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IssuesArchive of Issues2009-6pp.907-914

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V. M. Vorobel’, G. Ya. Popov, and V. V. Reut, "Forced Vibrations of a Boxed Shell of Square Cross-Section," Mech. Solids. 44 (6), 907-914 (2009)
Year 2009 Volume 44 Number 6 Pages 907-914
DOI 10.3103/S0025654409060089
Title Forced Vibrations of a Boxed Shell of Square Cross-Section
Author(s) V. M. Vorobel’ (Mechnikov Odessa National University, Dvoryanskaya 2, Odessa, 65082 Ukraine, vrbl@rambler.ru)
G. Ya. Popov (Mechnikov Odessa National University, Dvoryanskaya 2, Odessa, 65082 Ukraine, popov@onu.edu.ua)
V. V. Reut (Mechnikov Odessa National University, Dvoryanskaya 2, Odessa, 65082 Ukraine, reut@onu.edu.ua)
Abstract We construct the solution of the problem on the steady-state vibrations of a finite boxed shell of square cross-section with symmetry conditions at the shell ends. We present the dispersion curves, find the natural frequencies, and study the stress distribution in the shell. We obtain a simple formula for the approximate analysis of the shell in the case of low-frequency vibrations on the basis of the expansion of the solution in two small parameters and on the Lagrange interpolation formula.
Keywords forced vibrations, boxed shell, asymptotics, stressed state
References
1.  V. I. Mossakovskii and D. V. Kulikov, "The Method of Homogeneous Solutions for Box-Type Shells under Dynamic Loads," Dokl. Akad. Nauk Ukr. SSR. Ser. A, No. 1, 24-27 (1987).
2.  Yu. I. Bobrovnitskii and M. D. Genkin, "Wave Propagation in Thin-Walled Rods," in Vibration Isolation Systems in Machines and Structures (Nauka, Moscow, 1977), pp. 32-48 [in Russian].
3.  V. A. Grishin, G. Ya. Popov, and V. V. Reut, "Analysis of Box-Like Shells of Rectangular Cross-Section," Prikl. Mat. Mekh. 54 (4), 605-612 (1990) [J. Appl. Math. Mech. (Engl. Transl.) 54 (4), 501-507 (1990)].
Received 29 August 2007
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