Bending Vibrations of a Pipe Line Containing Flowing Fluid

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Abstract
Both free vibrations and forced motions due to crosswinds may create important problems in the design of pipe lines supported above ground. An analytic investigation, based on simple beam theory, shows that the flow of fluid in such a pipe line has no beneficial effect upon the vibrations. The fluid velocity causes a dynamic coupling of the simple modes of vibration so that the normal modes of vibration are of complex shape with 90-deg out-of-phase components. The solution is presented for free vibrations and for steady-state forced vibrations, and it is shown that large amplitudes may be developed if the amount of damping is too small. It is shown that at low fluid velocities there is negligible effect upon the vibration of the pipe line, and at a certain high critical velocity the fluid flow causes a dynamic instability. The present analysis revises the conclusions which appeared in an earlier publication.

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