Enhancing elastic energy focusing in multimode strain regions via Bayesian optimization of gradient-index phononic crystals for energy harvesting

Abstract

Metamaterials composed of gradient-index (GRIN) phononic crystals (PnCs), which contain unit cells whose sizes vary perpendicular to the direction of wave propagation, serve as a means of focusing elastic waves for energy harvesting. Owing to the finite wavelength of the propagating wave, GRIN PnCs localize the wave within a finite-sized region, which experiences multimodal strains instead of focusing on a single focal point with a single mode of strain. Consequently, the energy harvesting of elastic waves across a localized, finite region has recently gained research interest. This is due to the advantage of harvesting more energy through a properly designed piezoelectric energy harvester (PEH) that is larger than the wavelength of the elastic wave. However, the design of unit cells in GRIN PnC has been predominantly limited to simple shapes. This study introduces random hole shapes in GRIN PnC to enhance the intensity of elastic energy localization across targeted finite-sized region, utilizing a data-efficient surrogate model through Bayesian optimization (BO). Additionally, the developed BO method identifies a unit cell design that offers wave focusing intensity comparable to that of benchmark deep neural network (DNN)-based optimization, while requiring only 5.9% of the dataset. This advancement in wave localization significantly enhances the wave localization intensity in the target region by 36% and improves power generation by up to 1.5 times compared to GRIN PnC design with simple circular hole. © 2026