 | | 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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| V. K. Lashchenov, "On steady motion of elastic beams along the boundary of an isotropic elastic strip," Mech. Solids. 37 (4), 136-146 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
4 |
Pages |
136-146 |
| Title |
On steady motion of elastic beams along the boundary of an isotropic elastic strip |
| Author(s) |
V. K. Lashchenov (St. Petersburg) |
| Abstract |
We consider a mixed stationary problem describing the motion of
a finite elastic beam along the boundary of an isotropic strip.
The problem is solved by the method of piecewise homogeneous solutions [1]
with the help of a relation of generalized orthogonality for homogeneous
solutions. A solution of the problem for a semi-infinite beam and a
system of piecewise homogeneous solutions are obtained in quadrature by
the Wiener-Hopf method. Numerical examples are given.
Previously, mixed nonstationary contact problems for a punch and a halfplane or
a halfspace were studied in [2-6], and similar problems for a composite plane
were considered in [7-8]. |
| References |
| 1. | B. M. Nuller, "Contact problems of a semi-infinite elastic
cylinder," PMM [Applied Mathematics and Mechanics], Vol. 34, No. 4, pp. 620-631, 1970. |
| 2. | L. A. Galin, Contact Problems of Elasticity [in Russian],
Gostekhizdat, Moscow, 1953. |
| 3. | V. M. Alexandrov and S. M. Mkhitatian,
Contact Problems for Bodies with Thin Coatings and Interlayers [in Russian],
Nauka, Moscow, 1983. |
| 4. | V. M. Alexandrov and E. V. Kovalenko,
Problems of Continuum Mechanics with Mixed Boundary Conditions [in Russian],
Nauka, Moscow, 1986. |
| 5. | V. A. Babeshko, E. V. Glushkov, and Zh. F. Zinchenko,
Dynamics of Nonhomogeneous Linearly Elastic Media [in Russian], Nauka, Moscow, 1989. |
| 6. | A. V. Belokon' and V. P. Shekhov,
"Mixed viscoelasticity problems with moving punches," in
Static and Dynamic Mixed Problems in Elasticity [in Russian], pp. 231-246,
Izd-vo Rostovsk. Un-ta, Rostov-on-Don, 1983. |
| 7. | I. V. Simonov,
"Dynamics of a tensile-shear crack on the interface
between two elastic materials," Doklady AN SSSR, Vol. 271, No. 1,
pp. 65-68, 1983. |
| 8. | E. L. Nakhmein and B. M. Nuller,
"On subsonic steady motion of punches
and flexible cover plates along the boundary of
an elastic halfplane and a composite halfplane," PMM [Applied Mathematics and Mechanics],
Vol. 53, No. 1, pp. 134-144, 1989. |
| 9. | V. K. Lashchenov and B. M. Nuller,
"The method of piecewise homogeneous solutions in
stationary problems of elasticity," PMM [Applied Mathematics and Mechanics], Vol. 64, No. 2,
pp. 321-331, 2000. |
| 10. | R. Bellman and K. L. Cooke,
Differential-Difference Equations, Academic Press, New York, 1963. |
| 11. | V. G. Gogoladze, "Dispersion of Rayleigh waves in a layer,"
Trudy Seismol. Inst. AN SSSR, Vol. 119, pp. 27-38, 1947. |
| 12. | V. K. Lashchenov and M. G. Sulimov,
"Roots of the dispersion equation for the problem of
motion of an elastic strip," Vestnik Leningr. Un-ta, Ser. 1,
Issue 1, No. 1, pp. 82-88, 1995. |
| 13. | F. D. Gakhov, Boundary-Value Problems [in Russian], Nauka, Moscow, 1977. |
| 14. | B. Noble, Methods Based on Wiener-Hopf Technique for the
Solution of Partial Differential Equations, Pergamon Press, London, 1958. |
|
| Received |
30 March 2000 |
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