Asymptotic behaviour of viscoelastic composites with almost periodic microstructures

TL;DR

This paper investigates the macroscopic acoustic properties of viscoelastic porous media with almost periodic microstructures, using advanced mathematical tools to derive effective medium behavior from complex micro-scale models.

Contribution

It introduces a novel homogenization approach for viscoelastic composites with almost periodic microstructures using sigma convergence techniques.

Findings

Derived the effective macroscopic model for viscoelastic porous media.

Established the use of sigma convergence for convolution sequences in this context.

Provided mathematical characterization of the asymptotic behavior of the composites.

Abstract

In this paper we study the acoustic properties of porous media saturated by an incompressible viscoelastic fluid. The model considered here consists of a linear deformable porous skeleton having memory that is surrounded by a viscoelastic Oldroyd fluid. Assuming the microstructures to be almost periodically distributed and under the almost periodicity hypothesis on the coefficients of the governing equations, we determine the macroscopic equivalent medium. To achieve our goal, we use some very recent tools about the sigma convergence of convolution sequences.