Wave transmission in quasi-periodic lattices

Structural lattices with quasi-periodic patterns possess interesting dynamic features that can be exploited to control, localize and redirect propagating waves. In this work, we show that the properties of a large class of quasi-periodic locally resonant systems (approximated as periodic, with arbitrarily large period) can be performed by defining an equivalent discrete system. Several properties of wave propagation can <i>a priori</i> be demonstrated with reference to this system. Results in terms of bulk spectrum, showing the Hofstadter butterfly pattern, and of topological modes are then discussed in detail with reference to a simple example of quasi-periodic lattice. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.