Application of PGD on Parametric Modeling of a Piezoelectric Energy Harvester

In this paper, a priori model reduction methods via low-rank tensor approximation are introduced for the parametric study of a piezoelectric energy harvester (EH). The EH, composed of a cantilevered piezoelectric bimorph connected with electrical loads, is modeled using 3-D finite elements (FEs). Solving the model for various excitation frequencies and electrical load using the conventional approach results in a large size problem that is costly in terms of CPU time. We propose an approach based on the proper generalized decomposition (PGD) that can effectively reduce the problem size with a good accuracy of the solutions. With the proposed approach, field variables of the coupled problem are decomposed into space, frequency, and electrical load associated components. To introduce PGD into the FE model, a method to model the electrodes and electrical charges in the EH is presented. Appropriate choices for stopping criterions in the method and accelerating the convergence through updating after each enrichment are investigated. The proposed method is validated through a representative numerical example.