Effects of Piezoactuator Failure on Active Control of Beam Vibration

Relatively large, alternating in time, operational deformations of distributed piezoelectric actuators used in active vibration control may create a hazard of material degradation and damage of the actuator/host structure coupling. In the presented study a beam-like system with a surface mounted piezoelectric sensor/actuator pair operating in a closed loop with velocity feedback is analysed. The applied actuator is a piezoelectric fiber composite (PFC) with PZT (lead-zirconate-titanate) fibers aligned and polarized longitudinally. The uniform field method based on the rule of mixtures is used to determine the effective properties of the piezocomposite. Two types of the actuator failure are taken into account. The first relates to the edge delamination modelled as a significant reduction of the adhesive interlayer shear stiffness. The second relates to the PFC material degradation, which is regarded as a softening of the matrix material surrounding PZT fibers. It is assumed that the damaged adhesive region of the constant shear stiffness extends uniformly across the actuator from its ends to the centre. In analysis the beam is divided into sections due to its geometry, external loading and the damaged regions supposed. The governing equations of the activated beam sections are coupled equations related to the electrically induced tension/compression of the actuator and bending of the beam, respectively. The obtained steady-state solution satisfies boundary conditions and continuity conditions at the borders of the beam and the actuator sections. Results of calculations show the effects of stiffness degradation of both the bonding interlayer and the piezocomposite matrix material on the beam deflection and transmitted shear stresses. Besides, dynamic responses of the active system regarding changes of the control effectiveness are numerically investigated and discussed.