Equivalent Circuit Parametrization Utilizing FE Model Order Reduction and its Application to Piezoelectric Generators and Actuators

Equivalent circuits are often the first choice for the modeling of piezoelectric systems, as they allow for the consideration of the complete electro-mechanical system with one or even more modes. The parameters of the equivalent circuit model are identified by a measured or simulated frequency response. In this contribution a method for a direct modal condensation of the equivalent parameters for arbitrary FE structures and loads is described and discussed. First the proposed method is demonstrated for a continuous piezoelectric rod and then applied to discrete finite element models. The derived equivalent circuit has an identical appearance to the classical solution, but additionally allows arbitrarily load conditions. Furthermore, the structure of the derived equivalent circuit depends on whether short- or open-circuited modes are used for the modal expansion. The influence of truncated modes is discussed utilizing residual terms, leading to a better understanding of the circuit parameters. Additionally the model based approaches in the third part an experimental parameter identification procedure for many modes is presented as well. The influence of the load and the quality of the model order reduction are discussed for piezoelectric rods. The methods are demonstrated for a base excited energy harvesting system an ultrasonic grubber.