Perturbation-based prediction of vibration phase shift along fluid-conveying pipes due to Coriolis forces, nonuniformity, and nonlinearity

Flexural vibrations of a fluid-conveying pipe are investigated theoretically, with special consideration to the spatial shift in vibration phase caused by fluid flow and various imperfections. The latter includes small nonuniformity or asymmetry in stiffness, mass, or damping, and weak stiffness and damping nonlinearity. Besides contributing general understanding of wave propagation in elastic media with gyroscopic forces, this is relevant for the design, control, and troubleshooting of phase shift measuring devices like Coriolis mass flowmeters. A multiple time-scaling perturbation analysis is employed with a simple model of a fluid-conveying pipe with relevant imperfections, resulting in simple analytical expressions for the prediction of phase shift. For applications like Coriolis flowmetering, this allows for readily examining effects of a variety of relevant features, like small sensors and actuators, production inaccuracies, mounting conditions, wear, contamination, and corrosion. To second order of accuracy, only mass flow and asymmetrically distributed damping are predicted to introduce spatial phase shift, while nonuniformly distributed linear mass and stiffness, symmetrically distributed linear damping, and uniformly nonlinear stiffness and damping are all negligible in comparison. The analytical predictions are illustrated by examples and validated with excellent agreement against numerical analysis for realistic magnitudes of parameters.