Modeling and nonlinear dynamics of cantilevered pipe with tapered free end concurrently subjected to axial internal and external flows

The current study aims to investigate stability and nonlinear dynamics of a cantilevered pipe with a tapered free end concurrently subjected to axial internal and external flows, with the purpose of regulating and controlling the vibration behavior of the pipe. A nonlinear governing equation accounting for the effects of axial internal and external flows on the nonlinear dynamics of the pipe is first established based on the modified Hamilton's principle. Then, a linear analysis is performed to investigate the stability region and instability mode, while considering the effect of length of the tapered free end. The results show that buckling, flutter and combined buckling flutter behaviors can occur with varying the internal and external flow velocities. Subsequently, a nonlinear analysis is conducted to further explore vibration amplitude and oscillation shape of the pipe with a tapered free end. It is found that for different values of internal flow velocity, the pipe displays quite distinct vibration behaviors with increasing external flow velocity. This study is expected to be beneficial for optimizing an underwater propulsion system based on oscillations of an attached pipe through adapting the flow velocity and shape of the free end.