Parametric study and shape optimization of Piezoelectric Energy Harvesters by isogeometric analysis and kriging metamodeling

Piezo-electric energy harvesters (PEHs) are widely used to recycle waste vibrations for powering small electronic devices. In this work, the performance of PEHs of non-conventional shapes is studied with the aim to optimize their design. A PEH is modeled as a bimorph cantilever Kirchhoff-Love plate subjected to base acceleration. The shape is described by Non Uniform Rational B-Splines (NURBS), and the problem is solved by the isogeometric analysis (IGA). Accuracy of the IGA solutions is demonstrated on two benchmark problems. Then, we conduct a parametric study to investigate the effect of shape perturbations on the fundamental frequency, the peak amplitude of the frequency response function (FRF) and the peak amplitude of the FRF per unit of area. Next, we build the Kriging meta-model to obtain the boundary shapes that maximize the peak amplitude of the FRF and the peak amplitude of the FRF per unit of area for a target frequency. The optimization is performed for three cases: with a fixed tip mass, without a tip mass and with a tip mass being one of the design parameters.