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Converging bounds for the effective shear speed in 2D phononic crystals

Calculation of the effective quasistatic shear speed $c$ in 2D solid phononic crystals is analyzed. The plane-wave expansion (PWE) and the monodromy-matrix (MM) methods are considered. For each method, the stepwise sequence of upper and lower bounds is obtained which monotonically converges to the exact value of $c$. It is proved that the two-sided MM bounds of $c$ are tighter and their convergence to $c$ is uniformly faster than that of the PWE bounds. Examples of the PWE and MM bounds of effective speed versus concentration of high-contrast inclusions are demonstrated.

preprint2013arXivOpen access
A. A. KutsenkoA. L. ShuvalovA. N. Norris
math-phmath.FAmath.MP
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A. A. KutsenkoA. L. ShuvalovA. N. Norris

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