 | | 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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| E. L. Gusev, "Periodicity of inhomogeneous structures realizing the limiting capabilities under the action of elastic waves," Mech. Solids. 37 (1), 92-98 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
1 |
Pages |
92-98 |
| Title |
Periodicity of inhomogeneous structures realizing the limiting capabilities under the action of elastic waves |
| Author(s) |
E. L. Gusev (Yakutsk) |
| Abstract |
Problems of optimal design are considered for inhomogeneous
structures realizing the limiting capabilities when subjected to
elastic waves. The problem of optimal synthesis consists in
choosing a structure of a composite material (physical properties of the layers,
layer thickness, number of layers, mutual position of layers with different
physical properties) ensuring that the energy characteristics of elastic waves
would be as close as possible to the desired ones.
On the basis of a qualitative analysis of necessary conditions of optimality
related to nonlocal variations of control parameters, it is shown that
the relations between the parameters of structures realizing the
limiting capabilities possess the periodicity property.
An a priori knowledge of such qualitative relationships leads to a substantial
reduction of the dimension of the original problem of optimal synthesis, which opens up
wide possibilities for the investigation of the limiting capabilities of
structures subjected to elastic waves. |
| References |
| 1. | E. L. Gusev, A priori Estimates in Problems of Synthesis
of Multi-layered Structures Interacting with Waves [in Russian], Preprint, YaF SO
AN SSSR, Yakutsk, 1990. |
| 2. | E. L. Gusev, Mathematical Methods of Synthesis of Stratified Structures [in Russian],
Nauka, Novosibirsk, 1993. |
| 3. | V. T. Grinchenko and V. V. Meleshko, Harmonic Vibrations and Waves
in Elastic Bodies [in Russian], Naukova Dumka, Kiev, 1981. |
| 4. | E. L. Gusev, "Qualitative relationships between parameters
of optimal structures in problems of optimal synthesis of inhomogeneous structures
with a given set of materials in the presence of waves,"
Doklady AN, Vol. 346, No. 3, pp. 324-326, 1996. |
| 5. | E. L. Gusev,
"An a priori restrictions on the class of admissible materials in problems of
optimal synthesis of structures made up of finitely many materials
under the action of wave processes," Doklady AN, Vol. 349, No. 3,
pp. 329-331, 1996. |
| 6. | E. L. Gusev, "Qualitative relationships in optimal structures
in problems of optimal synthesis of acoustic systems," Akust. Zh.,
Vol. 43, No. 5, pp. 704-708, 1997. |
| 7. | E. L. Gusev, "Narrowing of the region of search in problems of
optimal synthesis of layered structures with a set of properties," J.
Appl. Mech. Techn. Phys., Vol. 38, No. 5, pp. 768-773, 1997. |
| 8. | E. L. Gusev, "The property of internal symmetry in the relations
between the parameters of optimal structures in problems of optimal
synthesis of structures exposed to waves," in Proceedings of Intern.
Conf. "Symmetries in Natural Sciences" [in Russian], pp. 47-48, Krasnoyarsk,
1998. |
| 9. | E. L. Gusev, "Qualitative relationships between the parameters of
layered structures realizing the limiting capabilities," Akust. Zh.,
Vol. 45, No. 4, pp. 499-503, 1999. |
| 10. | L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and
E. F. Mishchenko, Mathematical Theory of Optimal Processes [in Russian],
Nauka, Moscow, 1983. |
|
| Received |
28 December 1999 |
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