Exact analyses for two kinds of piezoelectric hollow cylinders with graded properties

Based on the theory of piezo-elasticity, the paper obtains the exact solutions of functionally graded piezoelectric hollow cylinders with different piezoelectric parameter g31. Two kinds of piezoelectric hollow cylinders are considered herein. One is a multi-layered cylinder with different parameter g31 in different layers; the other is a continuously graded cylinder with arbitrarily variable g31. By using the Airy stress function method with plane strain assumptions, the exact solutions of the mechanic and electrical components of both cylinders are obtained when they are subjected to external voltage (actuator) and pressure (sensor), simultaneously. Furthermore, good agreement is achieved between the theoretical and numerical results, and useful conclusions are given.