Free vibrations of simply-supported piezoelectric adaptive plates: an exact sandwich formulation

An exact two-dimensional analytical solution is proposed for the free-vibration analysis of simply-supported piezoelectric adaptive plates. It is based on an original sandwich formulation that considers layerwise first-order shear-deformation theory and quadratic non-uniform electric potential, with no assumptions on electric field and displacement components. Thus, the electric-charge conservation equation is exactly satisfied and the induced potential, hence the electromechanical coupling, is correctly represented. Also, two-dimensional electromechanical equations of motion and generalized piezoelectric constitutive equations, corresponding to introduced stress and electric displacement resultants, are derived and presented for the first time. The proposed approach was numerically validated through modal analysis of several hybrid plates with graphite-epoxy cross-ply substrates and embedded or surface-bonded piezoelectric layers. Compared to available uncoupled and coupled (exact) three-dimensional elasticity (Navier and state space) and finite-element (layerwise and mixed equivalent single-layer/layerwise) solutions, the obtained results were the closest to the exact coupled three-dimensional ones, making the present approach very reliable.