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Nonlinear dynamics of a hanging cantilevered pipe simultaneously subjected to internal and external axial flows
Ahmed R. Abdelbaki, Michael P. Paidoussis, Arun K. Misra

Last modified: 2018-04-24

Abstract


A nonlinear model for the dynamics of a hanging cantilevered pipe simultaneously subjected to internal and external axial flows is developed in this paper. The pipe discharges fluid downwards, which then flows upwards through an annular region contained by a rigid channel. Thus, the external flow is dependent on the internal one, and confined over the whole length of the cantilever. A nonlinear equation of motion is derived for that system via Hamilton’s principle to third-order accuracy. The fluid-related forces associated with the external flow; namely the inviscid, hydrostatic and viscous forces are derived separately, as well as the non-conservative forces due to the internal flow. The equation of motion is nondimensionalized and then discretized utilizing Galerkin’s technique. The solution is obtained numerically and presented by means of bifurcation diagrams, time histories, power spectral density and phase-plane plots. The results are compared to those presented in experimental and linear theoretical studies from the literature having the same system parameters. It was found that the nonlinear theory can qualitatively predict the same dynamical behaviour as observed, and is in reasonable quantitative agreement with the recorded data. Moreover, this model provides a better estimation of the onset of instability compared to the linear one.


Keywords


hanging pipe; axial flow; nonlinear dynamics; instability

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