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Essential spectrum in vibrations of thin shells in membrane approximation: propagation of singularities
Author(s) -
Campbell Alain
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.579
Subject(s) - isotropy , gravitational singularity , mathematics , spectrum (functional analysis) , mathematical analysis , essential spectrum , boundary (topology) , shell (structure) , vibration , galerkin method , compact space , boundary value problem , geometry , physics , finite element method , optics , quantum mechanics , materials science , composite material , thermodynamics
The spectral problem of thin elastic shells in membrane approximation does not satisfy the classical properties of compactness and so there exists an essential spectrum. In the first part, we propose to determine this spectrum and the weakness directions in the shell. We particularly study the case of homogeneous and isotropic shells with some examples. In the second part, we consider an elementary model problem to study the propagation of singularities and their reflections at the boundary of the domain. In the last, we study the problem of propagation for an isotropic cylindrical shell and we show that the equation of propagation does not depend on the Poisson coefficient. Copyright © 2004 John Wiley & Sons, Ltd.