 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
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| In Russian (ÏÌÌ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| P.Ye. Tovstik, "The vibrations and stability of a prestressed plate on an elastic foundation," J. Appl. Math. Mech. 73 (1), 77-87 (2009) |
| Year |
2009 |
Volume |
73 |
Issue |
1 |
Pages |
77-87 |
| Title |
The vibrations and stability of a prestressed plate on an elastic foundation |
| Author(s) |
P.Ye. Tovstik (St Petersburg, Russia, peter.tovstik@mail.ru) |
| Abstract |
The free vibrations of a transversely isotropic prestressed linear elastic half-space, localized close to a free surface, are considered. The free vibrations of a prestressed transversely isotropic infinite plate, lying on an elastic foundation, are also considered. The dispersion equation is analysed as a function of the wave numbers, the elastic properties of the foundation and of the plate and the values of the prestresses. The investigation is confined to cases when the initial stresses are less than the critical values, while the elastic waves do not penetrate into the depth of the foundation but are localized close to the free surface. The stability of the half-space and the plate on an elastic foundation is also considered. When analysing the vibrations and the stability of the plate, the results in the three-dimensional formulation of the problem are compared with the results of the two–dimensional Kirchhoff-Love and Timoshenko-Reissner models. |
| References |
| 1. | V.A. Radionova, B.F. Titayev and K.R. Chernykh, The Applied Theory of Anisotropic Plates and Shells, Izd SP Univ, St Petersburg (1996). |
| 2. | V.V. Bolotin and Yu.N. Novichkov, The Mechanics of Laminated Structures, Mashinostroyeniye, Moscow (1980). |
| 3. | A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, Univ. Press, Cambridge (1927). |
| 4. | A.Yu. Ishlinskii, A limit transition in the theory of the stability of rectangular elastic plates, Dokl Akad Nauk SSSR 95 (3) (1954), pp. 477–479. |
| 5. | P.Ye. Tovstik, The Stability of Thin Shells, Nauka. Fizmatlit, Moscow (1995). |
| 6. | N.F. Morozov, M.V. Paukshto and P.Ye. Tovstik, The stability of the surface layer under thermal loading, Izv Ross Akad Nauk MTT 1 (1998), pp. 130–139. |
| 7. | M.A. Il’gamov, V.A. Ivanov and B.V. Gulin, Strength, Stability and Dynamics of Shells with an Elastic Filler, Nauka, Moscow (1977). |
| 8. | P.Ye. Tovstik, The reaction of a prestressed orthotropic foundation, Vestnik St Petersburg Univ Ser 1 4 (2006), pp. 98–108. |
| 9. | P.Ye. Tovstik, The local stability of plates and shallow shells on an elastic foundation, Izv Ross Akad Nauk MTT 1 (2005), pp. 147–160. |
| 10. | P.E. Tovstik and T.P. Tovstik, On the 2D models of plates and shells including the transversal shear, ZAMM 87 (2007), pp. 160–171. |
| 11. | In: I.A. Birger and YaG. Panovko, Editors, Strength, Stability and Vibrations. Vol. 3, Mashinostroyeniye, Moscow (1968). |
| 12. | P.Ye. Tovstik, The asymptotic character of approximate models of beams, plates and shells, Vestnik SPU Ser 1 (2007), pp. 49–54. |
| 13. | P.Ye. Tovstik, On the vibrations of pre-stressed anisotropic plates and shells lying on a pre-stressed anisotropic elastic foundation. EUROMECH Colloq. 481: Recent Advances in the Theory and Application of Surface and Edge Waves. Keele Univ. 2007, p. 38. |
| 14. | V.V. Bolotin, The edge effect in the vibrations of elastic shells, Prikl Mat Mekh 24 (5) (1960), pp. 831–842. |
| 15. | P.G. Ciarlet, Mathematical Elasticity, North-Holland, Amsterdam etc (1988). |
|
| Received |
27 November 2007 |
| Link to Fulltext |
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