Minimizing the number of layers of the quasi one-dimensional phononic structures

Abstract

In the work, multi-criteria optimization of phononic structures was performed to minimize the transmission in the frequency range of acoustic waves, eliminate high transmission peaks with a small half-width inside of the band gap, and what was the most important part of the work – to minimize the number of layers in the structure. Two types of the genetic algorithm were compared in the study. The first one was characterized by a constant number of layers (GACL) of the phononic structure of each individual in each population. Then, the algorithm was run for a different number of layers, as a result of which the structures with the best value of the objective function were determined. In the second version of the algorithm, individuals in populations had a variable number of layers (GAVL) which required a different type of target function and crossover procedure. The transmission for quasi-one-dimensional phononic structures was determined with the use of the transfer matrix method algorithm. Based on the research, it can be concluded that the developed GAVL algorithm with an appropriately selected objective function achieved optimal solutions in a much smaller number of iterations than the GACL algorithm, and the value of the k parameter below 1 leads to faster achievement of the optimal structure.