 | | 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
|
| In English (Mech. Solids): | | 4760 |
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| A.L. Levitin, S.A. Lychev, A.V. Manzhirov, and M.Yu. Shatalov, "Nonstationary Vibrations of a Discretely Accreted Thermoelastic Parallelepiped," Mech. Solids. 47 (6), 677-689 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
6 |
Pages |
677-689 |
| DOI |
10.3103/S0025654412060106 |
| Title |
Nonstationary Vibrations of a Discretely Accreted Thermoelastic Parallelepiped |
| Author(s) |
A.L. Levitin (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, alex_lev@ipmnet.ru)
S.A. Lychev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, lychevsa@mail.ru)
A.V. Manzhirov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, manzh@ipmnet.ru)
M.Yu. Shatalov (Tshwane University of Technology, P.B. X680, Pretoria, 0001 FIN-40014 South African Republic, mshatlov@csir.co.za) |
| Abstract |
A procedure for determining nonstationary vibrations of a discretely accreted thermoelastic body in the approximation of small deformations and thermal flows is developed. A closed-form solution is constructed for a growing parallelepiped under "smoothly rigid" heat-insulated fixation conditions for the stationary faces and the growing load-free face. The temperature field on the growing face is analyzed numerically for various accretion scenarios. |
| Keywords |
coupled thermoelasticity, micromechanics, growing bodies, discrete accretion, inconsistency |
| References |
| 1. | N. Kh. Arutyunyan, A. V. Manzhirov, and V. E. Naumov,
Contact Problems of Mechanics of Growing Bodies
(Nauka, Moscow, 1991)
[in Russian]. |
| 2. | S. A. Lychev, T. N. Lycheva, and A. V. Manzhirov,
"Unsteady Vibration of a Growing Circular Plate,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 199-208 (2011)
[Mech. Solids (Engl. Transl.)
46 (2), 325-333 (2011)]. |
| 3. | S. I. Kuznetsov, A. V. Manzhirov, and I. Fedotov,
"Heat Conduction Problem for a Growing Ball,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 139-148 (2011)
[Mech. Solids (Engl. Transl.)
46 (6), 929-936 (2011)]. |
| 4. | A. V. Manzhirov and S. A. Lychev,
"The Mathematical Theory of Growing Solids: Finite Deformations,"
Dokl. Ross. Akad. Nauk
443 (4), 438-441 (2012)
[Dokl. Phys. (Engl. Transl.)
57 (4), 160-163 (2012)] |
| 5. | S. A. Lychev and Yu. E. Senitskii,
"Nonsymmetric Finite Integral Transformations and Their Applications to Viscoelasticity Problems,"
Vestnik Samar. Gos. Univ. Estestvennonauchn. Ser., Special Issue,
16-38 (2002). |
| 6. | S. A. Lychev,
"Coupled Dynamic Thermoviscoelasticity Problem,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 95-113 (2008)
[Mech. Solids (Engl. Transl.)
43 (5), 769-784 (2008)]. |
| 7. | W. Nowacki,
Theory of Elasticity
(PWN, Warsaw, 1970; Mir, Moscow, 1975). |
| 8. | S. A. Lychev, A. V. Manzhirov, and S. V. Joubert,
"Closed Solutions of Boundary-Value Problems of Coupled Thermoelasticity,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 138-154 (2010)
[Mech. Solids (Engl. TRansl.)
45 (4), 610-623 (2010)]. |
| 9. | P. A. Zhilin and T. P. Il'icheva,
"Spectra and Oscillation Mode Shapes of a Rectangular Parallelepiped
Obtained Using Three-Dimensional Theory of Elasticity
and Theory of Plates,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 94-103 (1980)
[Mech. Solids (Engl. Transl.)]. |
| 10. | V. P. Mikhailov,
Partial Differential Equations
(Nauka, Moscow, 1976)
[in Russian]. |
| 11. | I. C. Gokhberg and M. G. Krein,
Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space
(Nauka, Moscow, 1965; AMS, 1969). |
| 12. | Online Materials Information Resource - MatWeb,
URL: http://matweb.com. |
|
| Received |
25 July 2012 |
| Link to Fulltext |
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