APPLICATION OF THE METHOD OF INTEGRAL-EQUATIONS TO DIFFRACTION OF ACOUSTIC-WAVES AT ELASTIC BODIES IN A LAYER OF LIQUID

The problem of the diffraction of acoustic waves at an infinite elastic cylinder in a plane waveguide with absolutely soft boundaries is numerically solved by the method of integral equations in combination with the Rayleigh method. The rapid convergence of the solution has been ensured by the choice of the Green's function in a form such that the scattered field satisfies the wave equation, the boundary condition, and the condition of radiation at infinity, while the total field satisfies the matching condition at the boundary of the cylinder. The efficiency of this approach is illustrated by the structure of the scattering matrix. The real and imaginary parts of its off-diagonal elements decrease by four to five orders of magnitude in three or four elements from the diagonal for modes with numbers less than three or four, and at the next element for modes with numbers higher than seven. To compute the amplitude coefficient accurate to 10(-6), it is sufficient to truncate the 15 x 15 matrix. Phase-frequency and amplitude-frequency characteristics are derived. In the vicinity of critical waveguide frequencies of odd orders, the amplitude-frequency characteristic suffers breaks associated with Wood's anomalies, which are related to a sharp growth of the density of acoustic energy in the waveguide. The effect of the elastic properties of the cylinder on the field structure manifests itself in resonance scattering. The structure of the acoustic field is considered for multimode propagation in a waveguide.