中文摘要：

将受迫晃动的液体速度势分解为刚体速度势和摄动速度势,分别得到满足椭圆环形边界条件的刚体速度势及以自由晃动模态为广义坐标系的摄动速度势。将两者代入液体自由表面波条件,通过自由晃动模态的正交完备性建立动力响应方程,求解得到液体晃动响应的解析解。计算结果与有限元结果非常吻合。分析结果表明：储液罐内液体超过一定高度后,液面晃动波高响应将不受液体高度变化的影响;液面晃动波高响应具有滞后性。

英文摘要：

A solution to liquid free vibration modes was introduced. The total velocity potential function of forced vibration was considered as the sum of rigid part and liquid perturbed part. The rigid potential satisfied the elliptical boundary conditions and the liquid perturbed potential expressed by free vibration modes with generalized coordinates were developed. The two parts were than brought into free surface wave conditions to solve the liquid free vibration response by establishing dynamic response equation according to the orthogonality of free vibration modes. Calculation results were in agreement with those obtained by finite element method. Analytical results showed that the surface sloshing response is hysteretic; it is not affected by liquid height in a tank beyond a certain level.