Abstract
We deal with an initial-boundary value problem describing the perpendicular vibrations of Kármán-Donnell shells with a rigid inner obstacle. The elastic as well the viscoelastic materials are considered. A weak formulation of the problems are in the form of the hyperbolic variational inequalities.We solve the problem using the penalization method.
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References
Bock, I.: On the semidiscretization and linearization of a pseudoparabolic von Kármán system for viscoelastic plates. Math. Meth. Appl. Sci. 29, 557–573 (2006)
Bock, I.: On a pseudoparabolic system for a viscoelastic shallow shell. PAMM Proc. Appl. Math. Mech. 6, 621–622 (2006)
Bock, I., Jarušek, J.: Unilateral dynamic contact of viscoelastic von Kármán plates. Advances in Math. Sci. and Appl. 16, 175–187 (2006)
Bock, I., Jarušek, J.: Solvability of dynamic contact problems for elastic von Kármán plates. SIAM J. Math. Anal. 41, 37–45 (2009)
Eck, C., Jarušek, J., Krbec, M.: Unilateral Contact Problems in Mechanics. Variational Methods and Existence Theorems. In: Monographs & Textbooks in Pure & Appl. Math., vol. 270. Taylor & Francis Group, Boca Raton (2005)
Voľmir, A.G.: Gibkije plastinky i oboločky, Gosizdat, Moskva (1956) (in Russian)
Vorovič, I.I., Lebedev, I.P.: Existence of solutions in nonlinear theory of shallow shells. Applied Mathematics and Mechanics 36(4), 691–704 (1972)
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Bock, I. (2011). Dynamic Contact Problems for Shells with Moderately Large Deflections. In: Stépán, G., Kovács, L.L., Tóth, A. (eds) IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments. IUTAM Bookseries, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1643-8_33
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DOI: https://doi.org/10.1007/978-94-007-1643-8_33
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-1642-1
Online ISBN: 978-94-007-1643-8
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