Topological modes, vibration attenuation, and energy harvesting in electromechanical metastructures

The dynamics of topological boundary modes in both periodic and quasi-periodic electromechanical metastructures is investigated, with a focus on their applications to energy harvesting and vibration reduction. The metastructure analyzed in this study is based on a shunted array of piezoelectric patches, with electrical parameters modulated according to the 1D Aubry–André–Harper model. As a result of this modulation, a fractal spectrum is generated near the central frequency of the resonators, a hallmark of nontrivial topology that enables the emergence of digitally controllable edge states and ensuing localization phenomena at subwavelength frequencies. In this framework, a detailed analysis of the metastructure spectral characteristics is conducted to investigate the influence of the modulation parameters on mode localization, both at the boundaries and within the interior of the beam. Such localization effects are then studied in relation to the energy harvesting, attenuation, and wave transport capabilities of the system. These functionalities point toward the realization of self-powered structures with low frequency and digitally controllable vibration attenuation capabilities, and are considered of significant technological interest in applications involving elastic waves and vibrations, where the ability to precisely control and harness these phenomena could lead to innovative solutions in energy-efficient and adaptive systems. • A fractal spectrum is found in piezoelectric-based electromechanical metastructures. • Low-frequency topological edge modes are tunable using shunt circuits. • The formation of a fractal Hofstadter spectrum allows widening the attenuation band. • Edge-to-edge and edge-to-interior transitions are found by parameter variation. • The localization properties are functional for energy harvesting and wave transport.