Comptes Rendus
no. 12
Asymptotics of eigenfrequencies of an elastic body with a heavy and hard peak-shaped inclusion
[Développement asymptotique des fréquences propres d'un corps élastique avec une inclusion lourde et de forme très pointue]

Présenté par : Évariste Sanchez-Palencia

Sergey A. Nazarov1
1 Institute of Mechanical Engineering Problems, V.O., Bol'shoi pr., 61, 199178 St. Petersburg, Russia
Comptes Rendus. Mécanique, Volume 335 (2007) no. 12, pp. 757-762.

Une inclusion lourde et dure de forme pointue dans un corps élastique provoque la concentration des valeurs propres dans le domaine basses fréquences du spectre et la localisation des modes propres correspondants près de l'extrémité du pic.

A heavy and hard peak-shaped inclusion in an elastic body provokes to concentration of eigenvalues in the low-frequency range of the spectrum and localization of the corresponding eigenmodes near the peak tip.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2007.06.004
Keywords: Computational solid mechanics, Elasticity system, Heavy and hard peak-shaped inclusion, Localization of eigenvectors
Mot clés : Mécanique des solides numérique, Système de l'elasticité, Inclusion lourde et de forme très pointue, Localisation des vecteurs propres
Sergey A. Nazarov 1

1 Institute of Mechanical Engineering Problems, V.O., Bol'shoi pr., 61, 199178 St. Petersburg, Russia 
@article{CRMECA_2007__335_12_757_0,
     author = {Sergey A. Nazarov},
     title = {Asymptotics of eigenfrequencies of an elastic body with a heavy and hard peak-shaped inclusion},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {757--762},
     publisher = {Elsevier},
     volume = {335},
     number = {12},
     year = {2007},
     doi = {10.1016/j.crme.2007.06.004},
     language = {en},
}
TY  - JOUR
AU  - Sergey A. Nazarov
TI  - Asymptotics of eigenfrequencies of an elastic body with a heavy and hard peak-shaped inclusion
JO  - Comptes Rendus. Mécanique
PY  - 2007
SP  - 757
EP  - 762
VL  - 335
IS  - 12
PB  - Elsevier
DO  - 10.1016/j.crme.2007.06.004
LA  - en
ID  - CRMECA_2007__335_12_757_0
ER  - 
%0 Journal Article
%A Sergey A. Nazarov
%T Asymptotics of eigenfrequencies of an elastic body with a heavy and hard peak-shaped inclusion
%J Comptes Rendus. Mécanique
%D 2007
%P 757-762
%V 335
%N 12
%I Elsevier
%R 10.1016/j.crme.2007.06.004
%G en
%F CRMECA_2007__335_12_757_0
Sergey A. Nazarov. Asymptotics of eigenfrequencies of an elastic body with a heavy and hard peak-shaped inclusion. Comptes Rendus. Mécanique, Volume 335 (2007) no. 12, pp. 757-762. doi : 10.1016/j.crme.2007.06.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.06.004/

[1] E. Sanchez-Palencia J. Math. Pures Appl., 71 (1992), pp. 379-406

[2] M. Lobo; E. Perez Math. Models Methods Appl. Sci., 7 (1997), pp. 291-311

[3] M.H. Lobo; S.A. Nazarov; M.E. Perez Dokl. Math., 67 (2003), pp. 271-274

[4] M. Lobo; S.A. Nazarov; E. Perez IMA J. Appl. Math., 70 (2005), pp. 419-458

[5] S.A. Nazarov Asymptotic Theory of Thin Plates and Rods, vol. 1. Dimension Reduction and Integral Estimates, Nauchnaya Kniga, Novosibirsk, 2001

[6] S.A. Nazarov A criterion of the continuous spectrum for elasticity and other self-adjoint systems on sharp peak-shaped domains, C. R. Mecanique, Volume 335 (2007) | DOI

[7] S.A. Nazarov Siberian Math. J., 41 (2000), pp. 744-759

[8] E. Sanchez-Palencia C. R. Acad. Sci. Paris, Ser. 2, 311 (1990), pp. 909-916

[9] J. Sanchez-Hubert; E. Sanchez-Palencia Vibration and Coupling of Continuous Systems. Asymptotic Methods, Springer-Verlag, Heidelberg, 1989

[10] S.A. Nazarov J. Math. Sci., 114 (2003), pp. 1657-1725

[11] S.A. Nazarov J. Appl. Math. Mech., 62 (1998), pp. 453-464

[12] D. Leguillon; E. Sanchez-Palencia Computation of Singular Solutions in Elliptic Problems and Elasticity, Masson–Wiley, Paris–New–York, 1987

[13] S.A. Nazarov Russian J. Math. Phys., 4 (1996), pp. 217-250

[14] A.B. Movchan; S.A. Nazarov IMA J. Appl. Math., 49 (1992), pp. 245-272

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

A criterion of the continuous spectrum for elasticity and other self-adjoint systems on sharp peak-shaped domains

Sergey A. Nazarov

C. R. Méca (2007)

A gap in the continuous spectrum of an elastic waveguide

Sergey A. Nazarov

C. R. Méca (2008)