Complex band structures of one-dimensional fluid-saturated porous phononic crystals in microscale

Abstract

Porous materials have enormous potential for constructing miniaturized phononic crystals (PCs) for high-frequency sound isolation and noise attenuation applications owing to their unique mechanical properties. This study established a theoretical model of elastic waves in microscale PCs formed by periodic arrangements of fluid-saturated porous materials and investigated the complex band structures of obliquely incident longitudinal waves in a one-dimensional case. The proposed model added the couple-stress theory to the Biot theory to take into account the size effect caused by the solid skeleton’s internal microstructures. The results showed that in the presence of wave-type conversion, there were three types of Bloch waves in the PCs, and an anti-crossing band gap was generated between each of the two waves. The shear-wave velocity and band-gap frequency increased considerably when the size effect was considered. The characteristic length and porosity of the softer material in the composition had the same impact on the band structure, and their increases can lead to a widening in the absolute band gaps. As the thickness difference between the two constituent materials of PCs decreased, the band gaps became increasingly noticeable.