The electromechanical behavior of a piezoelectric actuator bonded to a graded substrate including an adhesive layer

A theoretical model of a thin piezoelectric actuator attached to a graded half plane with an adhesive layer under an electrical loading is analyzed in the present paper. The shear modulus of the graded half plane is assumed to vary exponentially along its depth. The governing integro-differential equation for both the perfectly bonded condition and possible imperfect one is studied and solved numerically. The interfacial shear stress and the axial stress in the actuator affected by the inhomogeneity of the graded substrate, the adhesive layer, the debonding condition, etc are comprehensively studied. It is found that the electromechanical behavior of the piezoelectric actuator/substrate system can be modified by tuning the material and geometric parameters of both the actuator and the graded substrate. The results should be helpful for the design of smart systems and structures with thin piezoelectric actuator and functionally graded materials.