Effective medium method in the problem of axial elastic shear wave propagation through fiber composites

The effective medium method (EMM) is applied to the solution of the problem of monochromatic elastic shear wave propagation through matrix composite materials reinforced with cylindrical unidirected fibers. The dispersion equations for the wave numbers of the mean wave field in such composites are derived using two different versions of the EMM. Asymptotic solutions of these equations in the long and short wave regions are found in closed analytical forms. Numerical solutions of the dispersion equations are constructed in a wide region of frequencies of the incident field that covers long, middle and short wave regions of the mean wave field. Velocities and attenuation factors of the mean wave fields in the composites obtained by different versions of the EMM are compared for various volume concentrations and properties of the inclusions. The main discrepancies in the predictions of different versions of the EMM are indicated, analyzed and discussed.