 | | 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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| R. Yu. Amenzade and I. A. Kiiko, "Asymptotic analysis of the shear strain effect on the wave characteristics of a multilayered cylindrical shell filled with fluid," Mech. Solids. 42 (3), 422-428 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
3 |
Pages |
422-428 |
| Title |
Asymptotic analysis of the shear strain effect on the wave characteristics of a multilayered cylindrical shell filled with fluid |
| Author(s) |
R. Yu. Amenzade (Baku State University, Zahida Halilova 23, Baku, AZ, 1000, Azerbaijan)
I. A. Kiiko (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992, Russia, 66crock@rambler.ru) |
| Abstract |
It is commonly assumed that the theory based on the Kirchhoff hypotheses describes the properties inherent in the wave processes occurring in shells filled with fluids. But there are several new effects that cannot be described by this theory (in particular, the appearance of new types of waves). In this paper, we present a linearized description of axisymmetric wave motion of a perfect incompressible fluid in a multilayered cylindrical shell with allowance for shear strain; the shell is assumed to be infinite and simply supported. This description is aimed at finding new mechanical effects and hence at estimating the influence of the multiple layers and the shear strain on the wave characteristics. In a sense, it generalizes and develops well-known studies of this type.
Practice necessitates deriving equations constructed under the assumption that the physical and mechanical properties of the shell material are inhomogeneous along the thickness direction or the shell is multilayered; the development of refined theories (compared with the classical theory based on the Kirchhoff-Love straight normal hypothesis) is also inspired by practice. This is primarily related to the fact that multilayered thin-walled shells made of composite materials are used in various fields of technology. It is of interest to note that, as a result of long evolution, the phenomenon of being multilayered also predominates in living organisms. For example, this is typical of big blood vessels [1] (arteries and veins).
In [2], on the basis of a three-dimensional variational principle of mixed type, the equations of motion and physical relations for elastic anisotropic shells rigidly inhomogeneous in the thickness direction are derived under the assumptions of the theory of thin shells and with shear strains taken into account. It is also noted that the case of multilayered shells can be modeled by introducing functions with integrable singularities.
When studying wave propagation in deformable shells containing fluid, hydroelasticity problems arise; the solution of such problems is of both theoretical and practical importance. Of topical problems in this field, problems related to pulsating blood flow in big blood vessels [3] (the theory of pulse waves) are worth mentioning. The incentive for such studies is that they can help to understand the normal operation of the blood circulatory system, predict its reaction to variations, and propose methods for artificial intervention. Thus, diagnostics, surgery, and prosthesis are closely related to biomechanics. But the applied value of such problems is not bounded by their applications in hemodynamics. They are also very important in technology because of the wide use of systems of fluid and gas transportation through pipelines with corrosion-resistant coating. |
| References |
| 1. | A. S. Vol'mir and M. S. Gershtein,
"Problems of Blood Vessel Shell Dynamics,"
Mekh. Polim.,
No. 2, 373-379 (1970). |
| 2. | R. Yu. Amenzade, A. N. Alizade, and N. G. Damirov, "On Dynamic
Equations Describing Elastic Anisotropic Shells Inhomogeneous in
the Thickness Direction," in Proceedings of the Second
All-Union Scientific-Technical Conference "Strength, Rigidity,
and Workability of Objects Made of Composite Materials" (Izd-vo
Erevan Univ., Erevan, 1984), Vol. 1, pp. 35-40 [in Russian]. |
| 3. | T. J. Pedley, The Fluid Mechanics of Large Blood Vessels
(Cambridge Univ. Press, Cambridge, 1980; Mir, Moscow, 1983). |
| 4. | L. I. Sedov,
Mechanics of Continuous Media, Vol. 1
(Nauka, Moscow, 1976)
[in Russian]. |
| 5. | R. Yu. Amenzade, "Asymptotic Analysis of the Effect of Shear
Strain on Wave Propagation in a Shell Containing an Inviscid Fluid,"
Dokl. Ross. Akad. Nauk 347 (4), 475-477 (1996)
[Russian Acad. Sci. Dokl. Math.]. |
|
| Received |
23 May 2005 |
| Link to Fulltext |
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