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

Maz′ya, V.; Movchan, A.; Nieves, M.

doi:10.1090/spmj/1661

On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions
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by V. G. Maz′ya, A. B. Movchan and M. J. Nieves

St. Petersburg Math. J. 32, 551-564

DOI: https://doi.org/10.1090/spmj/1661

Published electronically: May 11, 2021

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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.

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