Yurii Z., Djafari-Rouhani B., Krokhin A. «Dynamical effective parameters of elastic superlattice with strong acoustic contrast between the constituents» Физика низких температур, 44, № 12, с. 1639-1644 (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.