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Vibrations of a folded plate. (English) Zbl 0712.73044

The purpose of this article is to derive two-dimensional eigenvalue problems that describe the limit behaviour of the three-dimensional eigenvalue problem of linearized elasticity in thin folded plates when the thickness of the plates tends to 0. This is a question of interest since the result provides a model for the free vibrations of folded plate structures.
It is shown that the eigenvalues and eigenvectors of the three- dimensional linearized elasticity operator in a thin folded plate converge toward the eigenvalues and eigenvectors of a limit 2d-2d model as the thickness of the plates tends to 0. The convergence of the associated stresses is also established.
[See also: the author, C. R. Acad. Sci., Paris, Ser. I 304, 571-573 (1987; Zbl 0634.73047), and P. G. Ciarlet and S. Kesavan, Comput. Methods Appl. Mech. Eng. 26, 145-172 (1981; Zbl 0489.73057).]
Reviewer: G.Ramaiah

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
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References:

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