Abstract
The paper shows how to use a genetic algorithm to design quasi one-dimensional structures with given properties. The superlattices were surrounded by water and made of epoxy resin and glass, with a layer thicknesses selected in such a way that a phononic bandgap occurs in the frequency range of acoustic waves. Multilayer transmission was calculated using the Transfer Matrix Method algorithm. In order to determine the optimal objective function for the genetic algorithm, the entire space of the possibility of the layers’ distribution for a six-layer structure was analyzed. The spread of the transmission integral values even for the 6-layer structure was significant and ranged from 11.9% to 81.5%. Minimizing the value of the transmission integral as an objective function could lead to a large number of high transmission peaks with a small half width. It allowed the determining of the optimal objective functions for minimizing transmission in a given frequency range, and another allowing for its maximization. The phase diagram of the solution space for the transmission integral from the integral of the absolute value of the transmission functions derivative was determined. Transmission of the most and the least optimal six-layer structures was shown depending on the assumed objective function. Then, the analysis of fifteen and thirty-layer structures was carried out. From the dependence of the objective function values for the best individuals for each generation, it was determined that despite carrying out a thousand iterations, the stable state was determined before reaching 250 iterations of the algorithm, and thus the optimal structure was determined. The transmissions ratio of analyzed structures in the studied frequency range (up to 20 kHz) to full transmission (without structures) in this acoustic frequency range for the analyzed optimal 6, 15 and 30-layer structures were 16.78%, 9.6% and 4.41%, respectively.
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