一类Cassini贮箱液体小幅晃动问题的研究

Study of small amplitude liquid sloshing problem in one kind Cassini tank

针对航天工程中常见的某一类特殊几何形状贮箱(腰为圆柱,两底为半球),利用R itz变分法研究了其中液体的小幅自由晃动问题和横向受迫晃动问题,得到常重下液体晃动的固有频率和振型、速度势分布、波高变化、压力分布、液体作用于贮箱壁的力等用于指导工程实践的重要物理量.同时得出一个对于以后的研究具有指导性意义的结论:对于轴对称形状贮箱,当其作任意横向运动时,其中液体只有对应周向模态阶数为1的反对称模态才被激发.

The small amplitude free sloshing problem and forced translational sloshing problem of liquid in one special geometrical shape tank are solved by Ritz variational method, that the middle is circular cylinder and the top and bottom are hemispheres, which used frequently in space engineering. The natural frequencies, the natural modes, the distribution of velocity potential, the wave elevation, the distribution of pressure and the sloshing force acted on the tank wall under ordinary gravity are derived, which are very important for the engi- neering practices. At the same time a very important conclusion is gained that only the sloshing antisymmetric modes that the circumferential mode is 1 are excited in axisymmetric tank when it subjected to arbitrary translation motion, which is directive for the future＇s study.