Geodesic
Analytical solutions for the free vibration problem of a thin rectangular parallelepiped (plate) with free edges
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 4, pp. 195-209 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using trigonometric basis functions we found exact analytical solutions for the free vibration problem of a thin rectangular plate with free edges. The problem was formulated by the three-dimensional equations of the theory of elasticity, which were simplified by supposing that the normal stress through the thickness of the plate is equal to zero.
Keywords: rectangular plate, free edges, free vibrations, simplified spatial problem, trigonometric basis functions, Bubnov method, vibration frequency, without shear mode, flexural-shear mode, purely shear mode.
Mots-clés : vibration mode 
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     title = {Analytical solutions for the free vibration problem of a~thin rectangular parallelepiped (plate) with free edges},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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V. N. Paimushin; T. V. Polyakova. Analytical solutions for the free vibration problem of a thin rectangular parallelepiped (plate) with free edges. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 4, pp. 195-209. http://geodesic.mathdoc.fr/item/UZKU_2010_152_4_a17/

[1] Paimushin V. N., Polyakova T. V., “Tochnye analiticheskie resheniya trekhmernoi zadachi o svobodnykh kolebaniyakh ortotropnogo pryamougolnogo parallelepipeda so svobodnymi granyami”, Mekhanika kompozitnykh materialov i konstruktsii, 12:3 (2006), 317–336

[2] Paimushin V. N., “Tochnye i priblizhennye resheniya zadachi o ploskikh formakh svobodnykh kolebanii pryamougolnoi plastiny so svobodnymi krayami, osnovannye na trigonometricheskikh bazisnykh funktsiyakh”, Mekhanika kompozitnykh materialov, 41:4 (2005), 461–488

[3] Paimushin V. N., Polyakova T. V., “Tochnye resheniya zadach ob izgibnykh i poperechno-sdvigovykh formakh poteri ustoichivosti i svobodnykh kolebanii pryamougolnoi ortotropnoi plastiny s nezakreplennymi krayami”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 152, no. 1, 2010, 181–198 | Zbl