 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| V.G. Grigor'ev and E.V. Grigor'eva, "Contact Interaction of a Bounded Liquid Volume with a Solid under the Action of Gravity Forces," Mech. Solids. 46 (2), 280-290 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
2 |
Pages |
280-290 |
| DOI |
10.3103/S0025654411020178 |
| Title |
Contact Interaction of a Bounded Liquid Volume with a Solid under the Action of Gravity Forces |
| Author(s) |
V.G. Grigor'ev (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia, valgrigg@rambler.ru)
E.V. Grigor'eva (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia) |
| Abstract |
A mathematical model of the interaction between a bounded liquid volume and a deformable solid under the action of a homogeneous gravitational field is developed. With this model, small vibrations of the hydroelastic system are studied. The mathematical formulation of the contact relations on the interface used is invariant to the curvilinear coordinates system introduced on the interface and is based on equations in vector form. A variational principle of mixed type is formulated which permits creating necessary prerequisites for finite-element models to be efficiently used to solve the problem and for the development of appropriate algorithms. An example of a liquid-solid system is studied which is sensitive to the proper consideration of the interaction factors determined by the action of the gravitational field. |
| Keywords |
three-dimensional elastic bodies, ideal incompressible liquid, gravitational field, media interaction, vibrations, Lagrangian of system |
| References |
| 1. | A. G. Gorshkov, V. I. Morozov, A. T. Ponomarev, and F. N. Shklyarchuk,
Aerohydroelasticity of Structures
(Nauka, Fizmatlit, Moscow, 2000)
[in Russian]. |
| 2. | E. I. Grigolyuk and F. N. Shklyarchuk,
"Equations of Perturbed Motion of a Body
with a Thin-Walled Elastic Shell Partially Pilled with a Liquid,"
Prikl. Mat. Mekh.
34 (3), 401-411 (1970)
[J. Appl. Math. Mech. (Engl. Transl.)
34 (3), 379-389 (1970)]. |
| 3. | V. G. Grigoriev,
"Techniques for Calculating the Parameters of a Dynamic Model
of an Elastic Structure Containing a Liquid,"
in Selected Problems of Applied Mechanics and Mathematics
(MAMI, Moscow, 2003),
pp. 93-126
[in Russian]. |
| 4. | V. G. Grigoriev,
"On the Vibration Analysis of Elastic Shells Filled with Liquid
under a Homogeneous Gravitational Field,"
in Mechanics of Shells and Plates. Proc. of 19th Intern. Conf. on the Theory of Shells and Plates
(Izd-vo NNGU, Nizhnii Novgorod, 1999),
pp. 51-54
[in Russian]. |
| 5. | A. A. Il'yushin,
Continuum Mechanics
(Izd-vo MGU, Moscow, 1971)
[in Russian]. |
| 6. | V. V. Bolotin,
Continuum Mechanics
(Izd-vo MGU, Moscow, 1978)
[in Russian]. |
| 7. | V. V. Novozhilov,
Foundations of the Nonlinear Theory of Elasticity
(Editorial, Moscow, 2003)
[in Russian]. |
| 8. | N. E. Kochin, I. A. Kibel, and N. V. Roze,
Theoretical Hydromechanics, Part 1
(Fizmatgiz, Moscow, 1963; Interscience, New York, 1964). |
|
| Received |
15 December 2010 |
| Link to Fulltext |
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