 | | 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 |
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| S.A. Lychev, A.V. Manzhirov, and S.V. Joubert, "Closed Solutions of Boundary-Value Problems of Coupled Thermoelasticity," Mech. Solids. 45 (4), 610-623 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
4 |
Pages |
610-623 |
| DOI |
10.3103/S0025654410040102 |
| Title |
Closed Solutions of Boundary-Value Problems of Coupled Thermoelasticity |
| Author(s) |
S.A. Lychev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, lychev@ipmnet.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)
S.V. Joubert (Tshwane University of Technology, P.B. X680, Pretoria, 0001 FIN-40014 South African Republic, joubertsv@tut.ac.za) |
| Abstract |
Coupled equations of thermoelasticity take into account the effect of nonuniform heating on the medium deformation and that of the dilatation rate on the temperature distribution. As a rule, the coupling coefficients are small and it is assumed, sometimes without proper justification, that the effect of the dilatation rate on the heat conduction process can be neglected. The aim of the present paper is to construct analytical solutions of some model boundary-value problems for a thermoelastic bounded body and to determine the body characteristic dimensions and the medium thermomechanical moduli for which it is necessary to take into account that the temperature and displacement fields are coupled. We consider some models constructed on the basis of the Fourier heat conduction law and the generalized Cattaneo-Jeffreys law in which the heat flux inertia is taken into account. The solution is constructed as an expansion in a biorthogonal system of eigenfunctions of the nonself-adjoint operator pencil generated by the coupled equations of motion and heat conduction. For the model problem, we choose a special class of boundary conditions that allows us to exactly determine the pencil eigenvalues. |
| Keywords |
coupled thermoelasticity, generalized Cattaneo-Jeffreys law, nonself-adjoint operators, biorthogonal systems, analytical solutions, micron-scale bodies, coupling effect evaluation |
| References |
| 1. | A. C. Eringen,
Mechanics of Continua
(Huntington, New York, 1980). |
| 2. | W. Nowacki,
Theory of Elasticity
(Mir, Moscow, 1975)
[in Russian]. |
| 3. | Yu. E. Senitskii,
"Solution of Coupled Dynamic Thermoelasticity Problem for an Infinite Cylinder and Sphere,"
Prikl. Mekh.
18 (6), 34-41 (1982)
[Int. Appl. Mech. (Engl. Transl.)
18 (6), 514-520 (1982)]. |
| 4. | B. Boley and J. Wiener,
Theory of Thermal Stresses
(Wiley, New Your, 1960; Mir, Moscow, 1964). |
| 5. | V. V. Lemanov and G. A. Smolenskii,
"Hypersonic Waves in Crystals,"
Uspekhi Fiz. Nauk,
108 (3), 465-501 (1972)
[Sov. Phys. Usp. (Engl. Transl)
15 (6), 708-727 (1973)]. |
| 6. | X. Wang and X. Xu,
"Thermoelastic Wave Induced by Pulsed Laser Heating,"
Appl. Phys. A
73, 107-114 (2001). |
| 7. | F. Cernuschi, A. Figari, and L. Fabbri,
"Thermal Wave Interferometry for Measuring the Thermal Diffusivity of Thin Slabs,"
J. Mat. Sci.
35 (23), 5891-5897 (2000). |
| 8. | Material Property Data,
MatWeb: www.matweb.com. |
| 9. | D. W. Tang and N. Araki,
"On Non-Fourier Temperature Wave and Thermal Relaxation Time,"
Int. J. Thermophys.
18 (2), 493-504 (1997). |
| 10. | A. Sommerfeld,
Partial Differential Equations in Physics
(Inostr. Lit., Moscow, 1950)
[in Russian]. |
| 11. | D. D. Joseph and L. Preziosi,
"Heat Waves,"
Mod. Phys.
61 (1), 41-73 (1989). |
| 12. | M. A. Naimark,
Linear Differential Operators
(Nauka, Moscow, 1950) [in Russian]. |
| 13. | 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)]. |
| 14. | 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). |
| 15. | A. S. Markus,
Introduction to the Spectral Theory of Polynomial Operator Pencils
(Shtiintsa, Kishinev, 1986; Amer. Math. Soc., Providence, R.I., 1988). |
| 16. | L. Collatz,
Eigenvalue Problems with Technical Applications
(Chelsea, New York, 1948; Nauka, Moscow, 1968). |
| 17. | Ph. M. Morse and H. Feshbach,
Methods of Theoretical Physics, Vol. 1
(Inostr. Lit., Moscow, 1958)
[in Russian]. |
| 18. | Ph. M. Morse and H. Feshbach,
Methods of Theoretical Physics, Vol. 2
(Inostr. Lit., Moscow, 1960)
[in Russian]. |
|
| Received |
15 March 2010 |
| Link to Fulltext |
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