Bending–torsional flutter of a cantilevered pipe conveying fluid with an inclined terminal nozzle

Stability analysis of a horizontal cantilevered pipe conveying fluid with an inclined terminal nozzle is considered in this paper. The pipe is modelled as a cantilevered Euler–Bernoulli beam, and the flow-induced inertia, Coriolis and centrifugal forces along the pipe as well as the follower force induced by the jet-flow are taken into account. The governing equations of the coupled bending–torsional vibrations of the pipe are obtained using extended Hamilton's principle and are then discretized via the Galerkin method. The resulting eigenvalue problem is then solved, and several cases are examined to determine the effect of nozzle inclination angle, nozzle aspect ratio, mass ratio and bending-to-torsional rigidity ratio on flutter speed of the system.