Optimal placement and size of piezoelectric patches on beams from the controllability perspective

This paper is concerned with the optimal design of a collocated pair of piezoelectric patch actuators that are surface bonded onto beams. The design involves selecting the optimal locations and sizes (or lengths) of the piezoelectric actuators based on a controllability perspective. The objective function is referred to as the controllability index, which is the singular value of a control matrix. The index measures the input energy required to achieve a desired structural control by the piezoelectric actuators. The controllability index is dependent on the placement and size of the piezoelectric patches, and thus by maximizing the index the designer can obtain the optimal design of the piezoelectric actuator. As illustrations, various beam examples with a pair of piezoelectric patch actuators are solved and the optimal design characteristics of the actuators are examined.