Analytical solution for EGP cylinder under internal pressure using Hyper geometric functions

Abstract In this study the hyper-geometric functions such as Whittaker M and Whittaker W, are employed to obtain a closed form solution for exponentially graded piezoelectric (EGP) hollow cylinder subjected to the internal pressure. The material properties except poisson’s ratio and thermal conduction coefficient are assumed to be exponentially distributed along radius. The governing equation in polarized form is shown to reduce to a second-order ordinary differential equation (ODE) with variable coefficients for the radial displacement. The electro-thermo-mechanical induced stresses and the electric potential distributions in the EGP cylinder are investigated for the piezo-ceramic PZT_۴. It is concluded that the inhomogeneity exponent μ plays a substantial role in radial and circumferential stress distributions. Therefore, results of this investigation can be used for optimum design of EGP thick-walled circular cylinders. Keywords: PZT۴, Analytical Solution, electric field, cylinder