General analytical solution for vibrations of pipes with arbitrary discontinuities and generalized boundary condition on Pasternak foundation

Discontinuities of the shear force, bending moment, slope, and deflection can be caused by span supports, valves, and cracks etc. For arbitrary discontinuities appearing in the oil-conveying pipe resting on Pasternak foundation, the general analytical solution for vibrations of this structure is pre...

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Bibliographic Details
Published in:Mechanical systems and signal processing 2022-01, Vol.162, p.107910, Article 107910
Main Authors: Li, M., Chen, X.C., Chang, X.P., Qin, Y., Li, Y.H.
Format: Article
Language:English
Subjects:
Bending moments
Boundary conditions
Cracks
Discontinuities
Discontinuity
Exact solutions
Generalized boundary condition
Laplace transforms
Nodes
Oil-conveying pipe
Parameters
Pasternak foundation
Physical properties
Pipes
Resonant frequencies
Shear forces
Springs (elastic)
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Summary:Discontinuities of the shear force, bending moment, slope, and deflection can be caused by span supports, valves, and cracks etc. For arbitrary discontinuities appearing in the oil-conveying pipe resting on Pasternak foundation, the general analytical solution for vibrations of this structure is presented in this paper. To deal with discontinuity terms, generalized functions are employed to express the model displacement of the entire pipe as a single function. This function is then solved by Laplace transform. Continuity conditions at discontinuity points are also given. In addition, the generalized boundary condition (BC), which can be degenerated to many classical BCs, is considered. Numerical section testifies the feasibility and the validity of present solutions, and discusses the effects of some physical parameters on natural frequencies. It is shown that the closer the cracks are to the nearest nodes of mode shapes, the less effects they have on the corresponding natural frequencies; locations of support springs change effects of cracks on natural frequencies by affecting positions of structural nodes; foundation parameters have different effects on natural frequencies. The present method can be applied in maintaining safety and integrity of structures of pipes.
ISSN:0888-3270
1096-1216
DOI:10.1016/j.ymssp.2021.107910