任意转动激励下液体对矩形容器作用的精确解

An Exact Solution of Fluid Action on Rectangular Tank Subjected to Arbitrary Pitching Excitation

摘要: 矩形贮液容器承受转动运动激励时，液体会产生晃动，从而对容器及相关的结构产生附加的动力效应，对相关结构安全性、稳定性以及动力学行为产生重要影响。基于晃动动力学的一般方程，在小晃动假设下，本文采用线性势流理论，给出了矩形贮液容器在纯转动激励下的液体晃动线性化控制方程，通过求解液体运动方程得到液体速度势函数，由Bernoulli方程得到矩形容器内液体压力分布的精确解，通过压力积分进而得到液体对矩形容器的动态力与翻转力矩精确解，进行了液体共振激励的响应计算。精确解的适用范围为转动激励下的线性晃动问题，研究结果可为液体晃动计算及相关工程设计提供参考。

Abstract: When a rectangular liquid-storage tank is subjected to a pitching excitation, a slosh of the contained liquid is excited. The additional dynamic effects of sloshing will be exerted on the tank and the associated structure, which will lead to an important influence on the safety, stability and dynamic behavior of the associated structure. Based on the general equations of sloshing dynamics, under the assumption of small sloshing, this paper uses the linear potential flow theory to derive the linearized governing equations of liquid sloshing subjected to a pure rotating excitation. The velocity potential function is obtained through solving the governing equations of liquid motion. The exact solution of the liquid pressure distribution in the rectangular container is solved by using Bernoulli equation. The exact dynamic force and the overturning moment that act on the tank are further obtained through a pressure integral. A numerical example of liquid resonance response of is calculated. The application cope of present exact solution is limited to the linear sloshing problem subjected to a pitching excitation. The present result can be used as a reference for sloshing computation and the related engineering designs.