Piezoelectric control of the static behaviour of flextensional actuators with constricted hinges

The objective of this paper is to present the mathematical modelling and computational testing of the static operational performance and effectiveness of flextensional actuators comprised of two rectilinear or initially deflected beams placed equidistantly from a centrally located piezoceramic stack in the form of a rod. The beams are mounted by stiff links with an offset to a piezoelectric transformer. A monolithic hinge lever mechanism is applied by cutting constricted hinges at the links to generate and magnify the in-plane displacement created by the application of a voltage to the piezorod. Structures of such a type have been commonly used as passive or active actuators since the manufacturing of the mechanism’s prototypes in the form of Moonie or cymbal actuators. An analytical model of the actuator is developed on the basis of stationary values of the total potential energy principle with the use of the von Kármán non-linear strains theory. During the numerical computations, the deflection and internal axial force generated by both the externally distributed load and the the application of an electric field are determined by changing the actuator properties such as the distance between the beams and the rod, the amplitude of the beam’s initial displacement as well as the stiffness of the constricted hinges. Additionally, the application of structure prestressing is considered to avoid an undesired stretching of the piezo stack. It has been shown that for the flextensional actuator with a very high flexibility of constricted hinges, the generated transverse displacement is limited by the maximum electric field as the characteristic property for each piezoceramic material. A vast number of numerical results exhibit the mechanical responses of the transducer of different geometrical and physical properties to piezoelectric stimulation; this has potential applications in the design process of such actuators.