Ultralow-frequency broadband Rayleigh wave attenuation performance of 3D embedded seismic metamaterial barrier

In recent years, the development of seismic metamaterials (SMs) has introduced new approaches for attenuating the vibrations caused by the earthquakes and traffic loads. This study focuses on the concept of locally resonant materials, which can achieve low-frequency wave control under the sub-wavelength size. Based on this concept, a three-dimensional embedded SM composed of common materials (i.e., soil, concrete, and rubber) is designed to attenuate low-frequency surface waves (SWs). The surface wave band gap (SWBG) is identified using the sound cone method and the strain energy density method, and its vibration mode at the start frequency is analyzed. Furthermore, the effects of key geometric and material parameters and three types of SMs with different rubber configurations on the SWBG characteristics are investigated. In the frequency domain analysis, the transmission loss spectrum with different numbers of unit cells is analyzed using the symmetrical structure, and the influences of viscosity effect in the rubber and substrate soil are studied. In the time domain analysis, the dynamic responses under harmonic load and real seismic load are calculated to validate the attenuation performance of proposed SMs on surface waves, respectively. The results show that the embedded SM with the petal-shaped rubber configuration can attenuate ultralow-frequency broadband surface waves (2.64 Hz-22.08 Hz). This study provides a robust framework for designing seismic metamaterials and highlights their potential for practical applications in infrastructure protection against seismic and ground-borne vibrations.