Impedance-Based Modeling of Actuators Bonded to Shell Structures

Abstract

When discrete piezoelectric actuator patches bonded on structures are used for active shape, vibration, and acoustic control, the desired deformation field in the structure is obtained through the application of localized line forces and moments generated by expanding or contracting bonded piezoelectric actuators. An impedance-based model to predict the dynamic response of cylindrical shells subjected to excitation from surface-bonded induced strain actuators is presented. The essence of the impedance approach is to match the actuator impedance with the structural impedance at the ends of the actuators, which will retain the dynamic characteristics of the actuators. A detailed derivation of the actuator and structural impedance is included. It is found that the actuator's output dynamic force in the axial and tangential direction are not equal. Various case studies of a cylindrical thin shell are performed to illustrate the capabilities of the developed impedance model. Out-of-phase actuation is shown to be the most efficient in exciting the lower order bending modes of shell structures. The paper is concluded with a finite element analysis verification of the derived impedance model.