Predicting phase shift of elastic waves in pipes due to fluid flow and imperfections

Flexural vibrations of a fluid-conveying pipe is investigated, with special consideration to the spatial shift in phase caused by fluid flow and various imperfections, e.g., non-ideal supports, non-uniform stiffness or mass, non-proportional damping, weak nonlinearity, and flow pulsation. This is relevant for understanding wave propagation in elastic media in general, and for the design and trouble-shooting of phase-shift measuring devices such as Coriolis mass flowmeters in particular.

A multiple time scaling perturbation analysis is employed for a simple model of a fluid-conveying pipe with imperfections. This leads to simple analytical expressions for the approximate prediction of phase shift, providing direct insight into which imperfections affect phase shift, and how. The analytical predictions are tested against results obtained by pure numerical analysis (Galerkin expansion), showing very good agreement.