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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.
Aiming at a kind of special geometry tank (waist cylinder, hemisphere hemisphere), which is common in aerospace engineering, the problem of slight free-swinging and lateral forced shaking of liquid is studied by Ritz’s variational method, The natural frequency and vibration mode of liquid sloshing, the velocity potential distribution, the wave height variation, the pressure distribution, the liquid acting on the tank wall force and so on are important physical quantities for guiding the engineering practice.At the same time, it is of guiding significance for the later research The conclusion is that for an axisymmetric shape tank, only the anti-symmetric mode corresponding to the order 1 in the liquid is excited when it is subjected to any transverse movement.