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Effective speed of sound in phononic crystals

A new formula for the effective quasistatic speed of sound $c$ in 2D and 3D periodic materials is reported. The approach uses a monodromy-matrix operator to enable direct integration in one of the coordinates and exponentially fast convergence in others. As a result, the solution for $c$ has a more closed form than previous formulas. It significantly improves the efficiency and accuracy of evaluating $c$ for high-contrast composites as demonstrated by a 2D example with extreme behavior.

preprint2011arXivOpen access
A. A. KutsenkoA. L. ShuvalovA. N. Norris
math-phmath.MP
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A. A. KutsenkoA. L. ShuvalovA. N. Norris

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