Unified mechanical approach to piezoelectric bender modeling
Anewanalytical modeling approach for piezoelectric bending elements is described. The approach is based on the beam theory under quasi-static equilibrium condition. It uses the theory of superposition of piezoelectric action in the bender and external moments and forces acting on the bender. Due to the differential approach, this model is applicable to any geometrical design for which the beam theory holds. The distinction between the piezoelectric action and the external loads makes the model applicable for any boundary conditions. The bottom-up approach from the electrically induced strain in the piezoelectric part enables the determination of stresses and strains at every point in the bender. The effects on internal strain distribution by the different kinds of actuation where demonstrated in an experiment. The resulting model from this approach will be well suited to design and optimize piezoelectric bending actuators for any purpose. The implied calculation of the strain and stress in the modeling allows the dimensioning of actuators that are equipped with strain gauges as well as the calculation of the electrical properties for capacitive transducers.