Novel Multi-Vibration Resonator with Wide Low-Frequency Bandgap for Rayleigh Waves Attenuation

Rayleigh waves are vertically elliptical surface waves traveling along the ground surface, which have been demonstrated to pose potential damage to buildings. However, traditional seismic barriers have limitations of high-frequency narrow bandgap or larger volume, which have constraints on the application in practical infrastructures. Thus, a new type seismic metamaterial needs to be further investigated to generate wide low-frequency bandgaps. Firstly, a resonator with a three-vibrator is proposed to effectively attenuate the Rayleigh waves. The attenuation characteristics of the resonator are investigated through theoretical and finite element methods, respectively. The theoretical formulas of the three-vibrator resonator are established based on the local resonance and mass-spring theories, which can generate wide low-frequency bandgaps. Subsequently, the frequency bandgaps of the resonator are calculated by the finite element software COMSOL5.6 based on the theoretical model and Floquet–Bloch theory with a wide ultra-low-frequency bandgap in 4.68–22.01 Hz. Finally, the transmission spectrum and time history analysis are used to analyze the influences of soil and material damping on the attenuation effect of resonators. The results indicate that the resonator can generate wide low-frequency bandgaps from 4.68 Hz to 22.01 Hz and the 10-cycle resonators could effectively attenuate Raleigh waves. Furthermore, the soil damping can effectively attenuate seismic waves in a band from 1.96 Hz to 20 Hz, whereas the material of the resonator has little effect on the propagation of the seismic waves. These results show that this resonator can be used to mitigate Rayleigh waves and provide a reference for the design of surface waves barrier structures.