Electromechanical behavior of a piezoelectric plate lying on a viscoelastic foundation

By state space vector and Fourier series, an analytical solution for a piezoelectric plate lying on a viscoelastic foundation is presented in this paper. The uniform distributed or concentrated electromechanical loads on partially electroded piezoelectric plate surface are considered and the relationship between the electromechanical behavior and the structural/material parameters are extensively studied. The results reveal that, the mechanical displacements increase with time in the case of mechanical effect dominates, and the behavior of the piezoelectric plate is similar to the strain creep of elastic plate bending; the behavior is regarded as electric relaxation in the case of electric effect dominates and the deformation in this case is not a simple bending deformation. The results also show that the load distribution on partially electroded plate has an important impact on the behavior. The deflection of the plate nonlinearity increases with the electroded area. It is also found that there are stress and electric field concentrations close to the electrode coverage, and the concentrations are even severe under point electric charge or concentrated force load conditions. Moreover, elastic foundation with high viscosity is found to be benefit to reducing these local effects. The results also show that the stresses and electric potentials vary with plate thickness distinctly when the length-to-height ratio increases. For thin plates (L/H>;6), the stresses and electric potential vary linearly across the thickness. For thick plates (L/H<;60;6), they vary nonlinearly across the thickness, and the viscoelastic foundation has a positive effect to such nonlinearity. It means we can hardly use layer-wise or low order shear plate theories when dynamic response of piezoelectric plate on viscoelastic foundation is considered.