Decay rates for a transversely isotropic piezoelectric hollow circular nanocolumn

Abstract

The decay rate of the elastic and electric fields along the growth direction of a transversely isotropic piezoelectric hollow or solid circular nanocolumn is investigated by developing the general solution for the corresponding three-dimensional problems. While the proposed method can be applied to asymmetric deformation, only axisymmetric deformation is considered in this paper. The derived results are first verified by comparison with existing elastic isotropic solutions. Then, the locus of smaller roots is plotted for different wall thicknesses, including also the limiting solid circular nanocolumn case. Owing to the material anisotropy and the coupling between the mechanical and electric fields, there exists an intriguing interaction of real and complex root loci for the torsionless axisymmetric deformation. The numerical results also show that the geometric parameter, material anisotropy, and piezoelectricity of the hollow or solid nanocolumn can substantially influence the decay rates, which can be applied to the strain relaxation analysis in novel semiconductor structures containing self-assembled nanoposts and nanocolumns.