 | | 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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| N. D. Vaisfel'd, "Unsteady problems of diffraction of elastic waves on defects in spherically layered media," Mech. Solids. 40 (3), 57-66 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
3 |
Pages |
57-66 |
| Title |
Unsteady problems of diffraction of elastic waves on defects in spherically layered media |
| Author(s) |
N. D. Vaisfel'd (Odessa) |
| Abstract |
A spherically layered medium under the action of an unsteady elastic wave
is considered. The elastic constants of the medium undergo a jump
discontinuity on the spherical surfaces, on which the defects in the form
of cracks or thin rigid inclusions are located. The method for solving
problems of diffraction of waves on such defects is based on
introducing new unknown functions instead of the displacements and the
stresses. These new functions are linear functions of the displacements
and stresses. The representation of these functions in terms of the
solutions of the wave equations makes it possible to solve the problem for
an arbitrary number of layers. The method is illustrated for the case of
the diffraction of an unsteady torsional wave on an interfacial crack
located in a two-layered medium. The problem is reduced to an integral
equation which is solved approximately. For the stress intensity factor,
the formula is obtained and the numerical investigation is performed. |
| References |
| 1. | M. A. Martynenko, "An axisymmetric problem for an elastic medium
containing a spherical inclusion weakened by an interfacial crack," Dokl.
AN UkrSSR. Ser. A., No. 7, pp. 39-44, 1983. |
| 2. | S. A. Smirnov, "A stress state of a two-layer thick-walled
spherical shell with cuts," Dokl. AN USSR. Ser. A., No. 9, pp. 97-101,
1991. |
| 3. | A. N. Guz', V. D. Kubenko, and M. A. Cherevko, Diffraction of
Elastic Waves [in Russian], Naukova Dumka, Kiev, 1978. |
| 4. | V. T. Golovchan and A. N. Guz', "On the solution of the problems
of diffraction of elastic waves on spherical cavities," Prikl. Mekhanika,
Vol. 8, No. 9, pp. 118-122, 1972. |
| 5. | A. G. Gorshkov and D. V. Tarlakovskii, Unsteady
Aerohydroelasticity of Spherically-shaped Bodies [in Russian], Nauka,
Moscow, 1990. |
| 6. | S. V. Shmegera, "A method for solving plane initial-boundary
value problems of dynamic elasticity theory," PMM [Applied Mathematics and Mechanics], Vol. 61, No. 2, pp. 263-274, 1997. |
| 7. | V. V. Levchenko, "Magneto-elastic volume shear waves in a
periodically-layered medium," Prikl. Mekhanika, Vol. 37, No. 4,
pp. 76-81, 2001. |
| 8. | M. V. Marchuk and N. N. Khomyak, "On the solution of the problem
of the stress state of layered spherical shells using an improved theory
based on the mixed method of finite elements," Prikl. Mekhanika,
Vol. 37, No. 12, pp. 94-102, 2001. |
| 9. | G. Ya. Popov, "On the solution of dynamic problems of
elastic-stress concentration near defects in spherically layered media,"
Doklady AN, Vol. 360, No. 4, pp. 483-487, 1998. |
| 10. | G. Ya. Popov, "Issues of elastic stress concentration near
defects in spherically layered media," PMM [Applied Mathematics and Mechanics],
Vol. 62, No. 5, pp. 840-853, 1998. |
| 11. | D. V. Grilitskii and A. P. Poddubnyak, "The dispersion of an
unsteady torsional wave on a fixed sphere in an elastic medium," Izv. AN
SSSR MTT [Mechanics of Solids], No. 5, pp. 86-92, 1980. |
| 12. | H. Bateman and A. Erdélyi, Tables of Integral Transforms,
McGraw-Hill, New York, etc., 1954. |
| 13. | E. Kamke, Hadbook on Ordinary Differential Equations [Russian
translation], Nauka, Moscow, 1965. |
| 14. | O. A. Nazarenko and G. Ya. Popov, "On the diffraction of elastic
waves on spherical defects," PMM [Applied Mathematics and Mechanics], Vol. 60,
No. 5, pp. 835-847, 1996. |
| 15. | E. M. Kartashov, Analytical Methods in Heat Conductivity of Solids [in Russian], Vysshaya
Shkola, Moscow, 1979. |
| 16. | M. Abramovitz and I. A. Stegun (Editors), Handbook of Mathematical
Functions with Formulas, Graphs and Mathematical Tables [Russian translation],
Nauka, Moscow, 1979. |
| 17. | G. Ya. Popov, Concentration of Elastic Stresses near Punches, Cuts, Thin Inclusions, and
Reinforcements [in Russian], Nauka, Moscow, 1982. |
| 18. | N. D. Vaisfel'd and G. Ya. Popov, "The problem of diffraction of
the torsion wave on a spherical crack," in Material Fracture Mechanics and
Strength of Structures [in Ukranian], Vol. 2, No. 2,
pp. 260-264, Lvov, 1999. |
|
| Received |
17 March 2003 |
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