 | | 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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| << Previous article | Volume 44, Issue 6 / 2009 | Next article >> |
| S. R. Amirova and G. A. Rogerson, "A Long Wave Low Frequency Motion Model for a Finitely Sheared Elastic Layer," Mech. Solids. 44 (6), 865-873 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
6 |
Pages |
865-873 |
| DOI |
10.3103/S0025654409060065 |
| Title |
A Long Wave Low Frequency Motion Model for a Finitely Sheared Elastic Layer |
| Author(s) |
S. R. Amirova (School of Computing and Mathematics, University of Keele, Staffordshire, ST5 5BG, UK, s.amirova@epsam.keele.ac.uk)
G. A. Rogerson (School of Computing and Mathematics, University of Keele, Staffordshire, ST5 5BG, UK, g.a.rogerson@maths.keele.ac.uk) |
| Abstract |
We consider two-dimensional long wave low frequency motion in a pre-stressed layer composed of neo-Hookean material. Specifically, the pre-stress is a simple shear deformation. Derivation of the dispersion relation associated with traction-free boundary conditions is briefly reviewed. Appropriate approximations are established for the two associated long wave modes. From these approximations it is clear that there may be either two, one or no real long wave limiting phase speeds. These approximations are also used to establish the relative asymptotic orders of the displacement components and pressure increment. Using these relative orders to motivate the introduction of appropriate a scales, an asymptotically consistent model long wave low frequency motion is established. It is shown that in the presence of shear there is neither bending nor extension, or analogues of their previously established pre-stressed counterparts. In fact, both the in-plane and normal displacement components have the same asymptotic orders and the derived governing equation is of vector form. |
| Keywords |
neo-Hookean material, shear, long wave approximation, phase speed |
| References |
| 1. | R. W. Ogden and D. G. Roxburg,
"The Effect of Pre-Stress on the Vibration and Stability of Elastic Plates,"
Int. J. Engng Sci.
31, 1611-1639 (1993). |
| 2. | G. A. Rogerson,
"Some Asymptotic Expansions of the Dispersion
Relation for an Incompressible Elastic Plate,"
Int. J. Solid Struct.
34, 2785-2802 (1997). |
| 3. | P. Connor and R. W. Ogden,
"The Influence of Shear Strain and Hydrostatic Stress on Stability and Elastic Waves in a Layer,"
Int. J. Engng Sci.
34, 375-397 (1996). |
| 4. | J. D. Kaplunov, L. Yu. Kossovich, and E. V. Nolde,
Dynamics of Thin Walled Elastic Bodies
(Academic Press, New York, 1998). |
| 5. | J. D. Kaplunov, E. V. Nolde, and G. A. Rogerson,
"A Low-Frequency Model for Dynamic Motion in Pre-
Stressed Incompressible Elastic Structures,"
Proc. R. Soc. Lond. A
456 (2003), 2589-2610 (2000). |
| 6. | Waterloo Maple Software,
Maple V Programming Guide
(Springer-Verlag, New York, 1996). |
|
| Received |
10 March 2008 |
| Link to Fulltext |
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