Acoustical multi-frequency filtering by a defective asymmetric phononic serial loop structure

In this paper, we investigate the existence of defect modes in the phononic band structure and in the transmission spectrum of a one-dimensional phononic asymmetric loop (ASL) structure. This structure exhibits large acoustic bandgaps that originate both from the periodicity of the system and the loop resonant modes that create zeros of transmission. The defect modes result from the presence of a defective segments and loops in the ASL structure and may occur in these gaps. The localized states (defect modes) appear as very narrow peaks in the transmission spectrum and in the map of transmission of a finite serial loop structure. The defect mode behavior is analyzed as a function of the defect lengths, the position of the defects, and the ratio between the loops undisturbed. Our theoretical analysis is performed using the continuous medium interface response theory, which makes it possible to calculate the Green function of any composite material.