Active Control of the Longitudinal-Lateral Vibration of a Shaft-Plate Coupled System

Abstract

The coupled longitudinal-lateral vibration of a shaft-plate system and its suppression by means of a feedback control scheme are discussed. A simplified model of the system is established through synthesis of frequency response functions (FRFs) and verified with the finite element method (FEM). This analytical model describes the coupled longitudinal-lateral vibration of the system induced by longitudinal periodic excitation at the free end of the shaft. Based on this model, vibration control via longitudinal actuation on the shaft and active vibration cancellation are studied. The active control scheme is based on an adaptive feedback scenario and a novel mechanism of adaptation of the controller’s gain, which is proposed for time-varying dynamics induced by the variation of the axial spring stiffness. Simulation results have demonstrated that the control scheme is effective in attenuating vibration of the system. Furthermore, axial actuation on the shaft is able to cancel the effect of the longitudinal disturbance acting at the free end of the shaft and consequently reduces the internal forces as well as the vibration in the plate. However, deviation of the actuation force from the shaft axis will deteriorate control of the lateral vibration and sufficiently small deviation needs to be guaranteed.