We study theoretically the propagation and localization of acoustic waves in quasi-periodic structures made of solid and fluid layers arranged according to a Fibonacci sequence. We consider two types of structures: either a given Fibonacci sequence or a periodic repetition of a given sequence called Fibonacci superlattice. Various properties of these systems such as: the scaling law and the self-similarity of the transmission spectra or the power law behavior of the measure of the energy spectrum have been highlighted for waves of sagittal polarization in normal and oblique incidence. In addition to the allowed modes which propagate along the system, we study surface modes induced by the surface of the Fibonacci superlattice. In comparison with solid-solid layered structures, the solid-fluid systems exhibit transmission zeros which can break the self-similarity behavior in the transmission spectra for a given sequence or induce additional gaps other than Bragg gaps in a periodic structure.
Keywords: Quasi-periodic structure; Self-similarity; Solid–fluid layers; Superlattice; Surface acoustic waves.
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