Nonlinear vibration control of a cantilevered fluid-conveying pipe using the idea of nonlinear energy sink

Different from the both-end supported pipe conveying fluid as a conservative system, the cantilevered fluid-transporting pipe is a non-conservative system and its dynamic behavior is more complex with flutter instabilities when the flow velocity is beyond the critical value. Indeed, controlling such a flutter system is always challenging in engineering applications. This study presents nonlinear vibrations of cantilevered pipe conveying fluid passively controlled via a nonlinear energy sink (NES). Based on the Hamilton principle, the nonlinear dynamic equations coupling with the NES are derived and discretized using high-order Galerkin method. It is indicated that increasing the mass and damping of NES results in an increase in critical flow velocity. Importantly, the optimal placed position of NES where the critical flow velocity is highest has a strong relationship with the pipe's flutter mode. In the following, the nonlinear analysis shows the dynamic controlling effect on vibration amplitude of the pipe can be classified to three suppression regions with increasing the flow velocity. Varying the mass, damping and stiffness of NES is followed by variations of the suppression regions which are associated with controlling effects and dynamic behaviors of the pipe system.