Piezoelectric (PZT) material is an active material with inherent electrical and mechanical coupling characteristics. The application of an electric field causes a mechanical deformation in the piezoceramic, resulting in significant mechanical forces that can be used for structural actuation [1]. Using these forces which can be considered as being concentrated at the edges of the PZT actuators, the vibrations are reduced by modifying the apparent structural impedance. Liang et al. [2] introduced this technique in the analysis of an active material system. Zhou et al. [3] extended this approach to the study of two-dimension PZT-driven structures. An electromechanical impedance-based system modeling technique has been developed in Cheng and Wang [4] to determine the output forces of multiple PZT actuators to produce a known vibration response and to suppress the vibration response at an arbitrary location on the PZT-driven structure.

In this paper in contrast with the existing vibration control methods in which most of the studies done to date have focused on different control strategies or being limited to the straightforward calculation of vibration responses, the E/M admittance data are used to control the vibration response. The E/M admittance is the inverse of the E/M impedance and it is one of the latest technique to model the interaction between the actuator and the structure. The major advantage of this method is that multiple locations can be tried with just one solution of the host structure's vibration problem. This is possible because the structure's mechanical impedances can be formed without the presence of the actuator in the model. This ability to easily try out multiple actuator locations helps the design engineer to maintain a high degree of physical insite into what is happening. In addition, this technique seems to have very good agreement with experimental measurements and it will be much easier to measure its variation in a given frequency range.

The design and analysis of large complicated structures with integrated PZT patches requires the development and implementation of finite element modeling [5]. In the present paper the concept of E/M admittance in connection with the finite element formulation is employed to produce a given, desired vibration response reduction. The proposed methodology leads to the computation of the required electric voltages, which give "secondary forces", to cancel the response caused by the external force, although these "secondary forces" are now produced by the PZT patches. In particular, the idea of this approach can be considered from the point of view of an inverse problem and an extension of a recent work of the present authors [6]. The solution of this inverse problem is achieved in a MATLAB [7] optimization environment minimizing the RMS residual errors between the computed and the desired E/M admittance signature in a pre-selected frequency range. To describe the dynamic response of the host structure and PZT patches, the commercial software package COMSOL 3.2a [8] is used to build and simulate a mathematical model.

1

B. Jaffe and W.R. Cook, "Piezoelectric Ceramics", Academic Press, 1971.

2

C. Liang, F.P. Sun and C.A. Rogers, "An Impedance Method for dynamic analysis of active material system", ASME J. Vibr. Acoust., 116, 121-128, 1994. doi:10.1115/1.2930387

3

S.W. Zhou, C. Liang and C.A. Rogers, "An impedance-based system modeling approach for induced strain actuator-driven structures", ASME J. Vibr. Acoust., 118, 323-331, 1996. doi:10.1115/1.2888185

4

C.C. Cheng and P.W. Wang, "Applications of the impedance method on multiple piezoelectric actuators driven structures", ASME J. Vibr. Acoust., 123, 262-268, 2001. doi:10.1115/1.1362322

5

J.W. Kim, V.V. Varadan and V.K. Varadan, "Finite element modeling of structures including piezoelectric active devices", Int J. Num. Meth. Engng., 40, 1-16, 1997. doi:10.1002/(SICI)1097-0207(19970315)40:5<817::AID-NME90>3.0.CO;2-B

6

C.P. Providakis, M.E. Voutetaki, M.E. Stavroulaki and D.-P.N. Kontoni, "FEM Modeling of electromechanical impedance for the analysis of smart damping treatments", Proceeding of first CISSE 2006, November 2005. doi:10.1007/1-4020-5261-8_22

7

MATLAB, The Mathworks Inc. Users Guide, www.mathworks.com, U.S, 2005.

8

COMSOL 3.2a Ltd., COMSOL Multiphysics Modeling 3.2a Users Guide, www.comsol.com, London, 2005.

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