Diffraction of a Plane Acoustic Wave from a Finite Soft (Rigid) Cone in Axial Irradiation

Abstract

The problem of diffraction of a plane acoustic wave by a finite soft (rigid) cone is investigated. This one is formulated as a mixed boundary value problem for the three-dimensional Helmholtz equation with Dirichlet (Neumann) boundary condition on the cone surface. The diffracted field is sought as expansion of unknown velocity potential in series of eigenfunctions for each region of the existence of sound pressure. The solution of the problem then is reduced to the infinite set of linear algebraic equations (ISLAE) of the first kind by means of mode matching technique and orthogonality properties of the Legendre functions. The main part of asymptotic of ISLAE matrix element determined for large indexes identifies the convolution type operator amenable to explicit inversion. This analytical treatment allows one to transform the initial diffraction problem into the ISLAE of the second kind that can be readily solved by the reduction method with desired accuracy depending on a number of truncation. All these determine the analytical regularization method for solution of wave diffraction problems for conical scatterers. The boundary transition to soft (rigid) disc is considered. The directivity factors, scattering cross sections, and far-field diffraction patterns are investigated in both soft and rigid cases whereas the main attention in the near-field is focused on the rigid case. The numerically obtained results are compared with those known for the disc.

Wave diffraction from the Biconical Section in the semi‐infinite conical region

“…Previously, this method was used to solve the problems of diffraction of electromagnetic and acoustic waves on separate conical surfaces. [16][17][18][19][20][21][22][23] The particular case of this problem, when the two cones form a biconical structure with only one edge, was considered in the previous studies. 24,25 The presence of the shoulder with more than one circular edge in the bicone greatly complicates the problem, because this presence creates the interaction of waves between the edges, which needs to be taken into account.…”

Scattering of the plane acoustic wave from a finite hollow rigid cone at oblique incidence

“…It can be readily solved by the truncation methods. The scopes and applicability of the analytical regularization technique to the diffraction problem from a set of circular cones in the acoustic context were demonstrated by us in []. They followed the papers in which the acoustic wave scattering from the group of cones was also be analyzed using various approaches: the geometrical and physical theories of diffraction, the mode matching technique; however, the obtained numerical results were poor.…”

“…They followed the papers in which the acoustic wave scattering from the group of cones was also be analyzed using various approaches: the geometrical and physical theories of diffraction, the mode matching technique; however, the obtained numerical results were poor. Such data deficiency stimulated our accurate analysis in [].…”

Axially-Symmetric Tm-Waves Diffraction by Sphere-Conical Cavity

“…In this particular case, we reduce our problem to Equation (24) using the positive indices given by the expression (36), and then derive Equation (33), where the regularisation operators (29), (30) are formed using expressions (36), (37). The formulas for effective calculation of the matrix elements in Eq.…”

“…The proposed approach is called the method of analytical regularization or semi-inversion method. This approach was used earlier for the studies of the diffraction of acoustic and electromagnetic waves from conical, bi-conical, and wedge structures [21][22][23][32][33][34][35][36][37][38][39][40].…”