Free Vibration of Axisymmetric Thin Oblate Shells Containing Fluid

Abstract

A theoretical analysis for the free , axisymmetric, vibrations of an isotropic thin
oblate spheroid shell filled partially or completely with an incompressible, non-viscous,
irrotational fluid is considered. The Rayleigh – Ritz's method is used to obtain an
approximate solution which coincides with the exact solution for the cases of an empty or
completely filled shell.
The vibration of the shell is examined using the non – shallow shell theory. The
analysis is based on considering the oblate spheroid as a continuous system constructed
from two spherical shell elements matched at the continuous boundaries. Solutions are
presented to show the effect of the angle of filling fluid on the shell natural frequencies.
The effect of shell geometric parameters on the frequencies is also investigated. Natural
frequencies are calculated for the shell in both empty and filled cases. It was found that
their frequencies are decreased with the increase of fluid level in the shell. The analytical
solution is compared with available test results. Good agreement is shown between test
results found in the literature and predicted natural frequencies