¹ Department of Science Research, Hebei University of Engineering, Handan, China
² College of Civil Engineering, Hebei University of Engineering, Handan, China

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Abstract—The study of the applications of piezoelectric materials in the active vibration control of flexible structures has been ongoing for more than a decade. Based on the Linear Quadratic Gauss (LQG) optimal control method, the paper introduces an effective procedure to suppress the vibration of flexible structures with the sensors/actuators are symmetrically collocated on both sides of the same position on the host structure. The model of a piezoelectric intelligent cantilever beam is built by the application of ANSYS software, and through the modal analysis, the first 4 ranks of modal frequencies and vibration shapes are extracted. The D-optimal design principle is adopted which is an optimal method which chosen by the maximum determinant of Fisher Information Matrix as the criteria function. Studies on the modal vibration shapes and dynamic characteristics of the structure, and converts the selected modes into a unitary form by a simple method, the optimal position of the piezoelectric elements can be confirmed by the mode shapes of the structures. Finally, the paper takes a piezoelectric cantilever beam as an example and gives the step response curve of the system at the two circumstance of when piezoelectric elements are bonded onto the optimal position of the host structure and not, the simulation results show the effectiveness of the method in this paper.

Index Terms—piezoelectric materials, intelligent structures, LQG optimal control, D-optimal design principle, active vibration control, ANSYS software

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Cite: Jingjun Zhang, Lili He, and Ercheng Wang, " Active Vibration Control of Piezoelectric Intelligent Structures," Journal of Computers vol. 5, no. 3, pp. 401-409, 2010.