Keywords: vibration, external water pressure, dynamic buckling, resonant frequencies, ANSYS, finite elements.

The aims of this study were to analyse the behaviour of a thin-walled hemi-spherical dome when vibrated under external water pressure, using the commercial computer package ANSYS 11.0; which has been used for the first time; together with a theoretical analysis from an in-house computer program. In order to achieve these aims, the dome was modelled and vibrated in air and then in water, before finally being vibrated under external water pressure. The results collected during each of the analyses were compared to the previous studies, and this demonstrated that ANSYS and the in-house program were suitable programs and produced accurate results for this type of analysis. In the case of ANSYS, excellent graphical displays were also produced. The analyses under external water pressure, clearly demonstrated that as the external water pressure was increased, the resonant frequencies decreased and a type of dynamic buckling became likely; because the static buckling eigenmode was similar to the vibration eigenmode. ANSYS compared favourably with the in-house software, but had the advantage that it produced graphical displays. This also led to the identification of previously undetected meridional modes of vibration; which were not detected with the in-house software.

Structures designed to withstand external water pressure usually appear in the form of thin-walled curved shells constructed from metals. These thin walled curved shell designs are used as it is more efficient to withstand an external pressure in a membrane manner rather than through bending [1].

The greatest danger to these pressure hulls is that they may exceed the pressure they can withstand and become damaged or, more likely, catastrophically fail. To this end there has been extensive research and development regarding the collapse of pressure vessels under uniform external pressure. However, there are many factors that must be considered in the design of a pressure hull and one of the lesser investigated features, is that of vibration and its effects.

Vibration in thin-walled pressure vessels can be the result of numerous cyclic forces, due to machinery or hydrodynamic flow. If these vibrations occur at resonant frequencies it is possible for the structure to fail at a lower pressure than predicted by static evaluation.

Previous studies [1,2] encompassed the comparison of theoretical analyses, provided by in-house finite element computer programs, namely, VIBCONE, VIBDOME, VIBVMC and SUBPRESS, developed by Ross [3,4], together with the experimental analyses for a number of hemi-ellipsoidal prolate and oblate domes with varying aspect ratios. The present investigation has been developed, using the earlier results for the hemi-spherical dome with aspect ratio of 1.0. In the present study, the ANSYS 11.0 finite element analysis software was used to carry out a number of theoretical analyses.

1

C.T.F. Ross, "Pressure Vessels: External Pressure Technology", Horwood Publishing Ltd, Chichester, UK, 2001.

2

O.C. Zienkiewicz, R.E. Newton, "Coupled Vibrations of a Structure Submerged in a Compressible Fluid", International Symposium on Finite Element Techniques, University of Stuttgart, Germany, 1969.

3

C.T.F. Ross, Emile, T. Johns, "Vibration of thin walled domes under external water pressure", Journal of Sound and Vibration, 114, 453-463, 1987. doi:10.1016/S0022-460X(87)80016-0

4

C.T.F. Ross, Emile, T. Johns, "Dynamic buckling of thin walled domes under external pressure", In A.S. Tooth, J. Spence, (Editors), "Applied Solid Mechanics", 2nd Ed., Elsevier Ltd, Amsterdam, 211-224, 1987.

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