Trees as large-scale natural phononic crystals: Simulation and experimental verification

Abstract

Urban trees are usually planted on a periodic layout in the spatial configuration. We regard urban trees as large-scale natural phononic crystals. The entire forest is reduced to a reasonable “tree-soil” unit cell based on the phononic crystal theory and finite element method by COMSOL software is used to obtain the dispersion curves. The Rayleigh wave band gaps of phononic trees are distinguished by the sound cone method. The influences of soil elastic modulus and tree height on band gaps are investigated. A three-dimensional simulation model and experiment test are applied to validate the effect of phononic trees on vibration control. The numerical frequency reduction zones coincide exactly with the theoretical band gaps. Increasing soil stiffness results in a higher-frequency and wider band gap. An increasing tree height is beneficial to obtain low-frequency band gaps. A periodically arranged plantation that Rayleigh wave band gaps at frequency ≤60 Hz could be designed. This study opens up a new theoretical basis for the quantitative analyses of urban trees to the ground vibration mitigation at a certain frequency range. Keywords: Urban trees, Phononic crystal, Dispersion curve, Band gap, Rayleigh wave