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.
@article{arxiv.1106.5412,
title = {Effective speed of sound in phononic crystals},
author = {A. A. Kutsenko and A. L. Shuvalov and A. N. Norris},
journal= {arXiv preprint arXiv:1106.5412},
year = {2011}
}