Induced guided acoustic waves by the presence of a defective guide in one dimensional asymmetric loop phononic crystal

Abstract

In our actual work, we investigate the propagation of acoustic/elastic waves in a periodic structure consisting of a segment of length d1 and two asymmetric loops of lengths d2 and d3 in each cellule of the periodic structure. The perfect periodic structure presents wide pass bands separated by wide forbidden bands (the propagation of the acoustic waves is prohibited). These band gaps come from the periodicity of the system and the localized modes of the loops. The width of these bands is sensitive to the length of the guide as well as the number of N sites. The presence of a defect on the guide (segment) inside this structure can create defect modes within forbidden bands. These localized states are sensitive to the lengths of the two loops, the periodicity of the structure, and the length of the defected guide. We see that the number of defect modes inside the band gap increases progressively from low to high frequencies with the variation of the defect guide. This structure can also be used as high performance and high transmittance acoustic filters when a defect guide is created into the finite periodic system. Our theoretical is carried out using the continuous medium interface response theory, which makes it possible to calculate the Green function of any composite material. This allows us to obtain all the physical properties of the periodic structure studied, in particular, the dispersion relation and the transmission coefficient.