Email this article 
Solution of the Dynamic Lame Problem
- Authors: Rasulova N.B.1, Mahmudzade T.M.2
-
Affiliations:
- Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, AZ1141, Baku, Azerbaijan
- Baku State University, AZ1148, Baku, Azerbaijan
- Issue: No 5 (2023)
- Pages: 131-137
- Section: Articles
- URL: https://ter-arkhiv.ru/1026-3519/article/view/672688
- DOI: https://doi.org/10.31857/S0572329922600542
- EDN: https://elibrary.ru/GABLBR
- ID: 672688
Cite item
Open Access
Access granted
Subscription Access
Abstract
The well-known Lame problem, posed in 1852, involves solving the static equilibrium of a parallelepiped with free side surfaces subjected to action of opposite end forces. In this article, the same problem for a more complicated case of impacts of end forces is considered.
An exact analytical solution of this problem is found.
Emphasizing the particular difficulty of solving this problem, Lamé, in his book “Leçons sur la thorie mathematique de Ielasticite des corps solides” (Paris, 1852), wrote: “C’est une sorte d’engine aussi digne d’exercer la sagasite des analystes que le fameux problem des trios corps de la Mécanique celeste”,—“This is a kind of drive, as worthy of training the clairvoyance of analysts as the famous three-body problem of celestial mechanics.” At that time, this problem was the subject of a prize from the Paris Academy of Sciences, that was intended for the one who solved the Lamé problem. Despite this, to date, no solution has been found even for a static case of this problem, not to mention the complicated version of the problem.
About the authors
N. B. Rasulova
Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, AZ1141, Baku, Azerbaijan
Email: rasulova@gmail.com
Азербайджан, Баку
T. M. Mahmudzade
Baku State University, AZ1148, Baku, Azerbaijan
Author for correspondence.
Email: tehminemahmudzade1996@gmail.com
Азербайджан, Баку
References
- Medick M.A. Extensional waves in elastic bars of rectangular cross sections // J. Acoust. Soc. Am. 1968. V. 43. № 1. P. 152–161. https://doi.org/10.1121/1.1910744
- Вовк А.Е., Гудков В.В., Левченкова Т.В., Тютекин В.В. Нормальные волны твердого прямоугольного волновода // Акустический журнал. 1980. Т. 26. В. 3. С. 365–363.
- Fraser W.B. Stress wave propagation in rectangular bars // Int. J. Solids Struct. 1969. V. 5. № 4. P. 379–397. https://doi.org/10.1016/0020-7683(69)90020-1
- Volterra E., Asce M. Dispersion of longitudinal waves // J. Eng. Mech. 1957. V. 83. № 3. P. 13–22. https://doi.org/10.1061/JMCEA3.0000032
- Hertelendy P. An approximate theory governing simmetric motions of elastic rods of rectangular or square cross section // J. Appl. Mech. 1968. V. 35. № 2. P. 333–341. https://doi.org/10.1115/1.3601200
- Tanaka K., Iwahashi Y. Dispersion relations of elastic wave in bars of rectangular cross sections // Bull. JSME. 1977. V. 20. № 146. P. 922–929. https://doi.org/10.1299/jsme1958.20.922
- Tanaka K., Iwahashi Y. Longitudinal impact of a semi-infinite rectangular bar // Bull. JSME. 1978. V. 21. № 156. P. 980–985. https://doi.org/10.1299/jsme1958.21.980
- Расулова Н.Б. Распространение волн в призматическом брусе, подверженном действию осевых сил // Изв. РАН. MTТ. 1997. № 6. С. 176–179.
- Rassoulova N.B. On dynamic of bar of rectangular cross section // J. Appl. Mech. 2001. V. 68. № 4. P. 662–666. https://doi.org/10.1115/1.1352063
- Расулова Н.Б., Шамилова Г.Р. Распространение волн напряжений в прямоугольном брусе // Изв. РАН. МТТ. 2016. № 4. С. 144–152.
Supplementary files
