Investigating topological modes in acoustic and elastic one-dimensional waveguides

Abstract

Interface modes have been investigated by the student on a first stage of Scientific Initiation. In this initial study, the phononic crystal (PC) from the work of Carneiro et al. (Carneiro et al., 2018) that is based on elastic rods, was used with the intention of understand and extrapolate the geometric phase determination methods developed in scientific literature (Xiao et al., 2014). To this end, the experimental data from the work of Carneiro et al. was used. Nevertheless, our attempts to obtain the geometric phases have not obtain success yet. Therefore, the suggestion is to focus the efforts upon that purpose. To perform such investigations, it is paramount to study the physical models and the mathematical methods that are more often used on the analysis of such periodic systems. The student has already been considering the topic and thus he could expose a brief historical review, tracing back to the Pythagorean studies of sound until more recently elaborated methods that rely on spectral analysis. Moreover, this text summarizes the lumped elements model and the models obtained from the spectral element method or SEM. Aiming validation of the models, it is made a comparison with the results from the classic modal analysis. In the light od two fundamental tools - dispersion relation diagrams and the concept of geometric phase (GP) - also previously studied by the student, as shown in the next section, it is proposed to acquire new measures with the model from Carneiro e al. experiment and to calculate the GPs of this system. Additionally, it will be designed a new system of PCs and it will be experimentally described, have in mind to improve the correlation between experimental and simulated data and develop deep understanding on the interpretation of the geometric phases for prediction of topological modes in elastic crystals. (AU)