Electrostatic Analysis of Functionally Graded Piezoelectric Cantilevers

Based on the theory of elasticity, the electrostatic behavior of functionally graded piezoelectric cantilevers is studied where the nonlinear profile of the piezoelectric parameter g ₃₁ is taken into account. Theoretical solutions and numerical results under both plane strain and plane stress conditions are obtained. It is found that the theoretical solutions obtained in the present study under the plane stress condition agree very well with both the finite element results and Hauke's experimental findings. Although no suitable experimental results under the plane strain condition can be used for a comparison at present, the theoretical solutions obtained in the present study under this loading case also agree very well with the numerical findings. At the end of this study, a general formula is suggested that can be used to calculate the tip deflection of a functionally graded piezoelectric actuator when neither the plane stress condition nor the plane strain condition is satisfied.