On the Coincidence of the Acoustical and Mechanical Natural Frequencies of a Pressure Vessel

A widespread conception among field engineers is that the coincidence of the structure and of the acoustic frequencies of a pressure vessel triggers a dramatic increase in the vibration level, leading to fatigue failure. The physics of fluid-structure interaction are revisited in order to clarify this effect, and a simple model of inertial coupling is proposed on the basis of one structure mode and one acoustic mode. It is shown that even if the uncoupled natural frequencies coincide, the coupled frequencies are split apart by an amount depending on the ratio of the fluid density and of the structure density, and on the spatial correlation of the fluid field. As a consequence, a large increase of the vibration level is more likely to occur in a gas system than in a liquid system. Illustrations based on dispersion equations are provided for cylindrical structures filled with vapor and water.