Control Stability Analysis of Smart Beams with Debonded Piezoelectric Actuator Layer

Abstract

Debonding of a piezoelectric actuator or sensor layer in an actively controlled structure may significantly affect its closed-loop control and even collapse the active control. Investigation of the effects of the debonded piezoelectric layer on the control stability of smart structures is very important. A state-equation-based method is presented to investigate the control stability of the beams controlled by partially debonded piezoelectric actuator and sensor layers. An analytical model of a beam with a debonded piezoelectric layer is given, in which the debonding of the piezoelectric layer is modeled by considering the adhesive layers. Both displacement continuity and force equilibrium conditions are imposed at the interfaces between the debonded and perfectly bonded regions. Based on this model, a characteristic equation for the controlled structure with debonded piezoelectric actuators and sensor is derived, from which the eigenvalues of the controlled system can be obtained. The control stability of a controlled mode can be evaluated by examining the sign of the real part of the corresponding eigenvalue. The simulation results show that even a 5% edge debonding of the actuator layer can destabilize the cantilevered beam controlled by an actuator/sensor pair, whereas a beam controlled by a self-sensing actuator layer can tolerate much larger edge debonding of the piezoelectric layer. More significant changes can be found in both the damping coefficient and the frequency of the mode whose frequency is close to one of the modal frequencies of the debonded part of the actuator.