Design of Piezoelectric Metastructures with Multi-Patch Isogeometric Analysis for Enhanced Energy Harvesting and Vibration Suppression

TL;DR

The paper addresses designing piezoelectric metastructures that harvest energy from low-frequency vibrations while suppressing unwanted vibrations. It develops a multi-patch isogeometric analysis framework based on Kirchhoff-Love plate theory and Nitsche's method to couple patches and incorporate piezoelectric actuation, with both single and independent electrical-circuit configurations. Through extensive numerical validations and experimental comparisons, it demonstrates accurate patch-interfaces, robust performance across diverse geometries, and a parametrized metastructure design that yields tunable bandgaps and enhanced energy harvesting. The framework is positioned for optimization-driven design and graded metastructures to maximize energy output and vibration attenuation in practical settings.

Abstract

Metastructures are engineered systems composed of periodic arrays of identical components, called resonators, designed to achieve specific dynamic effects, such as creating a band gap-a frequency range where waves cannot propagate through the structure. When equipped with patches of piezoelectric material, these metastructures exhibit an additional capability: they can harvest energy effectively even from frequencies much lower than the fundamental frequency of an individual resonator. This energy harvesting capability is particularly valuable for applications where low-frequency vibrations dominate. To support the design of metastructures for dual purposes, such as energy harvesting and vibration suppression (reducing unwanted oscillations in the structure), we develop a multi-patch isogeometric model of a piezoelectric energy harvester. This model is based on a piezoelectric Kirchhoff-Love plate-a thin, flexible structure with embedded piezoelectric patches-and uses Nitsche's method to enforce compatibility conditions in terms of displacement, rotations, shear force, and bending moments across the boundaries of different patches. The model is validated against experimental and numerical data from the literature. We then present a novel, parameterized metastructure plate design and conduct a parametric study to explore how resonator geometries affect key performance metrics, including the location and width of the band gap and the position of the first peak in the voltage frequency response function. This model can be integrated with optimization algorithms to maximize outcomes such as energy harvesting efficiency or vibration reduction, depending on application needs.

Figures (23)

• Figure 1: Schematics of the weak coupling of plate patches in Kirchhoff-Love plate.
• Figure 2: Scheme of a simply supported square plate under a sinusoidal load.
• Figure 3: Cases studied for the construction of the simply supported square plate and the rectangular piezoelectric harvester.
• Figure 4: Comparison of multi-patches IGA solutions in terms of $L_2$ error vs. the number of degrees of freedom for biquadratic NURBS (left) and bicubic NURBS (right).
• Figure 5: Schematic of the bimorph piezoelectric energy harvester with a rectangular shape, consisting of two piezoelectric layers and one substructure layer. The $x-z$ plane is on the left, and the $x-y$ plane is on the right.