充液航天器液体晃动问题解析求解方法研究

Analytic method about liquid sloshing for liquid-filled space vehicle

为给出微重力条件下Cassini贮箱液体晃动问题的解析求解方法,首先以静平衡液面为基准点线性化液体晃动方程,然后利用特征函数展开法、变分原理及Ritz法等方法,将微重力下自由晃动问题的求解转变为求解矩阵方程的特征值问题.从而利用给出的计算公式求得液体自由晃动的振型和固有频率.因此,通过求解两步矩阵特征值问题,即可解决微重力条件下Cassini贮箱液体晃动问题.

To get an analytic method for liquid sloshing problem under micro gravity condition of Cassini container, the liquid sloshing equation was linearized with the static balance liquid level as the datum mark. With the use of eigenfunction expansion, variation principle and Ritz method, etc., the free sloshing problem under micro gravity was converted into solving the eigenvalue of matrix equation. And the vibrancy type and natural frequency of free sloshing liquid can be solved. Therefore via solving eigenvalue of matrix equations by two steps, the liquid sloshing problem under micro gravity condition of Cassini container is solved.