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IssuesArchive of Issues2012-6pp.677-689

Archive of Issues

Total articles in the database: 4675
In Russian (. . ): 2249
In English (Mech. Solids): 2426

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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 http://link.springer.com/article/10.3103/S0025654412060106
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