Vibration analysis of liquid in an axisymmetric tank covered by a diaphragm

Abstract

The vibration of liquid in an axisymmetric tank covered by an elastic diaphragm is analyzed and an equivalent mechanical model for the coupled oscillation of the liquid and the diaphragm is developed. As a preliminary step to the vibration analysis, the static shape of the diaphragm is determined by solving nonlinear differential equations. The characteristic function for the liquid motion applicable to arbitrary axisymmetric tanks is analytically expressed in terms of the Gaussian hypergeometric series by introducing spherical coordinates. This expression enables reduced-order modeling for sloshing in arbitrary axisymmetric convex tanks, for which time-consuming and expensive numerical methods have been used in the past. The decreasing effects of the diaphragm on the sloshing force and moment are explained by developing a mechanical model for the coupled liquid-diaphragm system and comparing the model with that for free-surface sloshing.