Investigation of periodic resonators as wave barriers for mitigating surface seismic waves using Bloch-Floquet theory

Every year around the world, earthquakes and other seismic waves cause damage to civil infrastructures. The most harmful waves for civil infrastructure are surface waves, as this study focused on it. Therefore, this study aims to investigate the behavior of resonators as an approach to reducing surface seismic waves based on both infinite and finite lattices for the proposed resonator. To this end, first, an infinite lattice is evaluated using the Bloch-Floquet theory by modeling the smallest repetition of the considering lattice. The dispersion relation of the considered resonator is obtained by an eigenfrequency analysis for each wave vector in the first irreducible Brillouin zone. Then, the bandgap for surface waves is defined using the sound line concept, a common approach in solid-state physics to find the pure surface modes of the dispersion relation for resonators. The sound line concept is used to distinguish between the pure surface and other waves, such as body waves. In Bloch-Floquet theory, the lattice is assumed to have an infinite number of unit cells; however, in real applications, the lattice needs to have a finite number of unit cells. Therefore, the accuracy of the bandgap obtained for the infinite lattice is evaluated by considering a finite lattice model in both frequency and time domains to consider a more realistic case. The results show that the considered resonator has a notable surface wave bandgap. Moreover, the results of the finite lattice conform well to the results of the infinite lattice in both frequency and time domains. The proposed resonator is made of concrete and has a height of six meters, and the unit cell constant is considered two meters. The obtained bandgap is between 14 and 21 Hz, confirmed by a finite model in both frequency and time domains. As a result, the proposed resonator can reduce surface seismic waves efficiently.