Diffraction of a plane sound wave on two elastic cylinders with non-uniform coatings

In paper the analytical solution of a problem about diffraction of a plane sound wave on two uniform elastic cylinders with radially non-uniform coatings is received. Analytic expressions are obtained which describe the wave fields in the containing medium and the homogeneous elastic bodies. The boundary-value problem for the system of ordinary differential equations of the second order is constructed for determination of the displacement fields in non-uniform coatings.
By means of an continuous-non-uniform elastic coatings it is possible to change effectively scattering performances of bodies in determinate directions if to pick up corresponding the inhomogeneity laws for mechanical parametres of a coating. The problem is of interest for analysis of sound diffraction on a lattice of cylindrical bodies and also serves as a necessary element of solution by a method of imaginary sources of a problem about sound diffraction on the single homogeneous elastic cylinder with the non-uniform covering which is close to acoustically soft or absolutely rigid flat surfaces.