Attenuation analysis of low-frequency surface waves in the ultra-low-frequency bandgap of embedded seismic metamaterials

Seismic metamaterials (SMs) have potential applications in the protection of buildings from earthquake hazards, while research on the attenuation of low-frequency seismic waves is still limited. In this paper, an embedded seismic metamaterial with an ultra-low-frequency bandgap is proposed as a research object to analyze the attenuation of low-frequency seismic surface waves. The band structure of the proposed SM has the absence of surface wave solutions and has an ultra-low-frequency complete bandgap with a range of 0-16.3 Hz. Subsequently, the vibration modes and strain energy distribution of the SMs lattice, especially at low frequencies, are analyzed. The results show that there are vibration modes with energy concentrated in the SM and near the surface in the range of 0-1.3 Hz. According to the amplitude reduction analysis, the surface wave has no attenuation in the range of 0-1.3 Hz, and the attenuation zone is 1.3-20 Hz. Two types of actual seismic records are used as input signals to validate the attenuation zone. This indicates that some of the low-frequency surface waves in the ultra-low frequency-bandgap could not be attenuated. It is necessary to analyze the low-frequency band with large strain energy in conjunction with vibration modes and amplitude reduction when designing SMs with the ultra-low-frequency bandgap. Moreover, the effects of parameters and gradient arrangement on proposed SM attenuated low-frequency surface waves are analyzed, where the soil Young's modulus is the key factor affecting the SM attenuated low-frequency surface waves.