Band gaps of acoustic waves propagating in a solid/liquid phononic Fibonacci structure

We study the acoustic–phonon transmission spectra in quasiperiodic (Fibonacci type) superlattices made up from the solid crystal quartz and the liquid mercury (Hg). The phonon dynamics is described by a coupled elastic equations within the static field approximation model. We use a transfer-matrix treatment to simplify the algebra, which would be otherwise quite complicated, allowing a neat analytical expression for the phonon transmission coefficients. Numerical results is presented and discussed for both the transmittance spectra as well as the localization factor derived from the Lyapunov exponent, showing that the Fibonacci quasiperiodic structure acts as a filter for the phonon's transmission spectra.