Geodesic
1 : 3 Resonance is a possible cause of nonlinear panel flutter
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1266-1279 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A nonlinear boundary value problem modeling oscillations of a plate in a supersonic gas flow is considered. Using the normal forms method, the method of integral manifolds for dynamical systems with infinite-dimensional phase space, and asymptotic methods combined with numerical techniques, it is shown that the 1 : 3 resonance of eigenfrequencies of the linearized boundary value problem can be a cause of subcritical bifurcations and hard excitation of oscillations. 
@article{ZVMMF_2011_51_7_a7,
     author = {A. N. Kulikov},
     title = {1 : 3 {Resonance} is a~possible cause of nonlinear panel flutter},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1266--1279},
     year = {2011},
     volume = {51},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a7/}
}
TY  - JOUR
AU  - A. N. Kulikov
TI  - 1 : 3 Resonance is a possible cause of nonlinear panel flutter
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1266
EP  - 1279
VL  - 51
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a7/
LA  - ru
ID  - ZVMMF_2011_51_7_a7
ER  - 
%0 Journal Article
%A A. N. Kulikov
%T 1 : 3 Resonance is a possible cause of nonlinear panel flutter
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1266-1279
%V 51
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a7/
%G ru
%F ZVMMF_2011_51_7_a7
A. N. Kulikov. 1 : 3 Resonance is a possible cause of nonlinear panel flutter. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1266-1279. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a7/

[1] Bolotin V. V., Nekonservativnye zadachi teorii uprugoi ustoichivosti, Fizmatlit, M., 1961 | MR

[2] Gukenkheimer Dzh., Kholms F., Nelineinye kolebaniya, dinamicheskie sistemy i bifurkatsiya vektornykh polei, In-t kompyuternykh issl., M.-Izhevsk, 2002

[3] Holmes P. J., Marsden J. E., “Bifurcation to divergence and flutter in flow – induced oscillations: an infinite dimensional analysis”, Automatica, 14:4 (1978), 367–384 | DOI | MR | Zbl

[4] Ilyushin A. A., “Zakon ploskikh sechenii v aerodinamike bolshikh sverkhzvukovykh skorostei”, Prikl. matem. i mekhan., 20:6 (1956), 733–755

[5] Kulikov A. N., Liberman B. D., “O novom podkhode k issledovaniyu zadach nelineinogo panelnogo flattera”, Vestn. Yarosl. un-ta, 1976, no. 6, 118–139 | MR

[6] Kolesov V. S., Kolesov Yu. S., Kulikov A. N., Fedik I. I., “Ob odnoi matematicheskoi zadache teorii uprugoi ustoichivosti”, Prikl. matem. i mekhan., 42:3 (1978), 458–465 | MR | Zbl

[7] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969 | MR

[8] Kulikov A. N., “Bifurkatsiya avtokolebanii plastinki pri malom dempfirovanii v sverkhzvukovom potoke gaza”, Prikl. matem. i mekhan., 73:2 (2009), 271–281 | Zbl

[9] Kulikov A. N., “Resonance of proper frequence 1:2 as a reason for hard excitation of oscillations for the plate in ultrasonic gas”, Tr. Mezhdunar. kongressa ENOC-2008 (Saint-Petersburg, Russia), 1638–1643

[10] Yakubov S. Ya., “Razreshimost zadachi Koshi dlya abstraktnykh kvazilineinykh giperbolicheskikh uravnenii vtorogo poryadka i ikh prilozheniya”, Tr. Mosk. matem. ob-va, 23, M., 1970, 37–59

[11] Mischenko E. F., Sadovnichii V. A., Kolesov A. Yu., Rozov N. Kh., Avtovolnovye protsessy v nelineinykh sredakh s diffuziei, Fizmatlit, M., 2005

[12] Kolosov A. Yu., Rozov N. Kh., Invariantnye tory nelineinykh volnovykh uravnenii, Fizmatlit, M., 2004

[13] Kolesov A. Yu., Kulikov A. N., Rozov N. Kh., “Invariantnye tory odnogo klassa tochechnykh otobrazhenii: printsip koltsa”, Differents. ur-niya, 39:5 (2003), 584–601 | MR | Zbl

[14] Kolesov A. Yu., Kulikov A. N., Rozov N. Kh., “Invariantnye tory odnogo klassa tochechnykh otobrazhenii: sokhranenie invariantnogo tora pri vozmuscheniyakh”, Differents. ur-niya, 39:6 (2003), 738–753 | MR | Zbl

[15] Kolesov A. Yu., Kulikov A. N., Invariantnye tory nelineinykh evolyutsionnykh uravnenii, YarGU, Yaroslavl, 2003

[16] Funktsionalnyi analiz. Spravochnaya matematicheskaya biblioteka, Nauka, M., 1972

[17] Bekbulatova A. O., Kulikov A. N., “Nelineinyi panelnyi flatter. Rezonans 1:2 kak istochnik zhestkogo vozbuzhdeniya kolebanii”, Sovrem. probl. matem. i informatiki, 5 (2002), 22–27

[18] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Mekhanizm zhestkogo vozbuzhdeniya avtokolebanii, svyazannyi s rezonansom 1:2”, Zh. vychisl. matem. i matem. fiz., 45:11 (2005), 2000–2016 | MR | Zbl