Wave-number spectrum and normal mode solutions for sound scattering from internally loaded cylindrical shells

Abstract

In a companion paper [L. B. Felsen and Y. P. Guo, J. Acoust. Soc. Am. 94, ⧠⧠ (1993)], two-dimensional acoustic wave scattering from a thin elastic cylindrical shell with internal loading has been expressed in terms of a hybrid ray-mode algorithm that combines ray-type traveling wave fields in the fluid with resonant modes in the structure. The algorithm is based on decomposition of the overall problem into a background problem for the empty shell, on which the internal loads are accounted for by induced equivalent forces at the load attachment points. In the numerical implementation, it was found convenient to express the induced forces due to the internal loading and consequent modal resonances in harmonic series form. This use of the angular harmonics solution for the coupling forces is not only computationally efficient, but also reveals the mechanisms that are responsible for many features observed in the far field. Nevertheless, it is of interest to formulate and solve the problem entirely in a traveling-wave-based representation, which is the counterpoise to the previous solution strategy based entirely on angular harmonics [Y. P. Guo, ‘‘Sound scattering from an internally loaded cylindrical shell,’’ J. Acoust. Soc. Am. 91, 926–938 (1992)]. The traveling wave form isolates individual scattering events and charts the evolution of resonances by successive multiple interactions. Poisson summation is shown to transform one solution into the other, thereby exhibiting for each wave constituent the traveling versus standing wave alternatives.