Combined metamaterial barrier incorporating natural trees for low-frequency surface wave attenuation

Metamaterials have been extensively studied for the attenuation of surface waves, particularly in the form of barriers composed of artificial structures. Natural trees can also be regarded as a special type of natural metamaterial barrier. However, the random growth of trees makes it difficult to achieve predictable vibration attenuation, while the large material consumption limits the engineering applicability of purely artificial metamaterials. To address these research gaps, this study proposes metamaterial barriers formed by a combination of trees and artificial units for low-frequency surface wave attenuation. Frequency-domain analyses were conducted to evaluate the vibration attenuation and band gaps of different metamaterial barriers, and the layouts of combined barriers were further examined. Finally, the actual vibration attenuation performance was assessed under measured subway loads. The results indicate that the combined metamaterial barrier produces an effective attenuation domain spanning 10-30 Hz and 30-60 Hz. The average vibration reduction achieved by subway trains is 66.6% with combined sapling barriers, which is superior to that of pure natural barriers (39.5%) and pure artificial barriers (49.4%). Therefore, the combined barriers reduce the consumption of artificial materials and enhance the practical applicability of metamaterial barriers in residential environments.