Understanding and finessing nonlinearity in electro-mechanical actuators used for intelligent vibration control

The objectives of this dissertation study are (1) to gain a better understanding of the inherent nonlinearity in commonly-used transduction materials and devices for vibration control, specifically those based the piezoceramic materials, and (2) to understand its impact in the structural vibration control problem. At lower drive levels, nonlinearity in piezoceramics is dominated by irreversible rate-independent hysteresis. In this study, the applicability of and relationship between two rate-independent hysteresis models that have been used to describe hysteresis in piezoceramic transducers is investigated. It is shown that the generalized Maxwell resistive capacitor (MRC) hysteresis model and its inverse are particular subsets of the classical Preisach hysteresis model (CPM). Methods for MRC and inverse MRC online model identification of piezoceramic devices are developed along with an MRC-based framework for calculating continuous hysteretic energy loss for arbitrary loading histories. These developments are facilitated by use of the extensive mathematical framework that has been developed for Preisach models. Experimental studies on 1–3 piezoceramic composites, piezoceramic monolithic wafers and piezoceramic active fiber composites (AFC's) support the theoretical developments and assess their applicability and limitations with respect to commonly-used piezoceramic transducers.; To investigate the “smart material structure” or system with integrated transduction elements and numerous coupled dynamic degrees of freedom, the case of a monolithic piezoceramic wafer bonded to simply supported beam is investigated theoretically and experimentally. To model the hysteretic behavior of the PZT, again the rate-independent generalized MRC model is utilized. The coupled dynamic equations are developed for the nonlinear system consisting of the beam and PZT wafer that can be electrically shunted and/or electrically driven from an external voltage source for improved vibration suppression. Issues of vibratory energy transduction and dissipation in the hysteretic PZT element are investigated. A method of incorporating the MRC model in a feedforward control scheme for hysteresis compensation is also presented. Experimental studies on the simply supported beam structure with PZT support the theoretical developments. Preliminary investigations of passive, adaptive and active control concepts using the nonlinear patch and beam system help to identify areas for future research.