Vibrations of elastic systems with a large number of tiny heavy inclusions

Abstract

We consider a spectral problem modeling natural vibrations of a complex medium that consists of an elastic medium and tiny rigid inclusions. We study the asymptotic behaviour of solutions of this problem when the total number of inclusions and their density tend to infinity. We obtain a limit problem being a spectral problem for a linear fractional operator pencil that describes the macroscopic behaviour of the system (global vibrations). To cite this article: V. Rybalko, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 245–250.