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Modelling and optimal placement of piezoelectric actuators in isotropic plates using genetic algorithms

Theoretical modelling of the vibration of plate components of a space structure incorporating piezoelectric actuators is presented. The equations governing the dynamics of the plate, relating the strains in the piezoelectric elements to the strain induced in the system, are derived for isotropic plates using the Rayleigh-Ritz method. The developed model was used for a simply supported plate. The results show that the model can predict natural frequencies of the plate very accurately. Two criteria for the optimal placement of piezoelectric actuators were suggested using modal controllability and the controllability Grammian. The model was then used to predict the closed-loop frequency response of the plate for active vibration control studies with optimal locations of actuators successfully obtained using genetic algorithms. Significant vibration suppression was demonstrated using optimal actuator placement algorithm developed.