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

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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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     author = {V. N. Paimushin and T. V. Polyakova},
     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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     publisher = {mathdoc},
     volume = {152},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2010_152_4_a17/}
}
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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/