Concurrent design of a structure and its distributed piezoelectric actuators

A new concept for a simple arrangement of piezoelectric continuous actuators imbedded in a flexible structure is investigated. The arrangement is used to show the application of a systematic approach to simultaneously find the optimum parameters of a beam for its substructures and actuators. The procedure provides for the deflection of the structure into a desired shape represented by the superposition of its normal modes. Deflection equations allow for incorporation of the stiffness of the piezoelectric layers. Maximum-likelihood estimation and the simulated annealing method have been utilized to minimize the difference between a desired shape and the configuration obtained through a numerical process. Application to a simply supported multilayered beam with a prescribed length and width is presented. The optimum thickness of the layers of the substructure/actuators and the required electric fields for a desired shape of the structure are determined. The paper concludes with discussions on successful results, advantages, and possible modifications of the procedure.