  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.
