![]() ![]() The shell was filled in the internal liquid medium with the density ρ 2 and the sound velocity C 3 and it was placed in the external liquid medium with the density ρ 0 and the sound velocity C 0.įigure 5. The density of the material of the shell is ρ 1, the Lame’s coefficients―λ and μ. In the quality of such scatterer, we are going to consider the terminal isotropic elastic cylindrical shell with the semi-spheres on its ends (see Figure 5). ![]() We are going to spread the method of the integral equations, used in for the ideal non-analytical scatterers, on the elastic shell of the non-analytical form. The surface S consists of S 2 and the surfaces S 1 и S 3 (see Figure 1).įor the calculation of the integrals (2), (3) and (5), (6) on surface we are choose the grid of the nodal points ( Figure 2, Figure 3).Īt Figure 4 is present for the chosen parameters by (the curve 1 corresponds to method of the T―matrixes, but the curve 2―to the method of the integral equations). The scattered pressure can find either with the help of the integral (2), (3) (for the Fredholm equation of the first kind), or with the help of the Equation (5), (6) (for the Fredholm equation of the second kind). The scattered pressure in the point we are express through the function Ф: With the help Ψ we are find and the scattered pressure in the any point of the medium :įor the Neimann’s condition, we are bring the function ―the solution of the Fredholm equation of the second kind : The integral to the left of (4) must understand in the sense of the main meaning. The function we are find from the solution of the non-homogeneous Fredholm equation of the second kind : The non-analytical smooth scatterer in the form of the cylinder with the semispheres. ![]()
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