Abstract
Numerical experiments were conducted to determine the validity of the quasicrystalline approximation and coherent potential approximation methods for theoretically predicting the ensemble average response of a two-dimensional random medium. The medium was composed of a tensioned mesh to which springs of both positive and negative stiffness, acting transversely to the plane of the mesh, were randomly attached at the mesh intersection sites. Various combinations of scatterer density (the number of attached springs divided by the number of sites) and scatterer strength (the spring stiffness) were evaluated at two steady-state forcing frequencies. The theories yielded similar results unless the Waterman and Truell criterion became excessive; however, at that point, both theories failed. Hence, in terms of accuracy, neither theory was found to possess a distinct advantage over the other.
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