Static responses of a multilayered anisotropic piezoelectric structure to point force and point charge

This paper studies three-dimensional (3D) static responses of a multilayered anisotropic piezoelectric structure due to a point force and point charge. The materials in each layer are homogeneous, generally anisotropic, and linearly piezoelectric, and in general different from one another. The interfaces between adjacent layers are perfectly bonded. The generalized Stroh formalism and two-dimensional (2D) Fourier transforms are employed to find the responses in terms of a 2D integral. For a layered structure made of ten alternating layers of piezoelectric AIN and InN on an InN substrate, we show that the responses due to the point force and point charge are greatly influenced by the material layering, showing complicated patterns through the layer thickness. Furthermore, the responses exhibit the asymptotic behavior in the case of homogeneous infinite space/half-space in a very short distance to the point source, about one tenth of the layer thickness. The complicated responses due to the layered heterogeneity dictate the need for a general 3D analysis in the design of such smart structures.