Internally pressurized radially polarized piezoelectric cylinders

The piezoelectric phenomenon has been exploited in science and engineering for decades. Recent advances in smart structures technology have lead to a resurgence of interest in piezoelectricity, and in particular, in the solution of fundamental boundary-value problems. In this paper, we develop an analytic solution to the axisymmetric problem of an infinitely long, radially polarized, radially orthotropic piezoelectric hollow circular cylinder. The cylinder is subjected to uniform internal pressure, or a constant potential difference between its inner and outer surfaces, or both. An analytic solution to the governing equilibrium equations (a coupled system of second-order ordinary differential equations) is obtained. On application of the boundary conditions, the problem is reduced to solving a system of linear algebraic equations. The stress distributions in the cylinder are obtained numerically for two typical piezoceramics of technological interest, namely PZT-4 and BaTiO3. It is shown that the hoop stresses in a cylinder composed of these materials can be made virtually uniform throughout the cross-section by applying an appropriate set of boundary conditions.