 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| I.V. Kudinov and V.A. Kudinov, "Exact Closed-Form Solution of the Hyperbolic Equation of String Vibrations with Material Relaxation Properties Taken into Account," Mech. Solids. 49 (5), 531-542 (2014) |
| Year |
2014 |
Volume |
49 |
Number |
5 |
Pages |
531-542 |
| DOI |
10.3103/S0025654414050057 |
| Title |
Exact Closed-Form Solution of the Hyperbolic Equation of String Vibrations with Material Relaxation Properties Taken into Account |
| Author(s) |
I.V. Kudinov (Samara State Architecture and Civil Engineering University, ul. Molodogvardeyskaya 194, Samara, 443001 Russia, igor-kudinov@bk.ru)
V.A. Kudinov (Samara State Technical University, ul. Molodogvardeyskaya 244, Samara, 443100 Russia, totig@yandex.ru, kud-samgtu@yandex.ru) |
| Abstract |
The differential equation of damped string vibrations was obtained with the finite speed of extension and strain propagation in the Hooke's law formula taken into account. In contrast to the well-known equations, the obtained equation contains the first and third time derivatives of the displacement and the mixed derivative with respect to the space and time variables. Separation of variables was used to obtain its exact closed-form solution, whose analysis showed that, for large values of the relaxation coefficient, the string return to the initial state after its escape from equilibrium is accompanied by high-frequency low-amplitude damped vibrations, which occur on the initial time interval only in the region of positive displacements. And in the limit, for some large values of the relaxation coefficient, the string return to the initial state occurs practically without any oscillatory process. |
| Keywords |
hyperbolic equation, string vibrations, finite speed of perturbation propagation, relaxation coefficient, analytic solution, stress and strain relaxation |
| References |
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| 7. | V. A. Kudinov and I. V. Kudinov,
"Studying Heat Conduction Taking into Account the Finite Rate of Heat Propagation,"
Teplofiz. Vysokikh Temp.
51 (2), 301-310 (2013)
[High Tempr. (Engl. Transl.)
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| 8. | V. A. Kudinov and I. V. Kudinov,
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in the Accelerated Couette Flow,"
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No. 1, 119-133 (2012). |
| 9. | V. A. Kudinov and I. V. Kudinov,
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50 (1), 118-125 (2012)
[High Tempr. (Engl. Transl.)
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| 10. | V. A. Kudinov and I. V. Kudinov,
Analytic Solutions of Parabolic and Hyperbolic Equations of Heat and Mass Transfer
(INFRA-M, Moscow, 2013)
[in Russian]. |
| 11. | A. V. Lykov,
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|
| Received |
18 October 2012 |
| Link to Fulltext |
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