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

Kuryliak, D. B.; Nazarchuk, Z. T.; Trishchuk, O. B.

doi:10.2528/pierb16120904

Cited by 12 publications

(9 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now we eliminate the four unknown coefficients (18) and (19), and we are left with x n and y n . Passing to the limit P, K, N → ∞ (N = P + K) in the obtained system and arranging them according to (20), we arrive at the following ISLAE…”

Section: Solution Of the Wave Diffraction Problemmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Kuryliak

Sharabura

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

The electromagnetic problem by the finite bicone, which is formed with the perfectly conducting semi-infinite cone and the finite cone with truncated vertex, is studied. Bicone is excited axial-symmetrically by the ring magnetic source.The diffracted field is represented through the series of the transversal magnetic (TM) modes; the lower mode among them is called the transversal electromagnetic wave (TEM). On the basis of this representation and using the mode matching technique, we derive the series equations to determine the unknown complex modes magnitudes. In view of the electric field singularities at the conical edges, these equations are represented in the form of the limiting transition from the finite sums to the series. We derive the rule of this transition, as well as the procedure for reducing them to the infinite system of linear algebraic equations (ISLAE) of the first kind. We study asymptotic properties of the matrix elements and find that the main part of their static limit and their behavior for large indexes form the matrix operator of the convolution type; the corresponding inverted operator in the analytical form is obtained. Both these operators, which we call the regularization operators, are used for the transition from the ISLAE of the first kind to the ISLAE of the second kind. The ISLAE thus obtained allow for the solution of any geometrical parameters and frequency with the given accuracy. The asymptotic properties of their solutions are analyzed, and the numerical examinations of the far field patterns are provided.

show abstract

Section: Solution Of the Wave Diffraction Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Kuryliak

Sharabura

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…The analytical regularization technique which is used to solve the scattering problems from the conical structures first appeared in []. It allows to consider various class of complex conical structures in the electromagnetic context as the bi‐cone, the cone with azimuthal slot, and the sphere‐conical cavity . The core of this technique lays in the transformation of the series equation into an infinite system of linear algebraic equations (ISLAE) of the second kind.…”

Section: Introductionmentioning

confidence: 99%

“…It allows to consider various class of complex conical structures in the electromagnetic context as the bi-cone, [14,15] the cone with azimuthal slot, [16] and the sphere-conical cavity. [17] The core of this technique lays in the transformation of the series equation into an infinite system of linear algebraic equations (ISLAE) of the second kind. It can be readily solved by the truncation methods.…”

Section: Introductionmentioning

confidence: 99%

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

Kuryliak

Lysechko

2018

Z Angew Math Mech

View full text Add to dashboard Cite

The paper deals with solving of the diffraction plane wave problem from a finite rigid hollow cone at oblique incidence. The diffraction problem is treated in terms of the scattering velocity potential by means of the mode matching technique and the analytical regularization procedure. The unknown expansion coefficients are found from an infinite system of linear algebraic equations of the second kind which allows us to obtain a solution with a desired accuracy. The influence of the cone parameters and angles of plane wave incidence on scattering characteristics of the cone is discussed. The obtained numerical results are verified by testing the satisfaction of the mode matching conditions and by comparing our calculations with those known for the rigid disc.

show abstract

“…The analytical regularization technique for the solution of the different kinds of the wave diffraction problems was considered for hollow conical scatterers excited by the electromagnetic and acoustic waves in [14,[19][20][21][22][23][24]. Earlier in [25] we analysed the wave diffraction by the openended conical cavity formed by the truncated cone with the internal spherical diaphragm. This structure excited axially-symmetrically by the radial electric dipole and the resonance scattering of the different kinds of the open sphere-conical resonators were studied.…”

Section: Introductionmentioning

confidence: 99%

Wave Diffraction Problem From a Semi-Infinite Truncated Cone With the Closed End

Kuryliak¹,

Kobayashi²,

Nazarchuk³

2018

PIER C

Self Cite

View full text Add to dashboard Cite

The electromagnetic wave diffraction from the modified cone formed by a circular truncated cone whose aperture is closed by a spherical cap is considered. The problem is reduced to the solution of the mixed boundary value problem for the Helmholtz equation. The axially symmetric version of the problem, where the cone is excited by a radial electric dipole (E-polarization wave diffraction problem), is analyzed. A new approach to the solution is proposed. The solution includes the application of the Kontorovich-Lebedev integral transformation, the nonstandard procedure for derivation of the Wiener-Hopf equation and its reduction to the set of linear algebraic equations of the second kind. Their solution ensures the fulfillment of all the necessary conditions including the edge condition. The approximate equation for the sharp truncated cone terminated by the spherical cap is analyzed. The low frequency approximation as well as the transition to the plane which incorporates the hemispheric cavity is analysed. The numerical calculation results are presented.

show abstract

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

Cited by 12 publications

References 28 publications

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

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

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

Wave Diffraction Problem From a Semi-Infinite Truncated Cone With the Closed End

Contact Info

Product

Resources

About