Geodesic
Asymptotic analysis of geometrically nonlinear vibrations of long plates
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 162 (2020) no. 4, pp. 396-410

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this paper, we performed an asymptotic analysis for equations of the classical plate theory with the von Kármán strains under the assumption that the width of the plate is small compared with its length. A system of one-dimensional equations, which describes the nonlinear interaction of flexural and torsional vibrations of beams, was derived. This enables the possibility of exciting torsional vibrations by flexural vibrations. This possibility was analyzed for a model problem, when flexural vibrations occur in normal modes.
Keywords: asymptotic analysis, flexural vibrations, parametric resonance, resonance gaps
Mots-clés : torsional vibrations, Mathieu equation. 
@article{UZKU_2020_162_4_a1,
     author = {B. Affane and A. G. Egorov},
     title = {Asymptotic analysis of geometrically nonlinear vibrations of long plates},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {396--410},
     publisher = {mathdoc},
     volume = {162},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2020_162_4_a1/}
}
TY  - JOUR
AU  - B. Affane
AU  - A. G. Egorov
TI  - Asymptotic analysis of geometrically nonlinear vibrations of long plates
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2020
SP  - 396
EP  - 410
VL  - 162
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZKU_2020_162_4_a1/
LA  - ru
ID  - UZKU_2020_162_4_a1
ER  - 
%0 Journal Article
%A B. Affane
%A A. G. Egorov
%T Asymptotic analysis of geometrically nonlinear vibrations of long plates
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2020
%P 396-410
%V 162
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZKU_2020_162_4_a1/
%G ru
%F UZKU_2020_162_4_a1
B. Affane; A. G. Egorov. Asymptotic analysis of geometrically nonlinear vibrations of long plates. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 162 (2020) no. 4, pp. 396-410. http://geodesic.mathdoc.fr/item/UZKU_2020_162_4_a1/