Aplicação da teoria de estruturas periódicas na análise dinâmica de uma barra

Abstract

Vibration control at unwanted frequencies is necessary to prevent or avoid mechanical problems that may occur in equipment. One of the ways of doing this vibration control is with the help of periodic structures, which are nothing more than periodically distributed elements, with geometry or material variation. Bearing this in mind, the objective of this work is to present and analyze the influence of the periodicity of material and/or geometry of a bar in order to attenuate vibrations at unwanted frequencies through the Periodic Structure Theory. The analysis is carried out analytically, which results in the solution of a problem of eigenvalues associated with the Transfer Matrix of the studied bar. The analyzes were carried out with the aid of the Matlab program, where the stop bands (where the vibration is attenuated) and wave passage were determined for three specific cases of periodicity: geometry, material and geometry and material. To validate the results, a Finite Element model was developed and Frequency Response Functions were simulated to compare the results. Through the analyses, it is possible to observe that, for the analyzed frequency range, the material variation periodicity case presented the first stop band in a lower frequency range than the structure geometry periodicity case. It was also observed that there was a significant increase in the number of natural frequencies existing in the passbands. It appears that the application of periodic structures in a mechanical design can be used as a strategy to attenuate vibrations at certain frequencies.