非轴对称贮箱液体晃动的等效力学模型

摘要

针对非轴对称贮箱液体晃动问题,从一般意义上推导了作三维运动的任意三维贮箱内液体晃动的等效力学模型,采用有限元方法建立计算等效力学模型参数的数值算法,利用矩阵相似变换的性质分离液体零频以消除液体刚度矩阵的奇异性,从而将等效力学模型参数的计算归结为广义特征值问题和线性代数方程组的求解,具有较高的计算效率.通过非轴对称贮箱液体晃动的算例说明,不同的等效晃动方向可能不正交,晃动平面可能不过液体质心,因此非轴对称贮箱液体晃动的等效力学模型比轴对称贮箱液体晃动的更加复杂.最后以三棱柱形充液贮箱为例,采用商用CFD(计算流体动力学)分析软件FLOW-3D验证了在贮箱作典型三维运动时等效力学模型的有效性.%For dynamics of liquid-filled spacecraft , liquid sloshing in axisymmetric tanks is well investigated , while few studies are on the liquid sloshing in non-axisymmetric tanks. In a more general sense, an equivalent mechanical model of liquid sloshing in arbitrary 3D tank undergoing 3D motions is deduced in thia paper. An efficient numerical algorithm for calculating parameters of the equivalent mechanical model is proposed by using finite element method. The algorithm applies aimilarity transformation of matrix to eliminate the singularity of liquid stiffness matrix by separating the zero frequency. Thus, the calculation of equivalent mechanical model parameters is attributed to solve generalized eigenvalue problems and linear algebraic equations. Using PATRAN as the prepracessor, a custom program is composed for calculating parameters of equivalent mechanical model of arbitrary 3D tank. including pendulum length, sloshing direction, sloshing mass,rigidly-attached mass inertia, suspension position and so on. Based on several examples for liquid sloshing in non-axisymmetric tanks, it is discovered that different equivalent sloshing directions may be nonorthogonal and sloshing planes may not contain the centroid of liquid. Thus, the equivalent mechanical model of liquid sloshing in a non-axisymmetric tank would be more complicated than that of an axisymmetric tank. Finally, taking a triangular column tank as an example, the commercial CFD ( computational fluid dynamics) package, FLOW-3D, is used to numerically verify the equivalent mechanical model of the tank undergoing several typical 3D motions.