Bending-torsional instability of a viscoelastic cantilevered pipe conveying pulsating fluid with an inclined terminal nozzle

In the present study, dynamic stability of a viscoelastic cantilevered pipe conveying fluid which fluctuates harmonically about a mean flow velocity is considered; while the fluid flow is exhausted through an inclined end nozzle. The Euler-Bernoulli beam theory is used to model the pipe and fluid flow effects are modelled as a distributed load along the pipe which contains the inertia, Coriolis, centrifugal and induced pulsating fluid flow forces. Moreover, the end nozzle is modelled as a follower force which couples bending vibrations with torsional ones. The extended Hamilton's principle and the Galerkin method are used to derive the bending-torsional equations of motion. The coupled equations of motion are solved using Runge-Kutta algorithm with adaptive time step and the instability boundary is determined using the Floquet theory. Numerical results present effects of some parameters such as fluid flow fluctuation, bending-to-torsional rigidity ratio, nozzle inclination angle, nozzle mass and viscoelastic material on the stability margin of the system and some conclusions are drawn.