Two-dimensional exact analysis for piezoelectric curved actuators

In this paper, both piezoelectric curved multi-layered actuators and functionally gradient curved actuators made of functionally gradient materials (FGM) are investigated. The exact solutions of mechanical and electrical fields of the above two types of curved actuators are obtained on the basis of the theory of elasticity. Comparisons indicate that deflections of gradient curved actuators are slightly smaller than those of curved multi-layered actuators; however, the internal normal stresses of former ones are significantly smaller. Moreover, as the number of layers increases and the depth of layers decreases, the limitation of the results of a multi-layered actuator asymptotically approaches the results of gradient actuators. It is also found that, in general, non-zero stresses exist in the gradient piezoelectric curved actuator when the actuator is subject to an external voltage. This phenomenon is quite different from the results obtained for the gradient piezoelectric flat actuator. Finally, comparisons with the FGM results are performed and good agreements are shown.