MS23.7 - Vibro-Acoustics

Quasiperiodic systems are characterized by deterministic patterns that exhibit correlation in the long-range order and present unique properties that have been the subject of extensive research in various areas of physics as electronics, electromagnetics or elasticity. One of the most visible features of quasiperiodicity is the self-similarity of the spectrum of permitted modes and frequencies. Sturmian quasiperiodic lattices are under consideration in this work. A Sturmian word (or sequence) is a particular case of an infinite Word formed from a two-letter alphabet and, among other applications, allows the construction of quasiperiodic patterns. Such sequences, also called mechanical words, can be generated from real numbers. Here we propose to investigate systems structured according to quasiperiodic patterns governed by so-called Sturmian sequences. This research is carried out in the context of structural dynamics and allows the application to mechanical engineering of concepts that until now have been applied in other fields.

Hyperuniformity is a property of certain heterogenous media in which density fluctuations in the long wavelength range decay to zero. In reciprocal space this behavior translates into a decay of Fourier in- tensities in the range near small wavenumbers. In this paper quasiperiodic tilings constructed by word concatenation are under study. A lattice is generated from a parameter given by its continued fraction. Numerical simulations of such kind of media shows a quite regular quadratic decay of Fourier intensities.