的顶点的球坐标系,用高斯超几何级数解析表达速度势和波高的模态函数,通过伽辽金方法把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椭球形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,把所求结果和已有的理论和实验结果进行对照.
Aiming at the slight sway of the liquid in the rotating ellipsoidal tank, a spherical coordinate system is established with the vertexes of the conic whose tangent point is tangent to the tangent line of the tank in the tank. The velocity potential and wave height are analyzed by means of Gaussian hypergeometric series Modal function, the Galerkin method is used to transform the variational equation into a standard frequency equation in the form of eigenvalue problem. The solution of ellipsoidal tanks with different size ratios under different liquid filling ratios and different Bond numbers Slight shaking of the fundamental frequency, the results obtained and the existing theoretical and experimental results were compared.