Finite Element Study of Harmonic Forcing Function Scattering Mechanisms for Cylindrical Structures

Low frequency sound radiation from cylindrical structures is generally dominated by radiation from low order (M=0, 1) circumferential harmonic modes. The high order circumferential harmonic modes are inefficient radiators below the coincidence frequency. For cylindrical structures excited by low frequency, high circumferential order (e.g. N=10) forcing functions, the radiated sound will be dominated by radiation from the low order modes if the forcing function is scattered by structural asymmetries into these modes. In this study, cylindrical structures of varying levels of asymmetry are examined using finite element analysis to quantify the scattering of order N harmonic forcing functions into order M structural response harmonics. First, purely axially-symmetric structures are examined to verify the analysis method used. The models examined include a finite cylinder with constant cross-section and a finite cylinder with tapered cross-section. The constant cross-section cylinder is analyzed in vacuo, and the tapered cylinder is analyzed both in vacuo and with water loading. These structures show no harmonic scattering, as would be expected. Next, a finite tapered cylinder with cyclically symmetric impedance discontinuities and a finite tapered cylinder with an asymmetric large impedance discontinuities are analyzed, both with water loading, to determine the impact of structural discontinuity on the harmonic scattering and radiated sound spectra. The periodic and single discontinuities both show significant scattering into low order circumferential modes and corresponding increases in radiated sound.