http://iet.metastore.ingenta.com
1887

Fundamentals

Fundamentals

For access to this article, please select a purchase option:

Buy chapter PDF
£10.00
(plus tax if applicable)
Buy Knowledge Pack
10 chapters for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
Scattering of Wedges and Cones with Impedance Boundary Conditions — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

This chapter discusses several basic analytical tools to be repeatedly exploited in the main part of the monograph for dealing with diffraction of acoustic and electromagnetic waves by wedges and cones with impedance boundary conditions. We formulate basic equations, boundary, edge, and radiation conditions in the first three sections. Then Section 1.4 outlines different integral transforms and representations, including the Sommerfeld-Malyuzhinets and Kontorovich-Lebedev transforms. Section 1.5 expounds the solution to the so-called Malyuzhinets problem. The theory of Malyuzhinets functional difference equations for one unknown function is detailed in the last section of the chapter.

Chapter Contents:

  • 1.1 Equations for acoustic and electromagnetic waves
  • 1.1.1 Acoustic waves
  • 1.1.2 Electromagnetic waves
  • 1.2 Boundary conditions
  • 1.3 Edge and radiation conditions
  • 1.3.1 Vicinity of the edge and Meixner's condition
  • 1.3.2 On the behavior of solutions to the Helmholtz equation in the angular domain as r→0
  • 1.3.3 Radiation conditions: Formulation of the problem
  • 1.3.4 The limiting-absorption principle
  • 1.4 Integral transformations
  • 1.4.1 Fourier transform and the convolution theorem
  • 1.4.2 The Sommerfeld integral
  • 1.4.3 Malyuzhinets's theorem: Sommerfeld-Malyuzhinets (SM) transform
  • 1.4.4 Kontorovich-Lebedev (KL) transform and its connection with the Sommerfeld integral
  • 1.4.5 Watson-Bessel integral
  • 1.5 Malyuzhinets's solution for the impedance wedge diffraction problem
  • 1.5.1 Functional equations for the Malyuzhinets problem
  • 1.5.2 The multiplication principle and the auxiliary solution Ψ0(Z) to the functional equations (1.104)
  • 1.5.3 The Malyuzhinets function ΨΦ(Z) and its basic properties
  • 1.5.4 Examination of (d/dZ) lnΨΦ(Z)
  • 1.5.5 The Malyuzhinets function ΨΦ(Z)
  • 1.5.6 Completion of the construction of Ψ0(Z) and of s(Z)
  • 1.5.7 Far-field analysis of the exact solution
  • 1.6 Theory of Malyuzhinets functional equations for one unknown function
  • 1.6.1 General Malyuzhinets equations
  • 1.6.2 Solution to the homogeneous Malyuzhinets equations
  • 1.6.3 Solution to the inhomogeneous Malyuzhinets equations
  • 1.6.4 Modified Fourier transform and S-integrals
  • 1.6.5 The direct application of S-integrals

Inspec keywords: electromagnetic wave diffraction; boundary-value problems; acoustic wave diffraction; difference equations; functional equations; shapes (structures); transforms

Other keywords: Malyuzhinets functional difference equations; impedance boundary conditions; wedges; integral transforms; acoustic wave diffraction; electromagnetic wave diffraction; cones; Sommerfeld-Malyuzhinets transforms; Kontorovich-Lebedev transforms; integral representations; radiation conditions

Subjects: Electromagnetic wave propagation; Differential equations (numerical analysis); Integral transforms; Continuum mechanics; Electromagnetic waves: theory; Mathematical analysis; Function theory, analysis; Numerical approximation and analysis; Ultrasonics, quantum acoustics, and physical effects of sound

Preview this chapter:
Zoom in
Zoomout

Fundamentals, Page 1 of 2

| /docserver/preview/fulltext/books/ew/sbew501e/SBEW501E_ch1-1.gif /docserver/preview/fulltext/books/ew/sbew501e/SBEW501E_ch1-2.gif

Related content

content/books/10.1049/sbew501e_ch1
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address