Investigating Interface Modes on Periodic Acoustic Waveguides and Elastic Rods Using Spectral Elements

Due to their particular wave propagation characteristics, phononic crystals (PC’s) and acoustic metamaterials have numerous potential applications in passive vibration and noise control. In this context, some geometric phase concepts originally developed in electronics have inspired research in phononics. As a result of the non-trivial topology of the band structure, these concepts allow exploring particular behaviors such as edge and interface modes. For acoustic systems, it has been recently shown that interface modes appear at the boundary separating two PC’s having different Zak phases. In this paper, one-dimensional spectral elements are used to investigate interface modes in one-dimensional acoustic (tube) and elastic (rod) systems. The band structure and the forced response are computed using the spectral element method. It is shown that the interface mode appears within the second band gap when a geometrical parameter of one of the connected PC’s is varied so that this bandgap closes and reopens, characterizing a change in the Zak phase. The forced response at the interface mode frequency shows that the sound (acoustic) or vibration (elastic) is spatially concentrated (localisation phenomenon) at the interface. Different PC combinations and different excitation locations are investigated. This behavior may have useful engineering applications, such as in sound and vibration energy harvesting.