Keywords: piezoelectric actuator, plate vibration, shape and vibration control.

A model for a composite made of piezoelectric elements perfectly bonded on an elastic structure is proposed in this paper. The main goal of the present work is to predict the static and dynamic electromechanical responses of the composite structure under mechanical and electrical loads. More precisely, the study is devoted to the composite structure consisting of a piezoelectric actuator attached onto an elastic plate. The model itself is mostly based on the kinematical assumption of the Love-Kirchhoff thin plate theory including a shear function for the elastic displacement combined with a quadratic distribution for the electric potential through the piezoelectric element thickness [1]. A variational formulation extended to the piezoelectric body is then applied to the present piezoelectric composite to deduce the equations of motion for the reduced model. The set of equations includes the electric charge conservation law. The constitutive equations for the piezoelectric composite are also obtained for the reduced model for the generalized stress and electric charge resultants. An important point of the present approach is that the stiffness and inertial contributions of the piezoelectric element are not neglected. Consequently, the piezoelectric actuator introduces material and geometrical discontinuities leading to some mathematical difficulties [2]. Numerical simulations are performed to illustrate and to accurately characterize the global (elongation, deflection) and local (field distributions) responses of the composite structure in the case of the sandwich configuration (two identical piezoelectric actuators symmetrically attached onto the elastic plate). In addition, the plate vibration is also examined and the frequencies for the axial and flexural modes are obtained [3]. The spectra of the plate vibration with a time-harmonic electric potential are computed. The influence of the geometry and location of the piezoelectric actuator on the static and dynamic (vibration) electromechanical responses is discussed. At last some extensions of the model and applications are proposed.

1

A. Fernandes and J. Pouget, "An accurate modelling of piezoelectric plates. Single-layered plate", Arch. Appl. Mech., 71, 509-524, 2001. doi:10.1007/s004190100168

2

H. Abramovich, "Deflection control of laminated composite beams with piezoceramics layers - close-form solutionsquot;, Composite Structu., 93, 217-231, 1998. doi:10.1016/S0263-8223(98)00104-4

3

A. Fernandes and J. Pouget, "An accurate modelling of piezoelectric multi-layer plates", Eur. J. Mech. A/Solids, 21, 629-651, 2002. doi:10.1016/S0997-7538(02)01224-X

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