Abstract
A novel homogenization method for periodic structures that utilizes a local/global separation of the high and low wavenumber spectrum is presented. The low-wavenumber global problem has an infinite-order operator. The global problem is self-contained; local solutions can be reconstructed after the fact if desired. Global problems are constructed for a membrane and a plate in vacuo, each with periodic impedance discontinuities. A fluid-loading approximation is introduced in order to homogenize problems of interaction between fluid and structure. Radiating acoustic modes are contained in the smooth global problem, and the global structural operator accounts for an influence of evanescent acoustic modes. As an example, oblique sound reflection from a flexible barrier with impedance discontinuities is analyzed. Accurate results are obtained from the method.
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