Ta. Pitts et al., SOLUTION OF THE EULER FIELD-EQUATIONS FOR PLANE-WAVE SCATTERING BY ANEND-CAPPED CYLINDER VIA THE UNIFORM GEOMETRICAL-THEORY OF DIFFRACTION, The Journal of the Acoustical Society of America, 94(6), 1993, pp. 3437-3447
An approximate solution to the problem of plane-wave scattering by a f
inite, hemispherically terminated (end-capped) cylinder of circular cr
oss section is found via the uniform geometrical theory of diffraction
(UTD). Both Dirichlet and Neumann boundary conditions are considered.
A scattering model is applied in which a reduced set of geodesic path
s or rays is used to obtain the acoustic pressure field at any point i
n space where the UTD is valid. A standard method for obtaining transf
er functions describing the pressure field changes along the geodesic
paths is briefly outlined. This method uses asymptotic expansion of th
e exact solutions to two related problems (plane wave scattering by a
sphere and an infinite cylinder) whose ray sets together comprise the
total ray set for the end-capped cylinder problem. An approximation to
the total pressure field is then found for the case when an impinging
plane wave is scattered by an end-capped cylinder. The predicted scat
tered fields demonstrate the expected similarities to and differences
from the field patterns produced by the infinite cylinder and sphere t
argets. The origin and significance of a discontinuity in the pressure
field predictions is discussed.