Structural response of composite plates equipped with piezoelectric actuators

We propose the modelling of piezoelectric elements perfectly bonded on an elastic structure. The study aims at predicting the static and dynamic (vibration) electromechanical responses of the structure. The model is mostly based on the kinematic assumption of the Love–Kirchhoff thin plate theory including shear function with a quadratic variation of the electric potential along the thickness direction of the piezoelectric parts. A variational formulation of piezoelectricity leads to the equations of motion for an elastic plate equipped with piezoelectric elements. An important feature of the present investigation is that the stiffness and inertial contributions of the piezoelectric patch is not neglected. Moreover, the numerical simulations demonstrate the influence of the actuator position on the global and local responses of the elastic plate for two situations (i) bilayer and (ii) sandwich configurations. A number of benchmark tests are considered in order to characterize the plate deformation when applying an electric potential to the piezoelectric patch faces. Plate vibration problem is also presented and the frequencies for the axial and flexural modes are obtained. The spectra of vibration for the plate with a time-dependent electric potential are computed.