Geodesic
Determination of damping properties of an elongated plate with an integral damping coating on the base of studying complex eigenfrequencies
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 48-64.

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

The structure of a perspective integral damping coating consisting of two layers of a viscoelastic material with a thin reinforcing layer between them is presented. A four-layer finite element with fourteen degrees of freedom was developed for modeling a plate with a mentioned damping coating, which allows to take into account the effect of transversal compression of the damping layers during high-frequency oscillations of the plate. The generalized problem of complex eigenvalues based on the method of iterations in a subspace to determine several lower complex forms and frequencies of free vibrations of a damped plate was solved.
Keywords: plate, damping coating, damping constant, finite element, complex frequency. 
@article{IVM_2020_6_a6,
     author = {V. N. Paimushin and V. A. Firsov and V. M. Shishkin},
     title = {Determination of damping properties of an elongated plate with an integral damping coating on the base of studying complex eigenfrequencies},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {48--64},
     publisher = {mathdoc},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_6_a6/}
}
TY  - JOUR
AU  - V. N. Paimushin
AU  - V. A. Firsov
AU  - V. M. Shishkin
TI  - Determination of damping properties of an elongated plate with an integral damping coating on the base of studying complex eigenfrequencies
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2020
SP  - 48
EP  - 64
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2020_6_a6/
LA  - ru
ID  - IVM_2020_6_a6
ER  - 
%0 Journal Article
%A V. N. Paimushin
%A V. A. Firsov
%A V. M. Shishkin
%T Determination of damping properties of an elongated plate with an integral damping coating on the base of studying complex eigenfrequencies
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 48-64
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2020_6_a6/
%G ru
%F IVM_2020_6_a6
V. N. Paimushin; V. A. Firsov; V. M. Shishkin. Determination of damping properties of an elongated plate with an integral damping coating on the base of studying complex eigenfrequencies. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 48-64. http://geodesic.mathdoc.fr/item/IVM_2020_6_a6/

[1] Chernyshev V. M., Dempfirovanie kolebanii mekhanicheskikh sistem pokrytiyami iz polimernykh materialov, Nauka, M., 2004

[2] Kerwin E., “Damping of flexural waves by a constrained viscoelastic layer”, J. Acoustical Soc. America, 3:7 (1959), 952–962 | DOI

[3] Ungar E., “Loss factors of viscoelastically damped beam structures”, J. Acoustical Soc. America, 34:8 (1962), 1082–1089

[4] Amadori S., Catania G., “Damping contributions of coatings to the viscoelastic behaviour of mechanical components”, Proceedings of the Inter. Conf. Surveillance 9 (Fes. Morocco, 22–24 May 2017)

[5] Fisher D. K., Asthana S., Self-adhesive vibration damping tape and composition, Patent US 6828020 B2, 7.12.2004

[6] Pankov L. A., Fesina M. I., Krasnov A. V., Vibroshumodempfiruyuschaya ploskolistovaya prokladka, Patent RF No 2333545, 10.09.2008

[7] Tesse C., Stopin G., Constrained-layer damping material, 11.07.2012

[8] Nashif A., Dzhouns D., Khenderson Dzh., Dempfirovanie kolebanii, Mir, M., 1988

[9] Rikards R. B., Barkanov E. N., “Opredelenie dinamicheskikh kharakteristik vibropogloschayuschikh pokrytii metodom konechnykh elementov”, Mekhan. kompozit. mater., 5 (1991), 823–830

[10] Postnikov V. S., Vnutrennee trenie v metallakh, Metallurgiya, M., 1969

[11] Khilchevskii V. V., Dubenets V. G., Rasseyanie energii pri kolebaniyakh tonkostennykh elementov konstruktsii, Vischa shkola, Kiev, 1977

[12] Sorokin E. S., K teorii vnutrennego treniya pri kolebaniyakh uprugikh sistem, Gosstroiizdat, M., 1960

[13] Paimushin V. N., Firsov V. A., Gyunal I., Shishkin V. M., “Identification of the elastic and damping charac-teristics of soft materials based on the analysis of damped flexural vibrations of test specimens”, Mechan. of Composite Mater., 52:4 (2016), 435–454 | MR

[14] Norri D., de Friz Zh., Vvedenie v metod konechnykh elementov, Mir, M., 1981 | MR

[15] Segerlind L., Primenenie metoda konechnykh elementov, Mir, M., 1979

[16] Zenkevich O., Metod konechnykh elementov v tekhnike, Mir, M., 1975

[17] Demidovich B. P., Maron I. A., Osnovy vychislitelnoi matematiki, Mir, M., 1966

[18] Metyuz Dzhon G., Fink Kurtis D., Chislennye metody. Ispolzovanie MATLAB, 3-e izd., Izdat. dom “Vilyams”, M., 2001

[19] Dzhonson K. D., Kinkholts D. A., “Raschet dempfirovaniya kolebanii v konstruktsiyakh, soderzhaschikh zakreplennye vyazkouprugie sloi, metodom konechnykh elementov”, Aerokosmicheskaya tekhn., 1:4 (1983), 124–133

[20] Bate K., Vilson E., Chislennye metody analiza i metod konechnykh elementov, Stroiizdat, M., 1982

[21] Klaf R., Penzien Dzh., Dinamika sooruzhenii, Stroiizdat, M., 1979

[22] Parlett B., Simmetrichnaya problema sobstvennykh znachenii. Chislennye metody, Mir, M., 1983

[23] Paimushin V. N., Shishkin V. M., “Modeling the Elastic and Damping Properties of the Multilayered Torsion Bar-Blade Structure of Rotors of Light Helicopters of the New Generation. 1. Finite-Element Approximation of the Torsion Bar”, Mechan. Composite Mater., 51:5 (2015), 609–628 | DOI | MR

[24] Pisarenko G. S., Yakovlev A. P., Matveev V. V., Vibropogloschayuschie svoistva konstruktsionnykh materialov, Spravochnik, Naukova dumka, Kiev, 1971

[25] Caughey T. K., O, Kelly M. E. J., “Effect damping on the natural frequencies of linear dynamic system”, J. Acoustical Soc. America, 33:11 (1961), 1458–1461 | DOI | MR

[26] Barkanov E. N., “Metod kompleksnykh sobstvennykh chisel dlya issledovaniya dempfiruyuschikh svoistv konstruktsii tipa sandvich”, Mekhan. kompozit. mater., 29:1 (1993), 116–121