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

Nieves, Michael J ORCID: 0000-0003-4616-4548 and Movchan, Alexander B ORCID: 0000-0001-8902-9923 (2022) Asymptotic analysis of in-plane dynamic problems for elastic media with rigid clusters of small inclusions. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 380 (2237). 20210392-.

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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)'.

Item Type:	Article
Uncontrolled Keywords:	Dirichlet problems, asymptotic analysis, clusters of inclusions, in-plane elastodynamics, meso-scale approximations
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	11 Aug 2023 14:18
Last Modified:	11 Aug 2023 14:18
DOI:	10.1098/rsta.2021.0392
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3172181