Universal Representation of Dynamic Frequency Spectra for Canonical Generalised Quasicrystalline-Generated Waveguides

An effective way to describe the sequence of stop and pass bands in a one-dimensional phononic waveguide is represented by the \lq flow' line reported onto the plot of the relevant $\pi$-periodic reduced torus. In this chapter, these concepts are introduced for silver-mean quasicrystalline-generated elastic waveguides. Results are obtained for canonical configurations for which the dynamic frequency spectra are periodic. Application to finite-size waveguides is also illustrated. As the silver-mean sequence is one of the generalised Fibonacci sequences, the illustrated method can be easily extended to other quasicrystalline substitution rules.