The sphere is constructed by soft and hard circular segments in the field of plane acoustic wave

Abstract

The acoustic potential of the velocity of the plane wave, scattered on the sphere. The sphere is constructed by two soft and hard spherical circular segments is analysed. To find the potential the mixed boundary problem for Helmholtz equation is solved. The method of regularization of matrix operator of the problem is used. The method is based on analytical solutions of auxiliary integral Abel’s types equations. The discrete Fourier transform is applied. An infinite system of linear algebraic equations of Fredholm’s second kind is obtained. The system is solvable numerically and analytically in Hilbert space. Some variants of problem formulations and resonance properties of the structures are examined