Elastodynamical properties of Sturmian structured media

TL;DR

This paper investigates wave propagation in quasiperiodic media using Sturmian sequences, analyzing their fractal spectra and validating results through numerical examples applicable to various waveguides.

Contribution

It introduces a general methodology based on Sturmian sequences for modeling waveguides with quasiperiodic structures, applicable across different physical systems.

Findings

Bulk spectra exhibit fractal characteristics.

Different structured media produce diverse spectral shapes.

Theoretical results are validated with numerical examples.

Abstract

In this paper, wave propagation in structured media with quasiperiodic patterns is investigated. We propose a methodology based on Sturmian sequences for the generation of structured mechanical systems from a given parameter. The approach is presented in a general form so that it can be applied to waveguides of different nature, as long as they can be modeled with the transfer matrix method. The bulk spectrum is obtained and its fractal nature analyzed. For validation of the theoretical results, three numerical examples are presented. The obtained bulk spectra show different shapes for the studied examples, but they share features which can be explained from the proposed theoretical setting.