Forced Oscillations of a Fluid in a Cylindrical Tank Undergoing Both Translation and Rotation

摘要

The solution to the problem of forced oscillations of a fluid in a cylindrical tank undergoing translations and rotations along and about a transverse axis through its base is found by an extension of a previous solution for translations only. Through the use of the LaPlace transform, the results are written in the form of transfer functions giving the transverse force and moment about the tank bottom for arbitrary planar motions of the tank. Only the fundamental mode of fluid sloshing is considered in presenting the final results and only small disturbances are admitted. Solutions are presented both for a tank moving in a fixed acceleration field (as on earth) and in an acceleration field carried with the tank (as in a freely falling missile). A mechanical analogy of a fixed mass plus a pendulous mass is found to duplicate the forces and moments identically in both the fixed and carried acceleration field cases. The equations of motion are developed for a missile containing a large fluid tank through the use of the hydrodynamic transfer function. The resulting equations are shown to coincide with those which would be obtained through the use of the mechanical analogy. (Author)