On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions
Vladimir Gilelevich Maz'ya, A. B. Movchan, Michael J. Nieves · St Petersburg Mathematical Journal · 2021
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.