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Three-dimensional nonlinear dynamics of an extensible pipe conveying fluid
Abdolreza Askarian, Mojtaba Kheiri

Last modified: 2018-04-11


In this paper, the two- and three-dimensional (3D) nonlinear dynamics of extensible pipes conveying fluid are studied. The pipe could be either horizontal or vertical. Previous studies were mostly concerned about the dynamics of inextensible pipes. The only existing study on the dynamics of extensible pipes conveying fluid is limited to planar motions. In the present study, the cantilevered pipe is modelled by the nonlinear Euler-Bernoulli beam theory. The fluid forces include distributed inertia, Coriolis and centrifugal forces. Using the extended Hamilton’s principle along with Galerkin’s method, the coupled equations for longitudinal and transverse displacements (u-v-w) are obtained and are solved in both time and frequency domains. Results show that extensibility does not noticeably change stability of the pipe. In contrast to existing models based on the inextensibility assumption, the new model show that for the low post-critical flow velocities, the pipe always performs planar limit-cycle oscillations, regardless of the fluid-to-total mass ratio (mass ratio, in short). However, at sufficiently high post-critical flow velocities and for certain values of mass ratio, the pipe might perform circular or orbital (3D) motion.


3D nonlinear vibrations; extensible pipe; flutter; stability

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