Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine, the investigations on the mechanical responses of the pipes have attracted considerable attention. The fluid-structure interaction (FSI) between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes, especially when the pipe is highly flexible and usually undergoes large deformations. In this work, the geometrically exact model (GEM) for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle. The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow. Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid, which is often encountered in practical engineering. By constructing bifurcation diagrams, oscillating shapes, phase portraits, time traces, and Poincare maps, the dynamic responses of the curved pipe under various system parameters are revealed. The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical. The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors, including periodic and quasi-periodic motions. It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode. For a moderate value of the mass ratio, however, a third-mode flutter may occur, which is quite different from that of a straight pipe system.