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

Jon Juel Thomsen*, Niels Fuglede

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

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.
Original languageEnglish
JournalNonlinear Dynamics
ISSN0924-090X
DOIs
Publication statusAccepted/In press - 2019

Keywords

  • Mechanical nonlinearity
  • Perturbation analysis
  • Fluid-conveying pipes
  • Spatial phase shift
  • Structural imperfection
  • Coriolis flowmeter

Cite this

@article{108d35b1fe02413384f1e4ae329dcc3a,
title = "Perturbation-based prediction of vibration phase shift along fluid-conveying pipes due to Coriolis forces, nonuniformity, and nonlinearity",
abstract = "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.",
keywords = "Mechanical nonlinearity, Perturbation analysis, Fluid-conveying pipes, Spatial phase shift, Structural imperfection, Coriolis flowmeter",
author = "Thomsen, {Jon Juel} and Niels Fuglede",
year = "2019",
doi = "10.1007/s11071-019-04934-6",
language = "English",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Netherlands",

}

Perturbation-based prediction of vibration phase shift along fluid-conveying pipes due to Coriolis forces, nonuniformity, and nonlinearity. / Thomsen, Jon Juel; Fuglede, Niels.

In: Nonlinear Dynamics, 2019.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Perturbation-based prediction of vibration phase shift along fluid-conveying pipes due to Coriolis forces, nonuniformity, and nonlinearity

AU - Thomsen, Jon Juel

AU - Fuglede, Niels

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Mechanical nonlinearity

KW - Perturbation analysis

KW - Fluid-conveying pipes

KW - Spatial phase shift

KW - Structural imperfection

KW - Coriolis flowmeter

U2 - 10.1007/s11071-019-04934-6

DO - 10.1007/s11071-019-04934-6

M3 - Journal article

JO - Nonlinear Dynamics

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SN - 0924-090X

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