Natural seismic metamaterials: the role of tree branches in the birth of Rayleigh wave bandgap for ground born vibration attenuation

At the subwavelength scale, forest trees interact with the Rayleigh wave inducing extremely wide locally resonant bandgap in the earthquake frequency range of interest. To better understand this mechanism, we have considered the effect of bulky side branches connected with the main stem. We considered two types of trees configurations and the study is conducted by a computational approach based on the finite element method. The Rayleigh wave band structure is obtained by sound cone and elastic strain energy density methods. The later technique is found effective in detecting the higher surface Rayleigh modes that are undetectable by the sound cone technique. At the resonator attachment point, the wave mode coupling occurs between longitudinal modes of the resonator trees and vertical component of the Rayleigh wave. This coupling results in a π phase shift for incident Rayleigh wave and the periodic arrangement of trees act constructively to generate a wide bandgap. The tree bulky side branches seemed to further enhance the coupling strength. By constructing a finite length model and performing frequency domain and time history analyses based on the actual ground earthquake records, the performance and efficiency of the bandgap are validated. Both displacement field plots, time history signals and their Fourier spectra indicate significant amount of vibration mitigation within the bandgap frequency.