Asymptotic analysis of in-plane dynamic problems for elastic media with rigid clusters of small inclusions-Reference-Cited by-同舟云学术

Asymptotic analysis of in-plane dynamic problems for elastic media with rigid clusters of small inclusions

Published:2022-10-10 Issue:2237 Volume:380 Page:
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Nieves Michael J.¹^ORCID,Movchan Alexander B.²^ORCID

Affiliation:

1. School of Computer Science and Mathematics, Keele University,Keele ST5 5BG, UK

2. Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK

Abstract

We present formal asymptotic approximations of fields representing the in-plane dynamic response of elastic solids containing clusters of closely interacting small rigid inclusions. For finite densely perforated bodies, the asymptotic scheme is developed to approximate the eigenfrequencies and the associated eigenmodes of the elastic medium with clamped boundaries. The asymptotic algorithm is also adapted to address the scattering of in-plane waves in infinite elastic media containing dense clusters. The results are accompanied by numerical simulations that illustrate the accuracy of the asymptotic approach. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’.

Funder

H2020 Marie Skłodowska-Curie Actions

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2021.0392

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2. Asymptotic analysis of in-plane dynamic problems for elastic media with rigid clusters of small inclusions;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2022-10-10