Comparison of Different Impedance-Based Models for Out-of-Phase Actuation of Actuators Bonded on Ring Structures

Abstract

Two different impedance models representing out-of-phase actuation of induced strain actuators bonded to the surface of a circular ring are compared. The first impedance model derivation is based on the use of eigenfunctions to determine the structural impedance of the ring, while the second model is based on modal expansion. A discussion of the proper way to apply the equivalent loading due to the out-of-phase actuation is done. A finite element analysis using piezoelectric elements is performed. A comparison between the impedance modeling and the more conventional static modeling approach is also made. Based on the governing equations derivation, the equivalent actuator loading can be included either as an induced uniform moment over the footprint of the actuators or as an external line moment at the ends of the actuators. A dynamic finite element analysis is performed using ANSYS 5.0 piezoelectric elements. The structural responses predicted by both eigenfunctions and modal expansion impedance models show a good match with those obtained using finite element analysis.