Symmetrical electromagnetic field of a ring-shaped crack on the conical surface of finite length (Q2753416)
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scientific article; zbMATH DE number 1668328
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Symmetrical electromagnetic field of a ring-shaped crack on the conical surface of finite length |
scientific article; zbMATH DE number 1668328 |
Statements
4 November 2001
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Helmholtz equation
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Lebedev integral transform
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infinite algebraic system
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regularization
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directional diagram
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0.8511408
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0.82780486
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0.8245444
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0.82408017
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0.82326424
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0.82042766
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0.8149734
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0.8102215
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Symmetrical electromagnetic field of a ring-shaped crack on the conical surface of finite length (English)
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Mathematically the studied problem is formulated by a Neumann problem for the Helmholtz equation on the surface of a finite cone. The right-hand side of the boundary condition is represented by the Dirac function. Using the Lebedev integral transform and eigenfunction expansions, the original problem is reduced to an infinite system of linear algebraic equations with respect to coefficients of expansion of the radial electric field component into a series in McDonald functions. Regularization of the system is performed by the technique of ``semiinversion''. Using numerical modeling, the directional diagram of the conical surface as a function of the cone geometry and the localization of the crack is studied.
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