Nonlinear vibration and dynamic stability analysis of an axially moving beam with a nonlinear energy sink

This paper investigates the forced vibration and dynamic stability of a simply supported axially moving beam coupled to a nonlinear energy sink with the aim of passive vibration control. The equations of motion of the coupled system are solved using harmonic balance and pseudo-arc-length continuation methods. The impacts of the beam velocity, excitation frequency, and magnitude of the external force on the behavior of the system are studied. It is observed that the absorber should be designed in a way that the strongly modulated response (SMR) and weakly modulated response occur in the response of the system when the moving beam is excited near its primary resonances. The results show that the saddle node and Hopf bifurcations boundaries, as well as the absorber performance, would be reduced by increasing the beam velocity. It is also realized that the excitation frequency in which the response of the system enters the SMR region is decreased by enhancing the beam velocity, as well as the magnitude of the external force. Using the results of this paper, one can readily simulate the vibration control of simply supported moving beams utilizing a nonlinear energy sink.