Vibration mitigation of a rotating beam under external periodic force using a nonlinear energy sink (NES)

In this paper, the performance of a smooth nonlinear energy sink (NES) to mitigate vibration of a rotating beam under an external force is investigated. The rotating beam is modeled using the Euler-Bernoulli beam theory, and the centrifugal stiffening effect is considered. It is assumed that the nonlinear energy sink has a linear damping and an essentially nonlinear (nonlinearizable or cubic) stiffness. Required conditions for occurring Hopf bifurcation, saddle-node bifurcation and strongly modulated responses (SMR) in the system are investigated. The most important parameter to study NES performance is SMR occurrence range in the detuning parameter span. Effects of position and damping of the NES and magnitude of the external force on the vibration mitigation of the rotating beam are studied. The Complexification-Averaging and the Runge Kutta methods are employed for analytical and numerical investigations, respectively. Finally, the efficiency of an optimal linear absorber and an optimal NES in the vibration mitigation of the rotating beam are compared. It is shown that the best range for the parameters of the NES is the one in which SMR and weak modulated response occur simultaneously. Furthermore, the best position for connecting the NES to a rotating beam is at the beam tip.