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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2010, Volume 152, Book 4, Pages 195–209 (Mi uzku897)  
The 2nd International Conference "The Problems of Nonlinear Mechanics of Deformable Solids"

Analytical solutions for the free vibration problem of a thin rectangular parallelepiped (plate) with free edges

V. N. Paimushina, T. V. Polyakovab

a Tupolev Kazan State Technical University
b Scientific Technical Centre of Kazan State Technical University
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Abstract: 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, vibration mode, without shear mode, flexural-shear mode, purely shear mode.
Received: 19.06.2010
Document Type: Article
UDC: 519.958
Language: Russian
Citation: V. N. Paimushin, T. V. Polyakova, “Analytical solutions for the free vibration problem of a thin rectangular parallelepiped (plate) with free edges”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 152, no. 4, Kazan University, Kazan, 2010, 195–209
Citation in format AMSBIB
\Bibitem{PaiPol10}
\by V.~N.~Paimushin, T.~V.~Polyakova
\paper Analytical solutions for the free vibration problem of a~thin rectangular parallelepiped (plate) with free edges
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2010
\vol 152
\issue 4
\pages 195--209
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku897}
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