微重力环境下充液球腔非线性耦合动力学研究

采用球坐标系描述球腔中的液体动力学特性并建立一种轴对称贮腔类液刚耦合系统动力学模型．采用模态展开方法分析了微重环境下球形贮箱中的液体晃动问题,给出了球形贮箱内液体晃动速度势函数和波高函数的Gauss超几何级数解析表达式．采用变分原理推导了系统动力学系模型，利用Galerkin 方法对变分方程进行特征频率分析．运用Lagrange方法及非线性动力学方法导出了微重力环境下贮箱中液体与航天器结构耦合的动力学方程组,并对该方程组进行了数值计算,绘出了非线性耦合充液系统自由度随时间的变化历程．

Nonlinear Coupling Dynamics of Liquid Filled Spherical Container in Microgravity

Nonlinear coupled dynamics of liquid-filled spherical container in microgravity is investigated.The goveniing equations of the low-gravity liquid sloshing in a convex asymmetrical container subjected to lateral excitation was obtained by variational principle and solved by a modal analysis method.The variational formulas were transformed into a fiequency equation in the form of a standard eigenvalue problem by the Galerldn method,in which admissible functions for the velocity potential and the liquid free surface displacement were determined analytically in terns of the Gauss hypergeometric series.The coupled dynamic equations of the liquid-filled container were derived using Ia,grange's method,and are numerically solved.The time histories of the modal solutions were obtained by numerical simulations.