Geodesic
Chladni figures of a~circular plate floating in bounded and unbounded water bodies with securing support at the center
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 1, pp. 31-40.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the framework of circular symmetry, we carry out numerical and analytical research into the Chladni modes an elastic plate that floats on the surface of a fluid and is cantilever fitted at the center to a vertical support. Using the theory of long waves in shallow water and the approximation of the vibrations of an Euler beam for bounded and unbounded water bodies, we obtain the expressions for the dependency of the natural and quasi-natural frequencies of the Chladni figures on the geometric parameters of the plate and the vibration domain with the bottom irregularity taken into account.
Keywords: flexural-gravity vibration, natural vibration, hydroelasticity, shallow water, circular plate, Chladni figures of a supported floating plate. 
@article{SJIM_2017_20_1_a3,
     author = {A. G. Greshilov and S. V. Sukhinin},
     title = {Chladni figures of a~circular plate floating in bounded and unbounded water bodies with securing support at the center},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {31--40},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a3/}
}
TY  - JOUR
AU  - A. G. Greshilov
AU  - S. V. Sukhinin
TI  - Chladni figures of a~circular plate floating in bounded and unbounded water bodies with securing support at the center
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2017
SP  - 31
EP  - 40
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a3/
LA  - ru
ID  - SJIM_2017_20_1_a3
ER  - 
%0 Journal Article
%A A. G. Greshilov
%A S. V. Sukhinin
%T Chladni figures of a~circular plate floating in bounded and unbounded water bodies with securing support at the center
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2017
%P 31-40
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a3/
%G ru
%F SJIM_2017_20_1_a3
A. G. Greshilov; S. V. Sukhinin. Chladni figures of a~circular plate floating in bounded and unbounded water bodies with securing support at the center. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 1, pp. 31-40. http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a3/

[1] Tkacheva L. A., “Sobstvennye kolebaniya uprugoi platformy, plavayuschei na melkovode”, Prikl. mekhanika i tekhn. fizika, 41:1 (2000), 173–181 | Zbl

[2] Sturova I. V., “Deistvie nestatsionarnoi vneshnei nagruzki na upruguyu krugluyu plastinu, plavayuschuyu na melkovode”, Prikl. matematika i mekhanika, 67:3 (2003), 453–463 | Zbl

[3] Korobkin A. A., Khabakhpasheva T. I., “Postroenie tochnykh reshenii v zadache o plavayuschei plastine”, Prikl. matematika i mekhanika, 71:2 (2007), 321–328 | MR | Zbl

[4] Sturova I. V., “Vliyanie topografii dna na nestatsionarnoe povedenie uprugoi plastiny, plavayuschei na melkovode”, Prikl. matematika i mekhanika, 72:4 (2008), 588–600 | MR | Zbl

[5] Alekseev V. V., Indeitsev D. A., Mochalova Yu. A., “Kolebaniya uprugoi plastiny, kontaktiruyuschei so svobodnoi poverkhnostyu tyazheloi zhidkosti”, Zhurn. teor. fiziki, 72:5 (2002), 16–21

[6] Meleshko V. V., Papkov S. O., “Izgibnye kolebaniya uprugikh pryamougolnykh plastin so svobodnymi krayami: ot Khladni (1809) i Rittsa (1909) do nashikh dnei”, Akustichnii visnik, 12:4 (2009), 34–51

[7] Maylan M. H., “An Application of Scattring Frequencies to Hydroelasticity”, Proc. 11 Offshore and Polar Engineering Conf. (Stavanger, Norway, June 17–22, 2001)

[8] Grigolyuk E. A., Selezov I. T., Neklassicheskie teorii kolebanii sterzhnei, plastin i obolochek, Itogi nauki i tekhniki. Mekhanika tverdykh deformiruemykh tel, 5, VINITI, M., 1973

[9] Timoshenko S., Woinowsky-Krieger S., Theory of Plates and Shells, McGraw-Hill, N.Y., 1959

[10] Stoker Dzh. Dzh., Volny na vode, Izd-vo inostr. lit., M., 1959

[11] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1988

[12] Zilman G., Miloh T., “Hydroelastic buoyant circular plate in shallow water: a closed form solution”, Appl. Ocean Research, 22 (2000), 191–198 | DOI