V. G. Maz'ya, A. B. Movchan, M. J. Nieves, “On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions”, Algebra i Analiz, 2020, Volume 32, Issue 3,Pages <nobr>219

This article is cited in 6 papers

Research Papers

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

V. G. Maz'ya^abc, A. B. Movchan^b, M. J. Nieves^de

^a Department of Mathematics, Linköping University, Linköping S--581 83, Sweden
^b Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
^c RUDN University, 6 Miklukho-Maklay St, 117198 Moscow, Russia
^d School of Computing and Mathematics, Keele University, Staffordshire, ST5 5BG, UK
^e Department of Mechanical, Chemical and Material Engineering, University of Cagliari, 09123 Cagliari, Italy

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.

Keywords: two-dimensional elastic membranes, clusters of small inclusions, inertia of inclusions.

Received: 11.05.2019

Language: English