Wave propagation in phononic materials based on the reduced micromorphic model by one-sided Fourier transform
Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt
2 Department of Mathematics, Faculty of Science, Cairo University, 12613, Giza, Egypt
Accepted: 22 March 2022
Published online: 8 April 2022
A one-dimensional problem of wave propagation in phononic materials is solved under the reduced micromorphic model introduced recently. An efficient technique is used for the solution, based on one-sided Fourier transform. This allows obtaining an exact solution in closed form, which can be utilized to check approximate solutions obtained by other methods. The results are confirmed numerically by the method of finite differences. They illustrate the existence of frequency band gaps.
© The Author(s) 2022
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.