Simplified equations of motion for the radial-axial vibrations of fluid filled pipes

The equations of motion for straight fluid filled pipes are greatly simplified. It is found, for frequencies below a third of the ring frequency, that the radial-axial waves in cylinders are as if the circumferential motion were inextensional. This is the fundamental assumption for the analysis. The derivation is also based on the assumption of long axial wavelengths, resulting in the axial inertia of the fluid and the axial flexural stiffness of the pipe wall being negligible. The formulation is restricted to frequencies well below the cut-on of higher order fluid modes. For such frequencies, the compressibility of the fluid is neglected and the internal fluid loading, on the pipe, is approximated as an increase in the radial inertia. Upon this basis, the equations of motion, for each circumferential mode, are similar to those for a Timoshenko beam on a Winkler foundation. Numerical experiments are made, comparing the approximate theory with results from calculations from the Helmholtz equation for the fluid and accurate thin-walled cylinder theory. Criteria for the application of the simplified theory are formulated. (C) 1997 Academic Press Limited.