Active vibration control of piezoelectric laminated beams with electroded actuators and sensors using an efficient finite element involving an electric node

This paper presents an efficient finite element (FE) model for the active vibration control response of smart laminated beams integrated with electroded piezoelectric sensors and actuators. The FE model is based on an efficient layerwise theory with a quadratic variation of electric potential across the piezoelectric layers. The beam element has two conventional nodes and one electric node, which has no physical coordinate. The electric potential degrees of freedom (DOF) at the electroded piezoelectric surfaces are attached to the electric node which is connected to multiple elements belonging to the same electroded surface. This models the equipotential surface of the electroded sensors and actuators conveniently, and eliminates the cumbersome task of averaging the electric DOF over the surface. The control system is designed using a reduced-order modal state space model. The constant gain velocity feedback (CGVF) and optimal control strategies are studied for smart composite and sandwich beams with single-input-single-output (SISO) and multi-input-multi-output (MIMO) configurations under step and impulse excitations. The numerical study for CGVF control is performed on cantilever smart beams with both conventionally and 'truly' collocated actuators and sensors. The reasons for experimentally observed instability in CGVF control with conventional collocated sensors and actuators is explained. The effect of multiple segmentation of electrodes on the control performance is investigated.