Leopold B. Felsen
Ronald Shaya
Dept. of Elec. Eng., Polytechnic Univ., Six Metrotech Center, Brooklyn, NY 11201
A previous angular harmonic series analysis of scattering from a periodically ribbed submerged elastic infinite cylindrical thin shell [C. B. Burroughs, J. Acoust. Soc. Am. 75, 715--722 (1984)] is converted into a wave-based analysis that emphasizes circumferential wave phenomena in the scattering process. The conversion is accomplished by extending the azimuthal mode index from its periodicity-constrained integer values n to a (nu) continuum in periodic infinite angular domain. Subject to the n->(nu) replacement, the Burroughs solution furnishes the integrand in the ((nu),(beta)) spectral wave-number domain that corresponds to the ((phi),z) angular-axial space coordinates. The analytic properties of the spectral integrand, which is separated into bare-shell and angular-rib-induced scatterings, are examined, and the ((nu),(beta)) spectral synthesis is performed in a manner that favors extraction of ray-acoustic phenomenology by high-frequency asymptotics. The asymptotic reduction of this ray-acoustically parametrized solution for the acoustic pressure, which is exact except for thin shell asymptotics, is performed in the companion paper [L. B. Felsen and R. Shaya, following paper].