Active Stiffening and Active Damping Effects on Closed Loop Vibration Control of Composite Beams and Plates

Abstract

The influences of active stiffening (displacement control) and active damping (velocity control) effects introduced by collocated piezoelectric actuators and sensors on vibration control of composite structures are studied in this paper. A nine-node piezoelectric plate finite element is derived using the first order shear deformation theory to model the distributed actuation and sensing numerically. An output feedback control strategy is developed with the linear quadratic regulator theory in modal domain to estimate the optimal gains for different control efforts off line. Further, the developed control procedure is realised experimentally in an active control system. As an illustration, the effects of both displacement and velocity controls are shown on a CFRP beam. A periodic excitation is applied as disturbance and the amplitude response control is achieved by controlling the displacement and velocity of the vibrating system. It is observed that the active stiffening effect through displacement control is more effective for modes that have the amplitude of vibration relatively high. However, the active damping effect introduced by velocity control is efficient in the third mode control, which shows that a small amount of active damping is sufficient to stabilise a mode having comparatively less amplitude of vibration. Influence of active stiffening on the closed loop system frequency is observed to be more than that of active damping effect.