Piezoelectric Behavior of an Inhomogeneous Hollow Cylinder with Thermal Gradient

Abstract

An analytical solution to the axisymmetric problem of a radially polarized, radially orthotropic piezoelectric hollow cylinder with a thermal gradient and subjected to various boundary conditions is developed. The elastic coefficients, piezoelectric coefficients, stress-temperature moduli, dielectric coefficient, pyroelectric coefficients, thermal conductivity coefficient, and thermal expansion coefficients of the hollow cylinder are assumed to be graded in the radial direction according to a simple power-law distribution. The governing second-order differential equations are derived from the equilibrium equation, the charge equation of electrostatics, and steady state heat transfer equation through the radial direction of the inhomogeneous hollow cylinder. The displacement, stresses, and potential field distributions in the cylinder are examined. The influence of the inhomogeneity parameter on the numerical results is investigated.