Propagating modes of periodic solid layers in an ideal or viscous fluid by homogenization analysis

This study is aimed at investigation of propagating modes of acoustic waves in periodic solid layers in ideal or viscous fluids. In particular, at the long-wavelength limit, a three-scale homogenization analysis is developed to derive the effective group velocities in analytical forms for the shear-vertical (SV) waves as well as for the longitudinal-shear-horizontal (P-SH) waves. It is found that propagating modes, i.e., modes with real group velocities, may be supported even if the fluid phase is viscous. A criterion for the existence of a vanishing effective viscosity is derived based on composite medium constants and the filling ratio of the fluid phase. The critical filling ratios at which an evanescent mode changes to a propagating mode are given for various solid-water systems.