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 -