Extremely low frequency wave localization via elastic foundation induced metamaterial with a spiral cavity

We proposed a metamaterial which exhibits elastic wave localization at extremely low frequencies. First, we opened an extremely low bandgap via elastic foundations. Subsequently, we investigated wave localization by imposing normal defect, which is widely used to capture waves in conventional wave localization systems. However, there were limitations: wave localization was not achieved when a weak bandgap is generated, and the operating frequency of localization is still in the upper part of the bandgap. To overcome wave localization via the normal defect, we proposed a novel metamaterial with a spiral cavity which can tune the resonating frequency depending on the length of the spiral path. By imposing on the spiral cavity inside the elastic foundation-induced metamaterial, we can shift the resonating frequency of the cavity down. Finally, we carried out wave simulations, not only to support the previous eigenfrequency study for the supercell, but also to verify that the finite-size metamaterial can also achieve wave localization at the extremely low frequencies. Through wave simulations, we could observe wave localization even at 77.3 Hz, which is definitely the lower part of the extremely low bandgap.