MATHEMATICAL MODELING OF ACOUSTIC WAVE PROPAGATION IN ELASTIC MATERIALS WITH MULTI-PERIODIC HIERARCHICAL STRUCTURE OF HETEROGENEITIES-Reference-Cited by-同舟云学术

MATHEMATICAL MODELING OF ACOUSTIC WAVE PROPAGATION IN ELASTIC MATERIALS WITH MULTI-PERIODIC HIERARCHICAL STRUCTURE OF HETEROGENEITIES

Published:2023 Issue:3 Volume:14 Page:45-72
ISSN:2152-2057
Container-title:Composites: Mechanics, Computations, Applications: An International Journal
language:en
Short-container-title:Comp Mech Comput Appl Int J

Author:

Savatorova Viktoria L.,Talonov Alexey V.

Abstract

An asymptotic homogenization procedure is applied for acoustic wave propagation in a heterogeneous elastic medium with a multi-periodic hierarchical structure of heterogeneities. We assume the existence of two periodic cells with characteristic sizes l2 and l1, respectively. The ratio ε = l2/l1 is considered to be small and of the same order of magnitude as the ratio l1 /L, where L is the macroscopic characteristic size of a system. The solution of the problem will be largely determined by the relation between the wavelength λ and the characteristic sizes of the system. For the case when λ/l1 ~ 1, we derive a homogenized macroscopic equation for the displacement and obtain approximations to the displacement and frequency. Several illustrative examples are considered to show the effect of peculiarities of the structure on two different spacial scales on energy distribution in the propagating wave.

Publisher

Begell House

Subject

Mechanics of Materials,Ceramics and Composites

Link

https://www.dl.begellhouse.com/download/article/4b0fdf2d57fcf116/CMCA1403(3)-47434.pdf

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