Asymptotics of eigen-oscillations of a~massive elastic body with a~thin baffle
Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 87-142
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We construct asymptotics of eigenvalues and eigenvectors in the
elasticity problem for an anisotropic body joined to a thin plate-baffle
(of variable thickness $O(h)$, $h\ll 1$). The spectrum contains two series
of eigenvalues with stable asymptotic behaviour. The first is formed
by eigenvalues $O(h^2)$ corresponding to the transversal vibrations of the
plate with rigidly clamped lateral surface, and the second contains
eigenvalues $O(1)$ generated by the longitudinal vibrations of the plate
as well as eigen-oscillations of the body without baffle. We verify the
convergence theorem for the first series, estimate the errors for both
series, and discuss the asymptotic correction terms and boundary layers.
Similar but simpler results are obtained in the scalar problem.
Keywords:
junction of a massive body and a thin plate, spectrum of an elastic body,
asymptotics of eigenvalues and eigenvectors, dimension reduction.
@article{IM2_2013_77_1_a5,
author = {S. A. Nazarov},
title = {Asymptotics of eigen-oscillations of a~massive elastic body with a~thin baffle},
journal = {Izvestiya. Mathematics },
pages = {87--142},
publisher = {mathdoc},
volume = {77},
number = {1},
year = {2013},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2013_77_1_a5/}
}
S. A. Nazarov. Asymptotics of eigen-oscillations of a~massive elastic body with a~thin baffle. Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 87-142. http://geodesic.mathdoc.fr/item/IM2_2013_77_1_a5/