This paper is concerned with the optimal design of a collocated pairof piezoelectric patch actuators that are surface bonded onto beams. Thedesign involves selecting the optimal locations and sizes (or lengths) of thepiezoelectric actuators based on a controllability perspective. The objectivefunction is referred to as the controllability index, which is the singularvalue of a control matrix. The index measures the input energy required toachieve a desired structural control by the piezoelectric actuators. Thecontrollability index is dependent on the placement and size of thepiezoelectric patches, and thus by maximizing the index the designer canobtain the optimal design of the piezoelectric actuator. As illustrations,various beam examples with a pair of piezoelectric patch actuators are solvedand the optimal design characteristics of the actuators are examined.
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