Vibration around non-trivial equilibrium of a supercritical Timoshenko pipe conveying fluid

Vibration around non-trivial equilibrium of a supercritical Timoshenko pipe conveying fluid Vibration characteristics of pipes conveying fluid in the super-critical range are investigated by using Timoshenko beam theory for the first time. Generalized Hamiltonian principle is applied to derive the nonlinear transverse vibration governing equation. The non-trivial static equilibrium configuration and critical flow velocity of the pipe are analytically deduced. These analytical results are verified by using the finite difference method. Compared with Euler-Bernoulli flow pipeline, it is found that the equilibrium configuration of Timoshenko pipe is larger. In the supercritical regime, natural frequencies of the Timoshenko flow pipe are produced by the Galerkin truncation method. Numerical examples illustrate that vibration characteristics of the pipe are highly sensitive to length, thickness, shear modulus and velocity. The relative difference between the two pipe models is influenced by the velocity of the flow and is likely to exceed 100%. In general, this work found that the flow velocity makes the Timoshenko beam theory even more needed for researching vibration properties of pipes conveying fluid, especially at a high velocity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Sound and Vibration Elsevier

Vibration around non-trivial equilibrium of a supercritical Timoshenko pipe conveying fluid

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Ltd
ISSN
0022-460X
eISSN
1095-8568
D.O.I.
10.1016/j.jsv.2018.04.041
Publisher site
See Article on Publisher Site

Abstract

Vibration characteristics of pipes conveying fluid in the super-critical range are investigated by using Timoshenko beam theory for the first time. Generalized Hamiltonian principle is applied to derive the nonlinear transverse vibration governing equation. The non-trivial static equilibrium configuration and critical flow velocity of the pipe are analytically deduced. These analytical results are verified by using the finite difference method. Compared with Euler-Bernoulli flow pipeline, it is found that the equilibrium configuration of Timoshenko pipe is larger. In the supercritical regime, natural frequencies of the Timoshenko flow pipe are produced by the Galerkin truncation method. Numerical examples illustrate that vibration characteristics of the pipe are highly sensitive to length, thickness, shear modulus and velocity. The relative difference between the two pipe models is influenced by the velocity of the flow and is likely to exceed 100%. In general, this work found that the flow velocity makes the Timoshenko beam theory even more needed for researching vibration properties of pipes conveying fluid, especially at a high velocity.

Journal

Journal of Sound and VibrationElsevier

Published: Aug 18, 2018

References

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