Multiple Scattering of Acoustoelastic Waves in Thin Plates for Enhanced Energy Harvesting

Harvesting of acoustoelastic wave energy in thin plates and other structures has recently gained attention from the energy harvesting community. To enhance the wave power generated, researchers have investigated metamaterial-inspired concepts to include funnels, mirrors, and defect-based resonators introduced in the metamaterial’s bandgap. Many of these concepts have been demonstrated experimentally using arrangements of cylindrical stubs mounted on the surface of a thin plate, where such stubs scatter plane and cylindrical waves in such a way as to focus mechanical energy. To support these studies, the authors have recently introduced an experimentally-verified analytical framework for investigating the coupled electromechanical response of a single circular piezoelectric harvester adhered to an infinite plate and excited by a distant harmonic point source. This paper extends these ideas to consider a similar physical system with the addition of multiple cylindrical inclusions. These additions require development of an electromechanically-coupled, multiple scattering formulation of significantly increased complexity. The formulation also includes an electrical circuit model for generating electrical current from incident waves interacting with the piezoelectric domain. Following development, the formulation is applied to the determination of optimal arrangements of scatterers which maximize the electrical power generated. Specifically, an optimization study is carried-out in which twenty-five scatterers are first placed in a semi-elliptical arrangement with the aim of focusing wave energy from one elliptical focus (i.e., source location) onto the other. It is known from past studies that additional side lobes are generated due to truncation of the ellipse, and thus not all of the energy can be focused at single point, as desired. To improve upon this situation, an optimization study is performed in which the aspect ratio of the ellipse is varied, with the goal of optimizing the power harvested from the focal point. Results from the optimization studies show conclusively that the side lobes can in fact be minimized, and that harvested power can be significantly improved.