TY - JOUR
T1 - High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero
AU - Chaussade-Beaudouin, Marie
AU - Dauge, Monique
AU - Faou, Erwan
AU - Yosibash, Zohar
N1 - Publisher Copyright:
© 2017 Springer International Publishing.
PY - 2017
Y1 - 2017
N2 - The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2ε) tends to zero. Using a novel asymptotic expansion we determine the behavior of the eigenvalue λ(ε) and the eigenvector angular frequency k(ε) for shells with Dirichlet boundary conditions along the lateral boundary, and natural boundary conditions on the other parts. First, the scalar Laplace operator for acoustics is addressed, for which k(ε) is always zero. In contrast to it, for the Lamé system of linear elasticity several different types of shells are defined, characterized by their geometry, for which k(ε) tends to infinity as ε tends to zero. For two families of shells: cylinders and elliptical barrels we explicitly provide λ(ε) and k(ε) and demonstrate by numerical examples the different behavior as e tends to zero.
AB - The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2ε) tends to zero. Using a novel asymptotic expansion we determine the behavior of the eigenvalue λ(ε) and the eigenvector angular frequency k(ε) for shells with Dirichlet boundary conditions along the lateral boundary, and natural boundary conditions on the other parts. First, the scalar Laplace operator for acoustics is addressed, for which k(ε) is always zero. In contrast to it, for the Lamé system of linear elasticity several different types of shells are defined, characterized by their geometry, for which k(ε) tends to infinity as ε tends to zero. For two families of shells: cylinders and elliptical barrels we explicitly provide λ(ε) and k(ε) and demonstrate by numerical examples the different behavior as e tends to zero.
KW - Axisymmetric shell
KW - Developable shell
KW - Koiter
KW - Lamé
KW - Sensitive shell
UR - http://www.scopus.com/inward/record.url?scp=85013941528&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-47079-5_5
DO - 10.1007/978-3-319-47079-5_5
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AN - SCOPUS:85013941528
SN - 0255-0156
VL - 258
SP - 89
EP - 110
JO - Operator Theory: Advances and Applications
JF - Operator Theory: Advances and Applications
ER -