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Reference [99] is:
[99] Bishop, R. E. D., and Fawzy, I., 1976, “Free and Forced Oscillations of a Vertical Tube Containing a Flowing Fluid,” Philos. Trans. R. Soc. London, Ser.A, 284, pp. 1–47.
This and the next image are from:
R. A. Ibrahim (Dept. of Mechanical Engineering, Wayne State University, Detroit, Michigan 48202, USA),
“Overview of mechanics of pipes conveying fluids—Part I: Fundamental studies”, J. Pressure Vessel Technol. — Trans. ASME 132 (3) (2010) 034001. DOI: 10.1115/1.4001271
ABSTRACT: This two-part review article presents an overview of mechanics of pipes conveying fluid and related problems such as the fluid-elastic instability under conditions of turbulence in nuclear power plants. In the first part, different types of modeling, dynamic analysis, and stability regimes of pipes conveying fluid restrained by elastic or inelastic barriers are described. The dynamic and stability behaviors of pinned-pinned, clamped-clamped, and cantilevered pipes conveying fluid together with curved and articulated pipes will be discussed. Other problems such as pipes made of viscoelastic materials and active control of severe pipe vibrations are considered. This part will be closed by conclusions highlighting resolved and nonresolved controversies reported in literature. The second part will address the problem of fluid-elastic instability in single- and two-phase flows and fretting wear in process equipment such as heat exchangers and steam generators. Connors critical velocity will be discussed as a measure of initiating fluid-elastic instability. Vibro-impact of heat exchanger tubes and the random excitation by the cross-flow can produce a progressive damage at the supports through fretting wear or fatigue. Antivibration bar supports used to limit pipe vibrations are described. An assessment of analytical, numerical, and experimental techniques of fretting wear problem of pipes in heat exchangers will be given. Other topics related to this part include remote impact analysis and parameter identification, pipe damage-induced by pressure elastic waves, the dynamic response and stability of long pipes, marine risers together with pipes aspirating fluid, and carbon nanotubes conveying fluid.
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