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.

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.

Citation

Maz′ya, V., Movchan, A., & Nieves, M. (2021). On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions. St. Petersburg Mathematical Journal, 32(3), 551 - 564. https://doi.org/10.1090/spmj/1661

• Journal Article Type: Article
• Acceptance Date: May 11, 2021
• Publication Date: May 11, 2021
• 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