Minkowski-like fractal seismic metamaterial with wide low-frequency band gaps on single and layered soil

Abstract In this paper, we propose a resource-efficient Minkowski-like fractal seismic metamaterial by hybridizing U-shaped and cross-shaped pillars, providing wide complete band gaps due to its multi-scale self-similar property. Numerical modeling of seismic surface waves is used to study the band structure and transmission of our seismic metamaterial. A comparison of the band structures of the developed seismic metamaterials with various levels reveals that the iteration order itself is responsible for the increase in the number of frequency bands and the decrease of the center frequencies of the band gaps. Furthermore, the vibration modes are calculated and examined to understand the mechanism of band gap generation. To demonstrate the efficiency of earthquake shielding in multiple complete band gaps, investigations of seismic surface waves propagation on a 1D array of Minkowski-like fractal structure units on the surface of single and layered semi-infinite substrates are employed, and the results show that the layered soil has the function of widening band gaps by itself. Our proposed Minkowski-like fractal structure due to its multi-scale and self-similarity mitigates the intrinsic drawback of the narrow band gap of resonant metamaterials, providing a superior alternative in seismology and related areas of multi-frequency band vibration reduction. Moreover, its green design and manufacturing due to low filling rates, strong wear resistance, and ductility, can realize the low-carbon and sustainable development of the construction industry.