 | | 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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| O.L. Kravchishin and V.F. Chekurin, "Acoustoelasticity Model of Inhomogeneously Deformed Bodies," Mech. Solids. 44 (5), 781-791 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
5 |
Pages |
781-791 |
| DOI |
10.3103/S0025654409050161 |
| Title |
Acoustoelasticity Model of Inhomogeneously Deformed Bodies |
| Author(s) |
O.L. Kravchishin (Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Naukova 3b, Lvov, 79060 Ukraine, oxana_kravch@mail.ru)
V.F. Chekurin (Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Naukova 3b, Lvov, 79060 Ukraine, chekurin@iapmm.lviv.ua) |
| Abstract |
We consider a mathematical model of dynamics of small elastic perturbations in an inhomogeneously deformed rigid body, where for the determining parameters of a local state we take the tensor characteristics of a given actual (strained) configuration (the Cauchy stress tensor and the Hencky or Almansi or Figner strain measure). An iteration algorithm is developed to solve the Cauchy problem stated in the framework of this model for a system of hyperbolic equations with variable coefficients that describes the propagation of elastic pulses in an inhomogeneous deformed continuum. In the case of two-dimensional stress fields, we obtain acoustoelasticity integral relations between the probing pulse parameters and the initial strain (stress) distribution in the direction of pulse propagation in the strained body. We also consider an example of application of the obtained integral relations in the inverse acoustic tomography problem for residual strains in a strip. |
| Keywords |
elastic perturbation in an inhomogeneously deformed body, acoustoelasticity integral relations, direct and inverse problems of acoustic tomography |
| References |
| 1. | A. I. Lurie,
Nonlinear Theory of Elasticity
(Nauka, Moscow, 1980)
[in Russian]. |
| 2. | R. A. Toupin and B. Bernstein,
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J. Acoust. Soc. America
33 (2), 216-225 (1961). |
| 3. | H. R. Dorfi, H. Bushy, and M. Janssen,
"Acoustoelasticity: Ultrasonic Stress Field Reconstruction,"
Experim. Mech.
36 (4), 325-332 (1996). |
| 4. | A. N. Guz',
Elastic Waves in Bodies with Initial (Residual) Stresses
(A. S. K., Kiev, 2004)
[in Russian]. |
| 5. | I. V. Anan'ev, V. V. Kalinchuk, and I. V. Poliakova,
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Prikl. Mat. Mekh.
47 (3), 483-489 (1983)
[J. Appl. Math. Mech. (Engl. Transl.)
47 (3), 408-413 (1983)]. |
| 6. | A. Ravasoo,
"Propagation of Waves in Media with Inhomogeneous Static Strains,"
Izv. Akad. Nauk Eston. SSR. Fiz. Mat.
31 (3), 277-283 (1982). |
| 7. | V. Chekurin and O. Kravchyshyn,
"A Theory for Acoustical Tomography of Tensor Fields in Solids,"
in 4th Ukrainian Polish Conf. "Environmental Mechanics,
Methods of Computer Science and Simulations"
(Lviv, 2004),
pp. 241-251. |
| 8. | O. Z. Kravchyshyn and V. F. Chekurin,
"On One Problem for a System of Hyperbolic Equations with Variable Coefficients,"
Visn. L'viv Univ. Ser. Prikl. Mat.,
No. 6, 64-67 (2003). |
| 9. | V. F. Chekurin and O. Z. Kravchyshyn,
"On the Theory of Acoustic Tomography of Stresses of Rigid Bodies,"
Fiz.-Khim. Mekh. Mater.
38 (2), 97-104 (2002). |
| 10. | V. F. Chekurin,
"A Variational Method for Solving Direct and Inverse Problems of Elasticity
for a Semi-Infinite Strip,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 58-70 (1999)
[Mech. Solids (Engl. Transl.)
34 (2), 49-59 (1999)]. |
|
| Received |
10 January 2007 |
| Link to Fulltext |
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