Mechanism For Local Resonant Acoustic Metamaterial

In recent years, extensive attention has been paid to the propagation of elastic waves and acoustic wave in phononic crystals and acoustic or acoustic meta-materials artificial complex structure. Due to the exists of phononic crystal band gap, the artificial controlling of acoustic or elastic wave becomes possible. The study found that elastic and acoustic waves propagating in the phononic crystals and acoustic meta-materials will show some unusual characteristics, such as the defect states, negative refraction phenomenon, so the materials show a huge potential application. In this paper, by taking the two-dimensional thin elastic plate with periodically arranged spring-mass resonators as example, we study systematically the mechanism of the local-resonant type acoustic meta-material. Results show that the wave dispersion of such kind of system determined not only by the propagating phase but also the scattering phase, where the propagating and scattering phase are defined respectively as the retarded phase change of the wave in background and the abrupt phase change of the wave when it is scattered by the resonator. Based on this understanding, the mechanism for defect modes at subwavelength scale and an alternative idea to realize negative refraction are presented. As a comparison, a real system with resonators on an elastic plate with finite thickness is also investigated. Results show that the understanding based on thin plate theory is also valid for the real plate. In detail, the following two mainly works has been done:(1) According to the traditional local resonance mechanism, the control of the local resonant band gap is only determined by the resonance characteristics of individual resonance unit, but the effect of the geometric phase about the wave propagation in the matrix on the band can be ignored. This paper selects the two-dimensional thin plate periodically distributed a "spring- mass" structure of resonator as an example to analyze the resonant meta-materials’ band gap mechanism, the factor that may affect the dispersion relation is derived, the resonance meta-material’ energy band is the result of combined action that scattering phase and geometric propagation phase, then analyze the relationship between these two kinds of phase. Results suggest that, in the resonant meta-materials, especially in mate-material which have strongly couple resonance type relatively, geometry propagation phase has great influence on the dispersion relation, the upper and lower edge of band gap changes, and the width of the band gap will change with the geometric phase. Even the long wavelength limit and geometric propagation phase is very small, the band upper gap edge is closed in the case of only considering the geometric phase. The real plate structure with a certain thickness is analyzed by finite element analysis, the results is coincident with that of the thin plate analysis model.(2) On the basis of local resonance theory above, the geometric phase and scattering phase determining the energy band collectively. Using the super cell method, and further explore the mechanism of defect states in sub-wavelength elastic waves in meta-materials. The defect states can be found through locally breaking the band gap, that is to say the defect states can be obtained by changing locally scattering phase or propagation phase. Finally, through adjusting and controling the modulation of the propagation phase, namely changing the lattice structure, the negative refraction phenomenon can be achieved.