Abstract
A new homogenization method for complex structures has been developed. The method utilizes a local/global decomposition to separate the low and high parts of the wave number spectrum. The low wave number global problem has an infinite-order structural operator, and structural discontinuities are replaced by an equivalent distributed suspension. The rapidly varying local problem, which provides transfer function information for the global problem, is solved separately. Once formulated for a specific structure, the self-contained global problem is solved first, and the local solution can be reconstructed afterwards. The LGH reformulation, which applies over the entire frequency range, allows the global problem to be solved at much lower resolution than the length of flexural waves on the original structure. To demonstrate the approach, the problem of sound reflection from a flexible barrier with impedance discontinuities in a channel is described. The effects of radiating acoustic modes are transferred entirely to the smooth global problem, whereas evanescent acoustic modes are contained within the global structural operator. Sample calculations are presented comparing the method with the exact solution.
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