Influence of Entrained Water Mass on the Vibration Modes of a Shell

Abstract

The virtual mass effect of a liquid annulus surrounding a shell is established in closed form. Simple support conditions for the shell and open end conditions for the liquid annulus are considered. In this fashion one arrives at a generalization of Stokes’ formula which treats the case when a rigid rod moves back and forth in the liquid. The present theory encompasses vibrations of the beam mode and breathing mode types. Availability of the entrained liquid mass expression is of importance in the computation of reactor and missile vibrations. The results for the beam modes of shell vibrations, for the example considered, are in satisfactory agreement with previous results obtained on the basis of beam analysis.