Stability analysis of oil-conveying pipes on two-parameter foundations with generalized boundary condition by means of Green’s functions

•Green’s functions of pipelines on Pasternak foundation are obtained.•Generalized boundary condition is taken into account specifically.•Parameter identification of boundary spring stiffness is studied numerically.•Critical flow velocities are gained by studying the system natural frequencies.•Effec...

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Bibliographic Details
Published in:Engineering structures 2018-10, Vol.173, p.300-312
Main Authors: Li, M., Zhao, X., Li, X., Chang, X.P., Li, Y.H.
Format: Article
Language:English
Subjects:
Boundary conditions
Conveying
Critical flow
Forced vibration
Foundations
Green’s functions
Laplace transforms
Mathematical models
Motivation
Oil-conveying pipe
Parameters
Pasternak foundation
Physical properties
Pipes
Reinforced concrete
Resonant frequencies
Stability
Stability analysis
Stiffness
Studies
Superposition (mathematics)
Vibration
Vibration control
Vibrations
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Summary:•Green’s functions of pipelines on Pasternak foundation are obtained.•Generalized boundary condition is taken into account specifically.•Parameter identification of boundary spring stiffness is studied numerically.•Critical flow velocities are gained by studying the system natural frequencies.•Effects of thickness-to-diameter and length-to-diameter ratios are studied. This paper mainly concentrates on obtaining the explicit solutions of the forced vibrations of oil-conveying pipes on two-parameter foundations and studying the stabilities of these pipes. With the assistance of the Euler-Bernoulli assumption, the dynamic equations of the pipes are modelled by means of Hamilton’s principle. The generalized boundary condition (BC), which can be reduced to many different simple BCs, is considered in the vibration problems. Green’s function and the superposition property of linear vibrations are employed to derive the analytical solutions, and the Laplace transforms are applied with intention of gaining the Green’s functions under various BCs. In the numerical section, the present solutions are validated by comparing with the results in the other literature. In addition, the effects of some important physical parameters, for instance boundary stiffness, foundation parameters, geometric parameters, etc., on the natural frequencies and the critical flow velocities are discussed as well.
ISSN:0141-0296
1873-7323
DOI:10.1016/j.engstruct.2018.07.001