Twisting and bending of pretwisted piezoelectric plates

The blades of helicopter rotors and turbine blades can be modeled as pretwisted beams/plates or shells. The angle of pretwist can affect the performance of these turbo-machinery systems. Being able to actively change the angle of pretwist even moderately can enhance or optimize these systems for various modes of operation. To actively change the angle of pretwist, a torque has to be introduced to the pretwisted member that will cause it to either increase (further twisting) or decrease (untwisting) the existing pretwist angle of the blade. By building piezoelectric layers into the blade/plate and applying a controlled voltage the shape and or position of the cross-section can be changed. Due to the coupling of both bending modes and the extensional and torsional modes in pretwisted members a piezoelectric material that can induce extension in the plate can also be used to twist or bend the shape of the plate. In this study a cantilevered pretwisted plate bonded to two piezoelectric layers on the outside is modeled using 3-D linear elastic finite element approach with the pretwist built into the formulation. The static response of the pretwisted plate to a uniform voltage applied to the piezoelectric layers is investigated. Twisting and bending of the plate is accomplished through coupling of the bending modes and extensional-torsional coupling. The piezoelectric layer itself is not isotropic and so introduces additional coupling into the system.