A new approach for determination of the attenuation bandwidth of a resonating metamaterial

Due to the presence of internal structures, metamaterials, a new class of artificial materials, can be engineered to have various unconventional properties during wave interaction. They can be rationally designed to offer controlled mechanical, acoustic or electromagnetic properties through resonant electromagnetic, acoustic or mechanical structures inside the metamaterial. Due to these properties, metamaterials have been effectively used for cloaking, wave guiding and designing filters in the field of optics, electromagnetics, acoustics and elastodynamics. In this paper, a Fourier transfer based methodology is proposed to determine the attenuation bandwidth of a metamaterial instead of using conventional Bloch's theorem. The applicability of this method is wider than that of Bloch's theorem, because this method allows analysis beyond the necessary periodicity of the metamaterial. All the governing equations are non-dimensionalised to effectively quantify the attenuation bandwidth at the lower and higher frequency range of the resonating frequency of the internal structures present in the matrix of the material. The attenuation bandwidth is characterized into low and high frequency parts to determine the effect of the variation of the mass ratio and the number of the repeating units on the attenuation bandwidth of the 1D metamaterial chain