Numerical analysis of wave scattering by a pair of soundproof spheres by orthogonal central compositional design method

In the paper, the analysis of wave scattering on a system of two soundproof spheres was carried out using the orthogonal central compositional design method. The main objectives of the work are to determine the main parameters, the change of which significantly affects on the whole system; to determine the variable parameter values of the system, at which the loss functions (the total scattering cross section and the normalized pressure at a fixed point) take the minimum and maximum values, and to study the system at optimal parameter values. The orthogonal compositional design method is implemented for a three-factor computational experiment, where three main parameters of the system were selected as factors: the wave radius, the ratio of the sphere radii, and the distance between the sphere centers. For the obtained regression equation, the significance of the coefficients was checked using Student’s t-test and the adequacy of the model using Fisher’s F-test. It was found that in the case of a spherical wave from a monopole radiation source, the nonlinear influence of the factors is more pronounced than in the case of a plane wave; normal pressure calculated at a fixed point is insensitive to changes in parameters in the case of a plane wave, as well as in the case of a monopole radiation source for small values of the sphere surface complex conductivity; the total scattering cross section is highly sensitive in the case of a system with ideally rigid spheres; the highest and lowest values of the loss functions are achieved at the boundary of the three-dimensional parametric region of factors changes. Pressure distribution diagrams were constructed, which made it possible to determine the zones of high or low pressure for the found optimal values of the factors.