Active control of natural frequencies of FGM plates by piezoelectric sensor/actuator pairs

An optimization strategy is presented for modifying the dynamic characteristics of functionally graded material (FGM) plates which are actively controlled by piezoelectric sensor/actuator (S/A) pairs. A finite element (FE) model is developed for static and dynamic analysis of FGM plates with collocated piezoelectric sensors and actuators. In this model, the feedback signal to each actuator patch is implemented as a function of the electric potential in its corresponding sensor patch in order to provide active control of the FGM plate in a closed loop system. Using the proposed FE model, a method based on the first-order and second-order approximations in a Taylor expansion is developed to calculate the corresponding changes in the parameters which characterize the piezoelectric patches (i.e. the patch thickness and the feedback gain in each S/A pair) in order to achieve the desired eigenfrequency shifts in the FGM plate. An FGM plate with eight separate S/A pairs is considered as a case study. A sensitivity analysis is initially performed to identify the S/A pairs which have the most influence on the natural frequencies of the plate. The proposed method is used to find a sequence of feedback gains for shifting the natural frequencies to the desired level