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

Garus Sebastian, Sochacki Wojciech, Kubanek Mariusz, Nabiałek Marcin

Bulletin of the Polish Academy of Sciences. Technical Sciences

2022

Vol. 70, nr 1

art. no. e139394

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.

High-performance quasi one-dimensional mirrors of mechanical waves built of periodic and aperiodic structures

Garus S., Sochacki W.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 4

19--24

The work studied the reflectance for quasi one-dimensional phononical structures. In composite superlattices, the thickness of the layers, their arrangement and selection of constituent materials with appropriate properties such as the density and velocity of mechanical waves propagation allows for the creation of a phononic band gap (PhBG) phenomenon. PhBG is characterized by high reflectance of the mechanical wave incident on the analyzed structure, which means that the wave does not propagate in the superlattice. The paper proposes periodic and aperiodic structures characterized by a wide range of reflectance for the ultrasonic frequencies of mechanical waves and shows how the change the thickness of the layer affects the properties of the analyzed structures.

One dimensional phononic FDTD algorithm and transfer matrix method implementation for Severin aperiodic multilayer

Garus S., Sochacki W.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 4

17--27

In this paper, the power spectrum and phononic properties of the quasi one-dimensional Severin aperiodic multilayer was investigated. Multilayer phononic structures with their phononic band gap properties can be used as filters of mechanical waves. In the paper, the implementation of the Finite Difference Time Domain (FDTD) algorithm with discrete Fourier transform and the Transfer Matrix Method algorithm in the Wolfram Language in Mathematica was made.