Applied theory of bending of a functional-gradient bimorph

This paper presents a study of the stress-strain state and distribution of the electric field in a functionally gradient bimorph piezoelectric plate during its cylindrical bending. It is assumed that the layers are made of porous ceramics, the volume fraction of porosity of which varies so that its effective properties have a quadratic dependence over the plate thickness. Based on the Hamilton principle, extended to the theory of electroelasticity, a system of differential equations and boundary conditions was obtained, in which the distribution of the electric potential over the thickness of the layers is considered quadratic, and it is taken as the unknown variable in the middle of the piezoactive layer. The results of a numerical experiment based on the obtained system of equations were compared with the data of finite element modeling.