 | | 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. A. Kovalev, L. Yu. Kossovich, and O. V. Taranov, "The far field of a Rayleigh wave in an elastic half-strip under end loads," Mech. Solids. 40 (5), 66-72 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
5 |
Pages |
66-72 |
| Title |
The far field of a Rayleigh wave in an elastic half-strip under end loads |
| Author(s) |
V. A. Kovalev (Moscow)
L. Yu. Kossovich (Saratov)
O. V. Taranov (Moscow) |
| Abstract |
The paper [1] gives a classification of nonstationary stress-strain states
of plates and shells under impact end loads. An application of asymptotic
methods permitted one [2-4] to split the nonstationary stress-strain state
due to longitudinal loads of tangential and bending types into components
with various variability and dynamic characteristics: one has used
tangential and transverse low-frequency approximations, parabolic boundary
layers in a neighborhood of the quasifront (the two-dimensional tensile
wave front), high-frequency short-wave approximations, and also hyperbolic
boundary layers in a small neighborhood of the extension wave front. The
proof of the existence of matching domains showed that the approximations
used are complete and the splitting scheme is well posed.
The nonstationary stress-strain state under normal end loads has a
distinguished position in the classification [1]. In this case, there is
quasifront in a neighborhood of the conventional front of the surface
Rayleigh wave, and the hyperbolic equations of a Timoshenko-type theory
mistake this quasifront for the front of a new special shear wave. This
property distinguishes this type of stress-strain states and prevents one
from using the splitting scheme described above in this case.
The paper [5] gives an asymptotic model aimed at the extraction of the
solution in a neighborhood of the conventional front of the surface
Rayleigh wave in the classical Lamb problem for an elastic half-space. In
this model, one first analyzes the hyperbolic equation describing
one-dimensional propagation of Rayleigh waves along the boundary of the
half-plane. At the second stage, one finds the signal attenuation in the
interior of the half-plane by successively solving two Neumann problems of
similar type. In [6], the same asymptotic method was used to construct the
far field equations for a Rayleigh wave in an infinite elastic layer.
The present paper is the first to construct equations determining the
solution in a neighborhood of the conventional front of surface Rayleigh
waves under normal end loads by an asymptotic method. The approach
developed has a general character and can be used when studying wave
propagation in shells. |
| References |
| 1. | U. Nigul, "Regions of effective application of the methods of
three-dimensional and two-dimensional analysis of transient stress waves in
shells and plates," Int. J. Solid and Structures, Vol. 5, No. 6,
pp. 607-627, 1969. |
| 2. | L. Yu. Kossovich, Nonstationary Problem of the Theory of Elastic
Thin Shells [in Russian], Izd-vo Saratovsk. Un-ta, Saratov, 1986. |
| 3. | J. D. Kaplunov, L. Yu. Kossovich, and E. V. Nolde, Dynamics of Thin
Walled Elastic Bodies, Academic Press, New York, 1998. |
| 4. | L. Yu. Kossovich and Yu. D. Kaplunov, "Asymptotic analysis of
nonstationary elastic waves in thin shells of revolution under impact end
loads," Izv. Saratovsk. Un-ta, Vol. 1, No. 2, pp. 111-131, 2001. |
| 5. | Yu. D. Kaplunov and L. Yu. Kossovich, "An asymptotic model for the
computation of the far field of a Rayleigh wave in the case of an elastic
half-plane," Doklady AN, Vol. 395, No. 4, pp. 482-484, 2004. |
| 6. | L. Yu. Kossovich and A. N. Kushekkaliev, "Rayleigh field in an
infinite elastic layer," in Collected Papers. Mathematics. Mechanics, Izd-vo
Saratovsk. Un-ta, No. 5, 2003, pp. 159-161. |
| 7. | A. I. Lur'e, 3D Problems of Elasticity [in Russian], Gostekhizdat,
Moscow, 1955. |
| 8. | L. Ya. Ainola and U. K. Nigul, "Wave Strain Processes in Elastic
Plates and Shells," Izv. AN ESSR, Vol. 14, No. 1, pp. 3-63, 1965. |
|
| Received |
10 October 2004 |
| << Previous article | Volume 40, Issue 5 / 2005 | Next article >> |
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