Research output: Contribution to journal › Article › peer-review
Asymptotics of eigen-oscillations of a massive elastic body with a thin baffle. / Nazarov, S.A.
In: Izvestiya: Mathematics, No. 1, 2013, p. 87-142.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Asymptotics of eigen-oscillations of a massive elastic body with a thin baffle
AU - Nazarov, S.A.
PY - 2013
Y1 - 2013
N2 - 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 ≪ 1). The spectrum contains two series of eigenvalues with stable asymptotic behaviour. The first is formed by eigenvalues O(h2) 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. © 2013 RAS(DoM) and LMS.
AB - 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 ≪ 1). The spectrum contains two series of eigenvalues with stable asymptotic behaviour. The first is formed by eigenvalues O(h2) 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. © 2013 RAS(DoM) and LMS.
U2 - 10.1070/IM2013v077n01ABEH002630
DO - 10.1070/IM2013v077n01ABEH002630
M3 - Article
SP - 87
EP - 142
JO - Izvestiya Mathematics
JF - Izvestiya Mathematics
SN - 1064-5632
IS - 1
ER -
ID: 7521614