This article is cited in 6 papers

On Eigenvibrations of a Body with Many Concentrated Masses Located Nonperiodically along the Boundary

E. I. Doronina, G. A. Chechkin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A boundary value problem is considered for a system of linear elasticity theory with nonperiodic rapidly varying boundary conditions and a large number of concentrated masses near the boundary. The asymptotic behavior of the solutions to this problem as well as the limit behavior of its spectrum are analyzed. It is assumed that the number of concentrated masses has a logarithmic growth with respect to a small parameter that characterizes the diameter of the concentrated masses. The case when the limit problem has the Fourier boundary condition and the density of inclusions is not very high is considered.

UDC: 517.956.226

Received in December 2000

 English version: Proceedings of the Steklov Institute of Mathematics, 2002, 236, 148–156

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