Near-field circular aperture formed by cutting of a semi-infinite cone apex

Based on the rigorous mathematical treatment of an acoustic plane wave diffraction by the semi-infinite truncated soft (rigid) cone, the characteristics of a near-field formation by its edge are established. The corresponding diffraction problem is solved in terms of the velocity potential of a diffracted field by the method of partial domains. Making use of the mode matching technique and orthogonality properties of eigenfunctions the problem is reduced to infinite system of the linear algebraic equations (ISLAE). Analytical regularization procedure is employed in order to extract the singular logarithmic part in ISLAE and exactly convert it and thus the solution of initial diffraction problem is obtained in the form of ISLAE of the second kind. The obtained system allows the solution with a desired accuracy using the reduction method and provides all necessary conditions, including edge conditions.