Trees as large-scale natural metamaterials for low-frequency vibration reduction

Abstract

Urban trees are often planted in a periodic arrangement in space. This study takes urban trees as natural metamaterials. Based on the metamaterial theorem, a three-dimensional unit cell is used to represent the entire forest, and finite element analysis via COMSOL software is implemented to identify dispersion relationships. The surface-wave band gaps of urban forests are identified using the sound cone method and strain energy method. The influences of soil elastic modulus, tree spacing, trunk radius, and tree height on band gaps are discussed. Finally, a three-dimensional simulation model is established to verify the effect of urban trees on vibration reduction. The results show that numerical frequency-reduction zones are consistent with theoretical surface-wave band gaps. An increasing soil modulus results in a wider and higher-frequency band gap. Urban forests with larger trunk diameters and smaller tree distance can generate lower-frequency and wider band gaps. It is beneficial to obtain low-frequency band gaps with increasing tree height. A manmade engineered array of trees can be designed with Rayleigh wave band gaps at a low frequency of ≤80 Hz. This study provides a new concept for the quantitative design of urban forests to reduce ground vibration in specific frequency ranges.