This study on the vibration control of smart piezoelectric composite plates investigates the effect of the stretching-bending coupling of the piezoelectric sensor/actuator pairs on the system stability of smart composite plates. Based on first-order shear theory and consistent methodology, a smart isoparametric finite element is formulated and the classical negative velocity feedback control method is adopted for the active vibration control analysis of smart composite plates with bonded or embedded distributed piezoelectric sensors and actuators. It is shown mathematically and demonstrated numerically that generally the coupling effect tends to result in system instability unless the sensor/actuator pairs are collocated or the plate simply supported. The result of this study can be used to aid the placement of piezoelectric sensor/actuator pairs of smart composite plates as well as for robust controller design.

In this paper on finite element linear quadratic regulator (LQR) vibration control of smart piezoelectric composite plates, we propose the use of the total weighted energy method to select the weighting matrices. By constructing the optimal performance function as a relative measure of the total kinetic energy, strain energy and input energy of the system, only three design variables need to be considered to achieve a balance between the desired higher damping effect and lower input cost. Modal control analysis is used to interpret the effects of three energy weight factors on the damping ratios and modal voltages and it is shown that the modal damping effect will increase with the kinetic energy weight factor, approaching √2/2 as the strain energy weight factor increases and decrease with the input energy weight factor. Numerical results agree well with those from the modal control analysis. Since the control problem is simplified to three design variables only, the computational cost will be greatly reduced and a more accurate structural control analysis becomes more attractive for large systems.