An equivalent model for smart beams with debonded piezoelectric patches

An equivalent model for smart beams with partially debonded piezoelectric actuator/sensor patches is presented to analyze the effect of the actuator debonding on both open loop and closed loop behaviors. To properly model the short debonded part of the actuator in the debonding region, both moment inertia and transverse shear effect are taken into account. Both displacement continuity and force balance are guaranteed by imposing continuity conditions at the interfaces between the debonded and perfectly bonded regions. The eigenvalue problem for the actively controlled beam with partially debonded actuator patches is derived. The effect of the actuator debonding on the modal shapes is investigated through an example, and the additional modal shapes induced by the debonding are also examined. Furthermore, a scheme of restoring the debonding degenerated active control is given based on real-time frequency updating in the controller, and both theoretical and experimental investigation on the control restoration are carried out. Comparison with the full model and the experiment shows that the equivalent model is effective for beams controlled by debonded piezoelectric actuators and sensors.