H-fractal seismic metamaterial with broadband low-frequency bandgaps

Abstract

The application of metamaterial in civil engineering to achieve isolation of a building by controlling the propagation of seismic waves is a substantial challenge because seismic waves, a superposition of longitudinal and shear waves, are more complex than electromagnetic and acoustic waves. In this paper, we design a broadband seismic metamaterial based on H-shaped fractal pillars and report numerical simulation of band structures for seismic surface waves propagating. Comparative study on the band structures of H-fractal seismic metamaterials with different levels shows that a new level of fractal structure creates new band gap, widens the total band gaps and shifts the same band gap towards lower frequencies. Moreover, the vibration modes for H-fractal seismic metamaterials are computed and analyzed to clarify the mechanism of widening band gaps. A numerical investigation of seismic surface waves propagation on a 2D array of fractal unit cells on the surface of semi-infinite substrate is proposed to show the efficiency of earthquake shielding in multiple complete band gaps.

A Review of Research on Seismic Metamaterials

“…In 2017, Achaoui et al buried periodic cylindrical columns and cross-shaped inclusions in the bedrock under the soil layer, [37] and Du et al investigated the protective effect of H-shaped fractal pillars and square concrete-filled piles which are better than hollow cylinder or square piles. [38,39] In 2018, Geng et al considered 1D binary SMs with two contrasting constituent materials, [40] and Zeng et al inspected I-shaped pillars arranged on a 2D ground surface. [41] Khlopotin et al studied the effect of a physically realizable cloak built up by unrestricted micropolar elastic media in the 2D form subjected to incident Rayleigh waves pertinent to seismic loading in 2015.…”

“…In recent years, significant research has introduced the local resonance mechanism in the construction of SMs. [6][7][8]14,[21][22][23][24][25][26][27][30][31][32][33][34][35][36]38,39,41,[47][48][49]55,56,61,62,64] The local resonance bandgap is the result of coupling between the long traveling wave property and the resonance characteristic of the periodic local oscillator in the matrix. The existence of coupling is the key factor to determine whether the bandgap is generated.…”

“…[39] Du et al, Zeng et al, and Muhammad et al studied the inhibition of seismic wave propagation by the local resonance of H-shaped, I-shaped, and built-up structural steel pillars with periodic arrangements, respectively. [38,41,47] Torres-Silva and Cabezas introduced negative bulk modulus using a chiral structure which can excite rotation resonance and then cause the imaginary wave vector to attenuate the seismic wave. They also pointed out that by controlling the width, the chirality, and the refractive index of the waveguide, the aseismic range of buildings can be adjusted as needed.…”

“…www.advancedsciencenews.com www.aem-journal.com construction of SMs and designed a wide-band SM based on H-shaped fractal columns. [38] 3.9. Structure Optimization Aiming at Wide Low-frequency Bandgaps Gao et al studied platonic crystals based on lattices of cavities containing N-beam resonators and designed single-phase metamaterial plates for the suppression of low-frequency flexural waves in a broad range of frequencies, [118] as shown in Figure 30.…”

“…At present, the research of SMs is mainly focused on the protection of the Rayleigh wave. [6,7,14,16,17,19,20,[33][34][35][36][37][38][42][43][44][45]123,125,127] However, due to the stratification characteristics of the actual soil, LOVE waves cannot be ignored. Although surface waves travel furthest and cause most of the damage, the damage caused by body waves also should not be ignored, especially where wave trapping occurs in sedimentary basins.…”