A New Method for the Determination of Far Fields With Applications to the Proble
A New Method for the Determination of Far Fields With Applications to the Proble
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II, Determination of Operator In the problems that follow we shall need an operator L that transforms the impedance boundary condition given by -u- m^Au^o » =o Hi -0 » -Of (2-1) (2-2) into the simpler boundary conditions given by V = O ^ O (2-3) |g = ^ a » o- '^I. C-^^fO^A (2. 5) where Cf(^^^) '^^se"**"" ' k=Zj4; 2f? (2-6) and D is the complex operator ^ . Along the real axis D has the value r-, and along the imaginary axis the value vi i i . Hence the appropriate operator for a wedge of angle ...•x- with an impedance boundary condition on the upper surface and a zero normal derivative condition on the lower surface becomes L = -^^ {a^ "fii+c^^ij -^] (2-7) The transformation that simplifies the original boundary conditions (2-1) and (2-2) is V s LUL (2-8) We make the important observation that the same operator and transformation applies to the case of a wedge of twice the exterior angle when the lower face has the same impedance boimdary condition as the upper face.
What to read after A New Method for the Determination of Far Fields With Applications to the Proble?
You can find similar books in the "Read Also" column, or choose other free books by Frank Karal to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
II, Determination of Operator In the problems that follow we shall need an operator L that transforms the impedance boundary condition given by -u- m^Au^o » =o Hi -0 » -Of (2-1) (2-2) into the simpler boundary conditions given by V = O ^ O (2-3) |g = ^ a » o- '^I. C-^^fO^A (2. 5) where Cf(^^^) '^^se"**"" ' k=Zj4; 2f? (2-6) and D is the complex operator ^ . Along the real axis D has the value r-, and along the imaginary axis the value vi i i . Hence the appropriate operator for a wedge of angle ...•x- with an impedance boundary condition on the upper surface and a zero normal derivative condition on the lower surface becomes L = -^^ {a^ "fii+c^^ij -^] (2-7) The transformation that simplifies the original boundary conditions (2-1) and (2-2) is V s LUL (2-8) We make the important observation that the same operator and transformation applies to the case of a wedge of twice the exterior angle when the lower face has the same impedance boimdary condition as the upper face.
What to read after A New Method for the Determination of Far Fields With Applications to the Proble?
You can find similar books in the "Read Also" column, or choose other free books by Frank Karal to read onlineMoreLess
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