Slow Sound Phenomena Caused by Frame Shrinkage in Square Frame Acoustic Metafluid

The present study investigates the equivalent bulk modulus and density of square frame underwater acoustic metafluid (AMF) cells with four distinct frame forms. It is observed that, besides frame thickness, a certain degree of shrinkage at the center of the frame also influences the equivalent parameters of cells. Specifically, this shrinkage leads to a decrease in the equivalent volume modulus and an increase in the equivalent density, ultimately resulting in the slow sound velocity phenomenon of the cell. The frame shrinkage causes part of the air to be replaced, resulting in an increase in density. At the same time, it makes the cell more prone to ``shrink and expand'' type volume deformation, resulting in the reduction of volume modulus. Finally, an impedance-matched slow sound velocity (0.5 times) metafluid cell is designed by frame shrinkage and verified by analyzing the transmission effect of a waveguide containing 20 cells and the sound pressure distribution at different positions in the waveguide.