Flow-induced instability and bifurcation in cantilevered composite double-pipe systems

In the present work, a cantilevered system consisting of two elastically connected fluid-conveying composite pipes is considered. The elastic connection between two pipes is reduced to distributed linear springs. And then the nonlinear governing equations of the system are truncated by Galerkin's method. Subsequently, flutter instability induced by two fluid flows is investigated by solving the eigenvalue issues of the system and performed through the Argand diagrams and stability maps. Also, based on the set of transferred second-order ordinary differential equations, one can readily study the nonlinear dynamics of system in the forms of bifurcation diagrams, time-history diagrams and phase trajectories. In numerical part, linear analysis shows flutter instability may occur to the system as two fluid velocities change, where two pipes are in flutter status simultaneously. Similar to single pipe, it is proved that the system loses stability by Hopf bifurcation in post-flutter region in nonlinear analysis, with motions of two pipes transferring to limit cycle motions together. Besides, abundant dynamical phenomena, e.g. periodic motion and quasi-period motion can be captured in post-flutter region. And it can be found that two fiber orientation approaches of two pipes may break the symmetric stability regions and bifurcation behavior of the system.