Download Scattering of Waves by Wedges and Cones with Impedance by Mikhail A. Lyalinov, Ning Yan Zhu PDF
By Mikhail A. Lyalinov, Ning Yan Zhu
This publication is a scientific and certain exposition of alternative analytical ideas utilized in learning of the canonical difficulties, the wave scattering by means of wedges or cones with impedance boundary stipulations. it's the first reference on novel, hugely effective analytical-numerical ways for wave diffraction via impedance wedges or cones. The applicability of the stated answer tactics and formulae to latest software program applications designed for real-world high-frequency difficulties encountered in antenna, wave propagation, and radar pass part.
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Extra resources for Scattering of Waves by Wedges and Cones with Impedance Boundary Conditions: ISMB Series
Sample text
83) 0 Inside the contour γ+ , the function f (α) satisfies the inequality | f (α)| < M1 exp [(1 − a) Im α] , Im α → +∞. 81). 2. 22]. Let a, b, c, and d be positive numbers; let 0 < b < π /2 and |arg(−ik)| < π /2. We consider a function of r , p(r ) = O(r a−1/2 exp(ikr cos b)), analytic for positive value of r and also in the entire region c < |kr | < ∞, |arg(r )| < 1 . Let k Ψ (α) = −2iπ +∞ p(r ) ikr cos α √ dr. 85) From the theory of the SM transform, Ψ (α) is an analytic function in the domain Re(−ik0 (cos α + cos b)) > 0, as |arg(−ik0 )| < |arg(−ik)| + 1 , and then in the strip |Re(α)| < π /2 − |arg(−ik)| + 1 .
32]) u(kr, ϕ) ∼ n eikr +iπ /4 u n + S(ϕ, ϕ0 ) √ + u+ + u−. 1. 117), res|z=±(3π/2+2Φ) ψΦ (z) = ψΦ (3π/2 − 2Φ) . 154) 1 Remark: Generally, the poles ±(π + Φ + θ± ) − ϕ never coincide with the saddle points ±π since |ϕ| < Φ, and the inequalities 0 < Re θ± < π /2, Im θ± < 0 are assumed. At the same time, the surface waves can noticeably contribute to the total far field only for moderate values of kr . For such kr the numerical values of Φ ∓ ϕ + θ± become relevant. 153) is used for accurate computations of the surface waves.
170); that is, s(z) is a piecewise regular, 4Φ-periodic function. 170). 170) one has i 8Φ iR dτ = cos μτ − sin μz n+ 3 z − 4 4Φ 1 . ) We study the analytic continuation of s(z) from any strip of regularity onto the whole complex plane. It is sufficient to consider the strip −3Φ < Re z < Φ. 171), one can write s(z) = i 8Φ iR F(τ ) − F(z − Φ) z +Φ dτ − F(z − Φ). 172) is a meromorphic function on the whole z-plane. 172) can have singularities at the poles of F(z − Φ) but has no singularities on the line Re z = Φ, that is, the points z = Φ + τ are regular points.