Multiple scattering of elastic waves by cylinders of arbitrary cross section. I. SH waves

A scattering matrix approach, that involves only the transition matrix of a single obstacle, is proposed for studying the multiple scattering of elastic waves in a medium (matrix) containing identical, long, parallel, randomly distributed cylinders of arbitrary cross section. The elastic properties of the cylinders are assumed to be different from those of the matrix. A statistical approach in conjunction with Lax’s ’’quasicrystalline’’ approximation is employed to obtain equations for the average amplitudes of the scattered and exciting fields which may then be solved to yield the dispersion relations of the composite medium. Dynamic elastic properties of the composite medium containing circular and elliptical cylinders are found in the Rayleigh or low-frequency limit. Numerical results displaying phase velocity and damping effect of the composite medium are presented for a wide range of frequencies.