On the methodology for evaluation of dynamic effects of a surface bonded piezoelectric patch for active vibration control

Abstract

The current work presents a semi-analytic approach for calculating the influence of surface bonded piezoelectric (PZT) actuators on the free vibration of a flexible beam. A transfer matrix technique, originally developed for analyses of non-proportionally damped flexible beams, was modified to incorporate the PZT actuators' effect. Specifically, the technique's recursive calculations were significantly altered to account for the PZT actuators' tendency to couple the dynamics of node points of the flexible beam. Unlike many analyses of PZT laminated beams, the technique requires no assumptions of the revised modes' shapes, and the limits imposed by saturation voltages were incorporated. The methodology was applied to a vibration suppression application. A simple case of a single PZT patch employing angular velocity feedback was used to demonstrate and validate the calculation methodology. The sensitivities of the beam modes of vibration to the location and control gain of the PZT patch were summarized. The implementation for cases of linear velocity feedback and cases of multiple PZT patches employing mixed feedback laws were also outlined. The calculation methodology is very flexible and is of great utility in the optimization based design of smart structures