Low-Frequency Elastic Wave Focusing and Harvesting via Locally Resonant Metamaterials

Elastic lens and mirror concepts that have been explored to date for enhanced structure-borne wave energy harvesting are suitable for relatively high-frequency waves (e.g. tens of kHz), which are very much outside the typical ambient structural frequency energy spectrum. One direct way of reducing the design frequency of such phononic crystal-based lens and reflector/mirror designs is to increase their size, which would yield very large dimensions to operate at ambient vibration frequencies (∼hundreds of Hz). In this work, we exploit locally resonant (LR) metamaterials to enable low-frequency elastic wave focusing via LR lens and mirror concepts with practical size limitations. LR lens is designed in a similar way to its phononic crystal counterpart by tailoring the refractive index profile of the LR unit cell distribution. However, LR approach enables altering the dispersion characteristics, and thereby the phase velocity distribution, at much lower frequencies right below the local resonance frequency. Other than the local resonance frequency of the unit cells, the key factor in design is the mass ratio of the resonators to achieve a desired refractive index profile and focusing. LR mirror uses the low-frequency bandgap which is right above the resonance frequency of the unit cells. LR unit cells arranged in the form of a parabola, for instance, makes a low-frequency LR mirror that operates in the bandgap for plane wave focusing. These LR focusing concepts can be used in vibration civil, aerospace, and mechanical systems to localize and harvest structure-borne wave energy.