Interaction between wave number pairs for a capped cylinder

When acoustic-structure interaction is analyzed according to the wave number-based version of the surface variational principle (SVP), considerable computational effort is required to generate each coefficient in the quadratic sum forming the variational quantity. Examination of the wet-surface impedance, which represents the spectrum of pressure amplitudes generated by a specified spectrum of surface velocity amplitudes, reveals that many cross-impedance terms are very small. This suggests that some coefficients need not be computed. The article introduces a priori criteria for selecting the impedance terms to be omitted, based on the supersonic cutoff wave number. Each truncation scheme is assessed by comparing its predictions to the convergent SVP solution. It is shown that, for the nonsymmetric azimuthal harmonics, the field quantities and the radiated power are well predicted if subsonic waves are ignored. In contrast, for the axisymmetric component, substantial errors (6 dB or more) for radiated power arise, unless a broad spectrum of subsonic waves are included in the formulation. The complex power is mostly reactive, being associated with an evanescent field, even for the supersonic spectrum. The study shows that small interactions between subsonic waves in the axisymmetric case can result in the high wave number spectrum being associated with substantial radiation contributions.