Closed loop finite element modeling of active structural damping in the frequency domain

This is the first attempt at closed loop numerical simulation in the frequency domain using control theory and detailed finite element modeling of a smart structure with embedded piezoelectric sensors and actuators. A three-dimensional finite element model is developed for analysing the response of active damping structures to steady state input in a closed loop. Control authority resulting from charge or voltage as the active control force applied to the actuator are studied for the first two modes of vibration of a flexible beam. Comparison between constant velocity feedback control and constant displacement feedback control is also investigated. By applying an appropriate feedback control using the voltage generated by the piezoelectric sensor, substantial reduction of the resonance amplitude peaks of the cantilever beam is obtained. Numerical results are present which indicate the increase in damping as the feedback gain is increased. The results obtained clearly demonstrate the significant and broad band attenuation capability of piezoelectric sensors and actuators. A major advantage of active damping is to reduce the resonance peak without significantly altering the structural mass or stiffness.