 | | 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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| B. E. Pobedrya, "Models of linear viscoelasticity," Mech. Solids. 38 (3), 95-106 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
3 |
Pages |
95-106 |
| Title |
Models of linear viscoelasticity |
| Author(s) |
B. E. Pobedrya (Moscow) |
| Abstract |
For the description of motion in continuum mechanics one often resorts to
"ideal" models such as a rigid body, ideal fluid, linearly
elastic
body, etc. However, in order to describe phenomena connected with
energy being spent on overcoming internal and external friction,
heat losses, and environment resistance, one has to introduce modified
models which in some sense should describe dissipation [1-3].
In this work, we consider models of linear viscoelasticity
based on fractional differentiation. |
| References |
| 1. | D. M. Klimov,
"Decay of free vibrations of gyro in gimbals with dry friction,"
Doklady AN SSSR, Vol. 123, No. 3, pp. 410-412, 1958. |
| 2. | B. E. Pobedrya,
Numerical Methods in Elasticity and Plasticity [in Russian], Izd-vo MGU,
Moscow, 1995. |
| 3. | A. A. Il'yushin and B. E. Pobedrya,
Fundamentals of Mathematical Thermoviscoelasticity [in Russian],
Nauka, Moscow, 1970. |
| 4. | T. A. Surguladze,
"On certain applications of fractional calculus to viscoelasticity,"
J. Math. Sci., Vol. 112, No. 5, pp. 4517-4557, 2002. |
| 5. | T. D. Shermergor,
"Applications of fractional differential operators for the
description of hereditary material properties,"
Zh. Prikl. Mekhaniki i Tekhn. Fiziki, No. 6, pp. 118-121, 1966. |
| 6. | Yu. N. Rabotnov,
Fundamentals of Hereditary Solid Mechanics [in Russian], Nauka, Moscow,
1977. |
| 7. | M. M. Dzhirbashyan,
Integral Transforms and Representations of Functions on the Complex Plane
[in Russian], Nauka, Moscow, 1966. |
| 8. | T. A. Surguladze,
"An application of the fractional Green function,"
Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 53-60, 2001. |
| 9. | A. A. Lokshin and Yu. V. Suvorova,
Mathematical Theory of Wave Propagation in Media with Memory [in Russian],
Izd-vo MGU, Moscow, 1982. |
| 10. | T. A. Surguladze,
"On the hyperbolicity of some one-dimensional equations of motion
in viscoelasticity," Matem. Model. Sist. Proces. No. 10, pp. 131-134, 2002. |
| 11. | T. A. Surguladze, "On the hyperbolicity of some three-dimensional
equations of motion in viscoelasticity,"
Vestnik MGU [Bulletin of Moscow State University], Ser.1, Mat. Mekh.,
No. 4, pp. 61-64, 2002. |
| 12. | Yu. A. Rossikhin and M. V. Shitikova,
"Analysis of the dynamical behavior of viscoelastic beams whose
rheological models contain fractional derivatives of two different
orders," Problems in Mechanics of Inelastic Deformations [in Russian], pp. 281-300, Fizmatgiz,
Moscow, 2001. |
| 13. | B. E. Pobedrya,
"Models in continuum mechanics," Izv. AN. MTT [Mechanics of Solids],
No. 3, pp. 47-59, 2000. |
| 14. | B. E. Pobedrya,
"On coupled problems in continuum mechanics,"
Elasticity and Inelasticity. Volume 2 [in Russian], pp. 224-253, Izd-vo
MGU, 1971. |
| 15. | D. L. Bykov and D. N. Konovalov,
"Applications of scattered energy functions for the description of
deformation and fracture in polymer structures,"
Elasticity and Inelasticity [in Russian], pp. 250-262, Izd-vo MGU, 2001. |
|
| Received |
10 February 2003 |
| << Previous article | Volume 38, Issue 3 / 2003 | Next article >> |
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