Vibration Control of Composite Plates via Optimal Placement of Piezoelectric Patches

A simple optimal placement strategy of piezoelectric sensor/actuator (S/A) pairs for vibration control of laminated composite plate is presented, where the active damping effect under a classical control framework is maximized using the finite element approach. The classical direct pattern search method is employed to obtain the local optimum, where two optimization performance indices based on modal and system controllability are studied. The start point for the pattern search is selected based on the maxima of integrated normal strains consistent with the size of the collocated piezoelectric patches used. This would maximize the virtual work done by the equivalent actuation forces along the strain field of an initial state. Numerical simulation using a cantilevered and a clamped composite square plate illustrate the effectiveness of the proposed strategy, where the results coincide with the global optimal layout from exhaustive search for both modal and system controllability indices. The number of trials to reach the optimal position is few compared to an initial blind discrete pattern search approach. The reduced control effectiveness of both plates under constrained input voltages is illustrated.