Wave propagation in one-dimensional fluid-saturated porous metamaterials

Fluid-saturated porous metamaterials described following Biot's theory support two longitudinal elastic waves. The phase velocity and attenuation of these waves depend nonlinearly on porosity and viscosity of the fluid. Furthermore, when two fluid-saturated porous metamaterials are arranged to form a periodic composite, different band gaps are opened for the two longitudinal waves and these couple to form anticrossings in the dispersion relation. The complex band structure of one-dimensional composites is derived and compared with numerical transmission through a finite sample obtained by the finite element method. It is found that the anticrossings disappear rapidly as viscosity increases, while attenuation band gaps become dominated by the fastest of the two longitudinal waves. Increasing porosity further leads to wider and lower-frequency band gaps. These results are relevant to practical applications of fluid-saturated porous metamaterials, e.g., to engineered soils.