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

Kuryliak, D. B.; Lysechko, Victor

doi:10.1002/zamm.201800127

Cited by 5 publications

(3 citation statements)

References 17 publications

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“…The ISLAE () is valid for

γ \neq π / 2

. The technique described above is elaborated in [16–20] and called the analytical regularization procedure. The ISLAE () admits the solution in the class of sequences

b (σ) : {| | X | | = \sup_{n \to \infty} | x_{n} |, \lim_{n \to \infty} | x_{n} n^{σ} | \to 0

for

0 \leq σ < 1 / 2}

.…”

Section: Analytical Regularization Techniquementioning

confidence: 99%

“…For this purpose, we simplify the problem and consider the axially symmetric TM excitation of the sphere-conical structure produced by the radial electric dipole. To find the solution we apply the analytical regularization procedure that we have used earlier for the rigorous analysis of the conical scatterers in homogeneous media [16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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The rigorous solution of the scattering problem for a finite cone embedded in a dielectric sphere surrounded by the dielectric medium

Kuryliak

2021

IET Microwaves Antenna & Prop

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Wave scattering from a finite hollow cone with perfectly conducting boundaries embedded in a dielectric sphere is considered. The structure is excited axially symmetrically by the radial electric dipole. The scattering problem is formulated in the spherical coordinate system as the boundary value problem for the Helmholtz equation. The diffracted field is given by expansion in the series of eigenfunctions. Owing to the enforcement of the conditions of continuity together with the orthogonality properties of the Legendre functions the diffraction problem is reduced to infinite system of linear algebraic equations (ISLAE) of the first kind. The usage of the analytical regularization approach transforms the ISLAE of the first kind to the second one and allows one to justify the truncation method for obtaining the numerical solution in the required class of sequences. This system is proved to be regularized by a pair of operators, which consist of the convolution type operator and the corresponding inverse one. The inverse operator is found analytically using the factorization technique. The numerical examples are presented. The static and the low-frequency approximations as well as the transition to the limiting case when the cone degenerates into the disc are considered.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…The ISLAE () is valid for

γ \neq π / 2

. The technique described above is elaborated in [16–20] and called the analytical regularization procedure. The ISLAE () admits the solution in the class of sequences

b (σ) : {| | X | | = \sup_{n \to \infty} | x_{n} |, \lim_{n \to \infty} | x_{n} n^{σ} | \to 0

for

0 \leq σ < 1 / 2}

.…”

Section: Analytical Regularization Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The rigorous solution of the scattering problem for a finite cone embedded in a dielectric sphere surrounded by the dielectric medium

Kuryliak

2021

IET Microwaves Antenna & Prop

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“…Therefore, it needs to be taken into account. In our previous study, an explicit inversion of the mode-matching singularity was proposed for finite/truncated conical and biconical scatterers [17][18][19][20][21][22][23][24][25]; this technique is generally called an analytical regularization procedure. The main reason for such processing is to guarantee an accurate solution to the problem which satisfies all the necessary conditions, including the edge condition, for any geometrical and frequency parameters except the spectrum points.…”

Section: Introductionmentioning

confidence: 99%

Wave Diffraction from a Bicone Conjoined with an Open-Ended Conical Cavity

Kuryliak

Sharabura

2023

Applied Sciences

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The problem of axially symmetric TM-wave diffraction from a bicone conjoined with an open-ended conical cavity is analysed rigorously. The scatterer is formed by the perfectly conducting semi-infinite and truncated semi-infinite conical surfaces; the spherical termination of an internal area of the truncated cone creates the open-ended cavity. In this paper the certain physical aspects of diffraction which are known to cause mathematical difficulties are considered. It includes an accurate analysis of the wave-mode transformation phenomena at the open end of the cavity, as well as a study of wave radiation from the cavity into the biconical waveguide. The primary outcome of this paper is a precise treatment of the wave diffraction problem mentioned above using new techniques and establishing new properties of resonance modes’ penetration into the biconical waveguide region.

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Wave diffraction from the finite bicone

Kuryliak

Sharabura

2021

Z. Angew. Math. Phys.

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

Cited by 5 publications

References 17 publications

The rigorous solution of the scattering problem for a finite cone embedded in a dielectric sphere surrounded by the dielectric medium

The rigorous solution of the scattering problem for a finite cone embedded in a dielectric sphere surrounded by the dielectric medium

Wave Diffraction from a Bicone Conjoined with an Open-Ended Conical Cavity

Wave diffraction from the finite bicone

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