Vibrating Systems with Many Concentrated Masses: On the Low Frequencies and the Local Problem
We consider the vibrations of a body occupying a domain Ω of ℝ n , n = 2,3, that contains many small regions of high density near the boundary, so-called concentrated masses. We refer to – for a previous study of these vibrating systems, and to – for vibrating systems with one single concentrated mass. We study the asymptotic behavior, as ε → 0, of the eigenelements (λε, u ε of the corresponding spectral problem (31.2).
KeywordsEigenvalue Problem Local Problem Spectral Problem Concentrate Masse Whisper Gallery Mode
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- 2.M. Lobo and E. Pérez, Vibrations of a body with many concentrated masses near the boundary: high frequency vibrations, in Spectral Analysis of Complex Structures, Travaux en Cours 49, E. Sanchez-Palencia ed., Hermann, Paris, 1995, 85–101.Google Scholar
- 7.J. Sanchez-Hubert and E. Sanchez-Palencia, Vibration and Coupling of Continuous Systems. Asymptotic Methods, Springer-Verlag, Heidelberg, 1989.Google Scholar