Bending Vibrations of a Pipe Line Containing Flowing Fluid

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Abstract
Free vibrations and forced motions due to cross winds may both 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 produces marked damping tendencies and thus may reduce the severity of loading encountered. The time dependence of the fundamental mode of a simply supported pipe line is calculated for a number of mass-flow rates, the damping being observed to increase rapidly and the frequency to remain nearly constant over the practically important range. A method is outlined for studying forced vibration, higher modes, and other end conditions. Finally the problem is discussed in terms of traveling waves on an “infinite” unsupported pipe line.

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