Dynamical effective parameters of elastic superlattice with strong acoustic contrast between the constituents
Yurii Zubov1, Bahram Djafari-Rouhani2, and Arkadii Krokhin1
1Department of Physics, University of North Texas, P.O. Box 311427, Denton, TX 76203 2Université de Lille, Department of Physics, Villeneuve d'Ascq 59655, France
Received July 9, 2018, published online October 26, 2018
Analytical formulas are obtained for frequency-dependent effective elastic modulus and effective mass density for a periodic layered structure. The proposed homogenization procedure is valid at sufficiently high frequencies well above the lowest band gap in the acoustic spectrum of the structure. It is shown that frequency-dependent effective parameters may take negative values either in different regions of frequencies or in the same quite narrow region. This property demonstrates that 1D elastic structure may behave in the limit of small Bloch wave vectors as a double-negative acoustic metamaterial.