Ga. Athanassoulis et Ka. Belibassakis, ALL-FREQUENCY NORMAL-MODE SOLUTION OF THE 3-DIMENSIONAL ACOUSTIC SCATTERING FROM A VERTICAL CYLINDER IN A PLANE-HORIZONTAL WAVE-GUIDE, The Journal of the Acoustical Society of America, 101(6), 1997, pp. 3371-3384
The three-dimensional acoustic scattering from a vertical, impenetrabl
e cylinder in a waveguide is studied. The analytical solution of the p
roblem, for a Dirichlet or a Neumann boundary condition on the scatter
er, has been derived recently by Athanassoulis and Prospathopoulos [J.
Acoust. Sec. Am. 100, 206-218 (1996)] in the form of a double-infinit
e normal-mode series, representing the total acoustic field. In order
to extend the applicability of this solution to higher frequencies, th
e total field is decomposed into the incident and the scattered parts.
A series expansion for the scattered field is obtained, and the criti
cal parameter controlling its azimuthal convergence is shown to be the
nondimensional wave number ka based on the radius a of the cylinder.
The general term of the series starts to decay exponentially immediate
ly after the azimuthal index has exceeded the critical value ka, a fac
t justifying the introduction of the concept of azimuthal-evanescent m
odes. By exploiting the above decomposition, the direct numerical summ
ation of the normal-mode series becomes feasible up to ka approximate
to 1000. For calculations at even higher frequencies (ka --> infinity)
, asymptotic expressions are derived by using appropriate integral rep
resentations of Bessel and Hankel functions, in conjunction with the m
ethod of stationary phase. The asymptotic analysis shows that the scat
tered field is obtained as a superposition of 2-D point sources lying
on the boundary of the vertical cylinder, with appropriate amplitudes
and phases. Excellent agreement between asymptotic and direct summatio
n numerical results has been demonstrated, at moderate frequencies, wh
ere both representations are expected to be valid. (C) 1997 Acoustical
Society of America.