Shape optimization of piezoelectric energy harvesters of variable thickness

Abstract

Recently, a model of a piezoelectric energy harvester (PEH), based on bimorph Kirchhoff–Love plate of variable shape and constant thickness was developed and subsequently discretized using isogeometric analysis (IGA). The model describes a wide class of non-conventional PEH configurations and can be paired with an optimization algorithm to identify the design shapes with the best outcomes in terms of the produced voltage and power. However, recent studies suggest that devices with variable thickness, in particular, devices of inverse trapezoidal shape, might produce higher power output. In this work, we investigate such possibility by extending the IGA PEH model to plates of variable thickness and performing a detailed parametric study for two families of through-thickness shapes: linear and quadratic. We explore the behavior of the first natural frequency, voltage Frequency Response Function (FRF), power FRF, and stress FRF, with their corresponding relation to the electrical resistance and the change in volume of the PEH. A multi-objective Kriging optimization of the thickness parameters is then performed to maximize the peak amplitude of the FRFs and minimize the volume of the substructure.