Eigenmode asymptotics in thin elastic plates

Journal des Mathematiques Pures et Appliquees

Volumn 78, Issue 9, 1999, Pages 925-964

  Dauge, M ^a   Djurdjevic, I ^b   Faou, E ^a   Rossle A ^b  

^a CNRS   (France)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Asymptotic expansion; Eigenvalues; Linear elasticity; Modal analysis; Thin plates

Indexed keywords

EID: 0033539438     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(99)00138-5     Document Type: Article

References (18)

1. V.L. Berdichevskii, Variational Principles of Continuum Mechanics, Nauka, Moscow, 1983 (in Russian).
2. P.G. Ciarlet,Mathematical Elasticity. Vol. II, Theory of Plates, North-Holland, Amsterdam, 1997.
3. P.G. Ciarlet and S. Kesavan, Two-dimensional approximation of three-dimensional eigenvalue problems in plate theory, Comput. Methods Appl. Mech. Engrg. 26 (1981) 149-172.
4. M. Dauge and I. Gruais, Asymptotics of arbitrary order for a thin elastic clamped plate. I: Optimal error estimates, Asymptotic Anal. 13 (1996) 167-197.
5. M. Dauge and I. Gruais, Asymptotics of arbitrary order for a thin elastic clamped plate. II: Analysis of the boundary layer terms, Asymptotic Anal. 16 (1998) 99-124.
6. M. Dauge, I. Gruais and A. Rössle, The influence of lateral boundary conditions on the asymptotics in thin elastic plates, to appear in SIAM J. Math. Anal. (1999).
7. N. Dunford and J. Schwartz, Linear Operators - Part II, Interscience Publishers, New York, 1963.
8. G. Duvaut and J.-L. Lions, Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972.
9. K.O. Friedrichs and R.F. Dressler, A boundary-layer theory for elastic plates, Comm. Pure Appl. Math. 14 (1961) 1-33.
10. R.D. Gregory and F.Y. Wan, Decaying states of plane strain in a semi-infinite strip and boundary conditions for plate theory, J. Elasticity 14 (1984) 27-64.
11. T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958) 261-322.
12. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1976.
13. V.G. Maz'ya, S.A. Nazarov and B.A. Plamenevskii, Asymptotische Theorie Elliptischer Randwertaufgaben in Singulär Gestörten Gebieten II, Mathematische Monographien, Band 83, Akademie Verlag, Berlin, 1991.
14. S.A. Nazarov, On the Spectrum Asymptotics in the Elasticity Theory for Thin Plates, 1998 (in Russian).
15. S.A. Nazarov, The spatial structure of the stress field in the neighbourhood of the corner point of a thin plate, J. Appl. Math. Mech. 55 (4) (1991) 523-530.
16. S.A. Nazarov, Two-term asymptotics of solutions of spectral problems with singular perturbation, Math. USSR Sbomik 69 (2) (1991) 307-340.
17. S.A. Nazarov and I.S. Zorin, Edge effect in the bending of a thin three-dimensional plate, Prikl. Mat. Mekh. 53 (4) (1989) 642-650. English translation J. Appl. Math. Mech. (1989) 500-507.
18. M.I. Vishik and L.A. Lyusternik, Regular degeneration and boundary layers for linear differential equations with small parameter, Amer. Math. Soc. Transl. (2) 20 (1962) 239-364.