Effective medium theory of the one-dimensional resonance phononic crystal

Abstract

A general theoretical scheme to describe the effective modulus and mass density foracoustic metamaterials is presented. For such a purpose, an effective medium theory of aone-dimensional acoustic waveguide containing subwavelength-sized Helmholtz resonatorsis formulated. It is shown that, when the wavelength is much larger than theperiodic length and the size of the resonators, the whole composite structure canbe treated as an effective homogeneous medium in accounting for its acousticproperties. It is also shown that the acoustic characteristics, such as the effectivemodulus and the effective mass density, can be determined precisely from thetransmission and the reflection data. The calculated effective modulus and effectivemass density confirm that this structure behaves as a homogeneous metamaterialwith a negative effective modulus in a frequency range just above the resonantfrequency.