The dynamic coupling and power flow in asymmetric piezoelectric bending actuators

An analytical model is developed for an asymmetric piezoelectric bending actuator consisting of a slender beam and a piezoelectric actuator patch that is bonded to one side of this beam. For the kinematical model of the laminate section of this actuator, the piezoelectric patch and the substrate beam are assumed to undergo bending as well as longitudinal deformation, while the bonding layer is modeled as purely shear elastic. In addition, this model accounts for the dielectric properties of the bonding layer. The boundaries of the actuator are described with dynamic stiffness matrices, which are given here for the two special cases of a free beam and for an ideally damped beam. The actuator losses are accounted for by using complex material parameters. Both special cases are verified experimentally for a free beam and for an ideally damped beam. The input electrical impedance of the actuator as well as the beam deflection are in excellent agreement with the model. The model is further used to optimize the geometrical dimensions of the piezoelectric patch in terms of a maximum power flux into the substrate beam.