Scattering from a Periodic Corrugated Surface. Part 4. Finite-Depth Alternately Filled Plates with Hard Boundaries.
NAVAL RESEARCH LAB WASHINGTON D C
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An incident plane wave is scattered from a periodic corrugated surface consisting of finite-depth parallel plates. Each period is further divided by an additional finite-depth parallel plate into two regions--one with the same density and wavenumber values as the free-space region above the plates, and the second with different but constant density and wavenumber values. The plates and bottoms have hard Neumann boundaries. Solutions of the Helmholtz equation, with unknown amplitude coefficients, are assumed in the various geometric regions. By requiring that the pressure and velocity be continuous functions at the boundaries, sets of linear equations are obtained that relate the amplitudes for arbitrary incident angles. Equations for normal incidence are solved using a variation of the modified residue calculus technique involving two zero shifts, and the results yield the amplitudes as values or residues of a meromorphic function. Author
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