Algoritmo genético aplicado à otimização da estrutura de bandas de cristais fonônicos 1d

Abstract

This work aims to optimize the band structures (dispersion diagrams) of 1D phononic crystal using genetic algorithms with the improved plane wave expansion (IPWE) method. The phononic crystals consist of a periodic network of dispersers immersed in a host environment. Due to band gaps, where there are only evanescent (non-propagating) mechanical (elastic or acoustic) waves, they have been extensively studied in recent decades. There are several applications of phononic crystals, for example vibroacoustic control. There are several techniques in the literature to obtain the band structures. One of the most used is the IPWE, which is applied in this study. The variation of the types of material and the filling factor of the phononic crystal can maximize prohibited bands, increasing the bandwidth. In this way, it is investigated the band structures obtained by IPWE for 1D phononic crystal rods and Euller-Bernoulli beams using a genetic algorithm. IPWE is a semi-analytical technique used for calculating the band structures, based on an eigenvalue-eigenvector problem, which is computationally solved. The optimization technique associated with IPWE is used considering the variation of the percentage of each material present in the unit cell of the phononic crystal and the selected materials, seeking an optimized value for the prohibited bandwidth. It is observed that the optimization technique associated with IPWE is effective to increase the prohibited bandwidth for a specific range of frequency