Converging Bounds for the Effective Shear Speed in 2D Phononic Crystals |
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| Authors: | A A Kutsenko A L Shuvalov A N Norris |
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| Institution: | 1. Institut de Mécanique et d’Ingénierie de Bordeaux, Université de Bordeaux, UMR 5295, Talence, 33405, France
2. Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ, 08854, USA
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| Abstract: | 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. |
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