Finite Element Formulation of Forced Vibration Problem of a Prestretched Plate Resting on a Rigid Foundation

Eröz, M.; Yildiz, A.

doi:https://doi.org/10.1155/2007/56360

Journal of Applied Mathematics

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Research Article | Open Access

Volume 2007 | Article ID 056360 | https://doi.org/10.1155/2007/56360

Finite Element Formulation of Forced Vibration Problem of a Prestretched Plate Resting on a Rigid Foundation

M. Eröz¹and A. Yildiz¹

Academic Editor: Heinz H. Bauschke

Received27 Apr 2007

Revised21 Jun 2007

Accepted03 Sept 2007

Published31 Dec 2007

Abstract

The three-dimensional linearized theory of elastodynamics mathematical formulation of the forced vibration of a prestretched plate resting on a rigid half-plane is given. The variational formulation of corresponding boundary-value problem is constructed. The first variational of the functional in the variational statement is equated to zero. In the framework of the virtual work principle, it is proved that appropriate equations and boundary conditions are derived. Using these conditions, finite element formulation of the prestretched plate is done. The numerical results obtained coincide with the ones given by Ufly and in 1963 for the static loading case.

References

A. N. Guz, Elastic Waves in a Body with Initial Stresses, I.General Theory, Naukova Dumka, Kiev, Russia, 1986.
View at: Google Scholar
A. N. Guz, Elastic Waves in a Body with Initial Stresses, II. Propagation Laws, Naukova Dumka, Kiev, Russia, 1986.
View at: Google Scholar
A. N. Guz, “Elastic waves in bodies with initial (Residual) stresses,” International Applied Mechanics, vol. 38, no. 1, pp. 35–78, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
V. B. Rudnitsky and N. N. Dikbtaryaruk, “Inintially stressed elastic strip strengthenedby elastic stringers,” International Applied Mechanics, vol. 38, no. 11, pp. 81–87, 2002.
View at: Google Scholar
S. V. Matniak, “On Rolling rigid cylinder along a band with initial stresses,” International Applied Mechanics, vol. 39, no. 3, pp. 81–87, 2003.
View at: Google Scholar
S. D. Akbarov, A. D. Zamanov, and T. R. Suleimanov, “Forced vibration of a prestretched two-layer slab on a rigid foundation,” Mechanics of Composite Materials, vol. 41, no. 3, pp. 229–240, 2005.
View at: Publisher Site | Google Scholar
S. D. Akbarov, “On the dynamical axisymmetric stress field in a finite pre-stretched bilayered slab resting on a rigid foundation,” Journal of Sound and Vibration, vol. 294, no. 1-2, pp. 221–237, 2006.
View at: Publisher Site | Google Scholar
S. D. Akbarov and C. Guler, “On the stress field in a half-plane covered by the pre-stretched layer under the action of arbitrary linearly located time-harmonic forces,” Applied Mathematical Modelling, vol. 31, no. 11, pp. 2375–2390, 2007.
View at: Publisher Site | Google Scholar
A. Cherkaev and E. Cherkaev, “Calculus of Variations and Applications,” Lecture Notes, 2003.
View at: Google Scholar
S. I. Uflyand, Integral Transformations in the Theory of Elastcity, Nauka, Moscow, Russia, 1963.
View at: Google Scholar

Copyright

Copyright © 2007 M. Eröz and A. Yildiz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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