| Piezoelectric elements can be used as sensors and induced strain actuators in active vibration control systems. Since the positioning of piezoelectric elements can affect control performance greatly, it has to be carefully determined, In this dissertation, detailed theoretical analysis and brief experimental study is made on the optimal positioning of piezoelectric elements for active vibration control applications.In theoretical analysis, Finite Element Method is firstly used to solve the mechanical-electric coupling problems in a flexible plate with piezoelectric elements and to obtain structural vibration modal shapes. Focusing on collocated type of piezoelectric sensors/actuators, the maximum determinant of Fisher Information Matrix Criteria is chosen as the optimization function and then simplified to determine an optimal principle for the best location of piezoelectric elements. Based on the simplified principle, the modal shapes of selected structural modes are converted into modal strains. To minimize the calculation error, curve-fitting technique is used in the process. The modal strains are summed together to determine the global distribution of the structure for selected vibration modes so that the position of piezoelectric elements could be optimally determined according to the simplified optimization principle.At last, an active vibration control system is set up for a flexible epoxy-glass composite plate. Piezoelectric sensors and actuators are bonded to the structure according to analytical results for the first a few vibration modes. Closed-loop experiments have also been conducted. The effectiveness of theoretical analysis has been verified by experimental results.The method proposed in this dissertation is an improvement to previous investigations. It combines Finite Element Method and the optimal design of piezoelectric elements together, and therefore can be applied to the vibration analysis and design of complex smart structures.
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