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 (BGs) 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 metamaterial with various levels reveals that the iteration order itself is responsible for the increase in the number of frequency bands and the decrease in the center frequencies of the BGs. Furthermore, the vibrational modes are calculated and examined to understand the mechanism of BG generation. To demonstrate the efficiency of earthquake shielding in multiple complete BGs, investigations of seismic surface wave propagation on a 1D array of Minkowski-like fractal structure units on the surface of single and layered semi-infinite substrates are employed. The results show that the layered soil has the function of widening BGs by itself. Our proposed Minkowski-like fractal structure due to its multi-scale self-similarity mitigates the intrinsic drawback of the narrow BG of resonant metamaterial, 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.