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On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions

Maz′ya, V.G.; Movchan, A.B.; Nieves, M.J.

On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions Thumbnail


Authors

V.G. Maz′ya

A.B. Movchan



Abstract

Formal asymptotic algorithms are considered for a class of meso-scale approximations for problems of vibration of elastic membranes that contain clusters of small inertial inclusions distributed along contours of predefined smooth shapes. Effective transmission conditions have been identified for inertial structured interfaces, and approximations to solutions of eigenvalue problems have been derived for domains containing lower-dimensional clusters of inclusions.

Journal Article Type Article
Acceptance Date May 11, 2021
Publication Date May 11, 2021
Publicly Available Date Mar 29, 2024
Print ISSN 1061-0022
Electronic ISSN 1547-7371
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
Volume 32
Issue 3
Pages 551 - 564
DOI https://doi.org/10.1090/spmj/1661
Keywords two-dimensional elastic membranes; clusters of small inclusions; inertia of inclusions
Publisher URL https://www.ams.org/journals/spmj/2021-32-03/S1061-0022-2021-01661-6/home.html

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