Effective speed of sound in phononic crystals

TL;DR

This paper introduces a new, efficient formula for calculating the effective speed of sound in 2D and 3D phononic crystals, improving accuracy especially for high-contrast composites.

Contribution

It presents a novel monodromy-matrix operator approach that yields a more closed-form, faster-converging solution for the effective sound speed in periodic materials.

Findings

The new formula achieves exponential convergence and higher accuracy.

Demonstrated effectiveness on a 2D high-contrast composite example.

Significantly improves computational efficiency for phononic crystal analysis.

Abstract

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.