Vibration of submerged hemi-ellipsoidal domes

Ten thin-walled hemi-ellipsoidal domes were vibrated in air and also underwater. The domes varied in shape from oblate hemi-ellipsoids to prolate ones, and the fundamental eigenmodes were either axisymmetric as asymmetric, depending on the profiles of the domes. A varying meridional curvature annular element was developed for the shell and a similar one for the fluid, except that the latter was of quadrilateral cross-section. For submerged vibration, the two finite elements were coupled together and solution carried out through simultaneous iteration. Theoretical analyses with these structural and fluid finite elements gave satisfactory results compared to the experiments.