Abstract
The goal of this paper is to establish a general homogenization result for linearized elasticity of an eigenvalue problem defined over perforated domains, beyond the periodic setting, within the framework of the H0-convergence theory. Our main homogenization result states that the knowledge of the fourth-order tensor A0, the H0-limit of Aε, is sufficient to determine the homogenized eigenvalue problem and preserve the structure of the spectrum. This theorem is proved essentially by using Tartar’s method of test functions, and some general arguments of spectral analysis used in the literature on the homogenization of eigenvalue problems. Moreover, we give a result on a particular case of a simple eigenvalue of the homogenized problem. We conclude our work by some comments and perspectives.
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The authors would like to thank the referees who provided valuable suggestions that greatly improved the quality of the manuscript.
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Ait Yahia, M.M.L., Haddadou, H. A general homogenization result of spectral problem for linearized elasticity in perforated domains. Appl Math 66, 701–724 (2021). https://doi.org/10.21136/AM.2021.0009-20
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DOI: https://doi.org/10.21136/AM.2021.0009-20