Numerical solution of acoustic radiation from fluid-loaded periodic structures using local-global homogenization

Fluid-loaded vehicle structures, such as fuselages and hulls, often have spatially periodic discontinuities such as braces, ribs, and attachments. The structural motion, the acoustic radiation and scattering, and the interior sound field are of interest. Calculating the motion of fluid-loaded structures is a difficult task because of the high complexity and a disparity of length scales requiring high numerical resolution. Discontinuities cause the structural response to occur in a broad spectrum of spatial wavenumbers, and to exhibit stop-band and pass-band behavior. Structural discontinuities broaden the spatial wavenumber spectrum, causing both supersonic (radiating) and subsonic (nonradiating) waves. An analysis method called local-global homogenization (LGH) is used to predict directly the low wavenumber smooth response of periodic fluid-loaded structures in a self-contained manner. The low wavenumber part of the response is efficiently coupled to the acoustic field, since low wavenumbers correspond to supersonic phase speeds. In the LGH reformulation, an infinite order operator that must be truncated for numerical solution governs the equivalent smooth global problem. The numerical implementation is described, including the treatment of boundary conditions, and sample calculations are compared to exact solutions. The size of the computational problem is dramatically reduced by the LGH analytical reformulation.