Geodesic
Mathematical modeling and experimental investigation of sound wave propagation through a deformable plate placed between two chambers
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 2, pp. 102-119 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper gives a numerical solution of the plane problem of propagation of a sound wave formed by a sound source in a high-pressure chamber through a deformable thin plate, and of formation of a wave emitted by the plate in a low-pressure chamber. The problem under study is related to the mathematical modeling of experimental determination of sound-insulating properties of thin-walled structures by the method of adjacent reverberation chambers in acoustic laboratories. Two statements of the problem, which differ in the way of specification of a sound source in the high-pressure chamber, are investigated based on the use of wave equations in a two-dimensional approximation. It is proved that both of the two considered statements lead to almost equal results in determination of the sound transmission loss of the plate. Theoretical results are compared with experimental research data.
Mots-clés : deformable plate, internal friction
Keywords: Kirchhoff–Love model, Voigt–Thompson–Kelvin model, acoustic insulation, wave equation, numerical method, experimental and theoretical investigations. 
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     title = {Mathematical modeling and experimental investigation of sound wave propagation through a~deformable plate placed between two chambers},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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V. N. Paimushin; R. K. Gazizullin; A. A. Sharapov. Mathematical modeling and experimental investigation of sound wave propagation through a deformable plate placed between two chambers. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 2, pp. 102-119. http://geodesic.mathdoc.fr/item/UZKU_2014_156_2_a9/

[1] Zaschita ot shuma, SP 51.13330.2011. Aktualizirovannaya red. SNiP 23-03-2003, M., 2011, 46 pp.

[2] Paimushin V. N., Gazizullin R. K., “Issledovanie zvukoizolyatsionnykh svoistv absolyutno zhestkoi plastiny, pomeschennoi na deformiruemykh opornykh elementakh mezhdu dvumya pregradami”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 3, 2013, 126–141

[3] Panovko Ya. G., Vnutrennee trenie pri kolebaniyakh uprugikh sistem, Fizmatgiz, M., 1960, 193 pp.

[4] Khilchevskii V. V., Dubenets V. G., Rasseyanie energii pri kolebaniyakh tonkostennykh elementov konstruktsii, Vischa shk., Kiev, 1977, 252 pp. | MR

[5] Vakhitov M. B., “Integriruyuschie matritsy – apparat chislennogo resheniya differentsialnykh uravnenii stroitelnoi mekhaniki”, Izv. vuzov. Aviats. tekhnika, 1966, no. 3, 50–61

[6] Dautov R. Z., Paimushin V. N., “O metode integriruyuschikh matrits resheniya kraevykh zadach dlya obyknovennykh uravnenii chetvertogo poryadka”, Izv. vuzov. Matem., 1996, no. 10, 13–25 | MR | Zbl

[7] Paimushin V. N., “O zadachakh izlucheniya zvukovoi volny pri dinamicheskom protsesse deformirovaniya plastin s uchetom vneshnego i vnutrennego dempfirovaniya”, Matem. metodi ta fiz.-mekh. polya, 56:2 (2013), 72–85 | MR

[8] Igumnov L. A., Lokteva N. A., Paimushin V. N., Tarlakovskii D. V., “Zvukoizolyatsionnye svoistva odnomernoi trekhsloinoi plastiny”, Matem. metodi ta fiz.-mekh. polya, 56:2 (2013), 86–93 | MR