Energy localization and topological protection of a locally resonant topological metamaterial for robust vibration energy harvesting

Abstract

During the past decade, metamaterial-based vibration energy harvesters (meta-VEHs) have been increasingly developed owing to the extraordinary characteristics of metamaterials, such as locally resonant bandgap, defect state, and wave focusing features. In this paper, the interface state, a feature recently found in topological metamaterials, is exploited for low-frequency vibration energy harvesting. The topological meta-VEH consists of two kinds of locally resonant metamaterials with different topological phases and a piezoelectric transducer being installed at the interface between these two metamaterials. First, the governing equations of the topological meta-VEH are established based on the mass-spring model. Subsequently, the dispersion relation of such a one-dimensional topological meta-VEH is obtained by applying Bloch's theorem. It is revealed that the interface mode can be attained in the low-frequency range through the band folding of the locally resonant metamaterial. Moreover, the finitely long model of this topological meta-VEH is built, and the transmittance response is calculated both analytically and numerically. Subsequently, the potential benefits of topological metamaterial, including wave localization and topological protection, are thoroughly investigated. It is found that the elastic energy in the interface state is localized at the interface position, resulting in a significant improvement in output power. Meanwhile, the topological protection property can significantly improve the robustness of the interface mode, thus achieving outstanding energy harvesting performance. Finally, to further enhance the energy harvesting performance, the stiffness tuning method and the defect enhancement method are proposed. It is found that integrating the defect mode and interface mode not only improves the output voltage but also achieves the capability of a highly robust energy harvesting.