Active damping of smart piezoelectric plates using variational approach

The control of vibrations in rectangular plates by distributed piezoelectric actuators is studied using a variational approach. An optimization problem is formulated that consists of finding the control voltage applied to distributed piezoelectric patch actuators which suppresses the transient displacements and velocities of plates with least control effort. The solution method is based on a combination of eigenfunction expansion and variational approaches. The method of eigenfunction expansion is used to transform the equation of motion into a number of coupled ordinary differential equations. By utilizing the variational theory an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations. The effectiveness of the methodology is demonstrated by applying it to a square plate subjected to a single actuator.