Converging bounds for the effective shear speed in 2D phononic crystals
arXiv:1309.4333 · doi:10.1007/s10659-012-9417-y
Abstract
Calculation of the effective quasistatic shear speed 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 . It is proved that the two-sided MM bounds of are tighter and their convergence to 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.
13 pages, 10 figures