The formal asymptotics of eigenmodes for oscillating elastic spatial body with concentrated masses

D. Gomez   ; S. A. Nazarov   ; M. E. Perez

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 36, Tome 342 (2007), pp. 31-76

Résumé

Limiting spectral problems are derived for the problem about eigen-oscillations of a solid with small heavy (or light) inclusions. The asymptotic ansätze for eigenvalues and eigenvectors as well as the limiting problems are crucially dependent on relation between the geometrical and physical parameters and also the disposition of inclusions. It is established that for heavy inclusions the limiting problems are linked together into the resultant spectral problem which describes “far-action” in the family of the inclusions.

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