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

Abstract

This paper presents an efficient finite element (FE) model for the active vibration controlresponse of smart laminated beams integrated with electroded piezoelectric sensors andactuators. The FE model is based on an efficient layerwise theory with a quadraticvariation of electric potential across the piezoelectric layers. The beam element hastwo conventional nodes and one electric node, which has no physical coordinate.The electric potential degrees of freedom (DOF) at the electroded piezoelectricsurfaces are attached to the electric node which is connected to multiple elementsbelonging to the same electroded surface. This models the equipotential surface of theelectroded sensors and actuators conveniently, and eliminates the cumbersome task ofaveraging the electric DOF over the surface. The control system is designed using areduced-order modal state space model. The constant gain velocity feedback (CGVF) andoptimal control strategies are studied for smart composite and sandwich beams withsingle-input–single-output (SISO) and multi-input–multi-output (MIMO) configurationsunder step and impulse excitations. The numerical study for CGVF control is performed oncantilever smart beams with both conventionally and ‘truly’ collocated actuators andsensors. The reasons for experimentally observed instability in CGVF controlwith conventional collocated sensors and actuators is explained. The effect ofmultiple segmentation of electrodes on the control performance is investigated.