An asymptotically consistent model for long-wave high-frequency motion in a pre-stressed elastic plate

Mathematics and Mechanics of Solids

Volumn 7, Issue 6, 2002, Pages 581-606

  Kaplunov, J D ^a  

^a INSTITUTE FOR PROBLEMS IN MECHANICS   (Russian Federation)

Author keywords

Asymptotics; Dispersion; Elastic plates; Pre stress

Indexed keywords

EID: 0003273007     PISSN: 10812865     EISSN: None     Source Type: Journal    
DOI: 10.1177/108128602029660     Document Type: Article

References (28)

1. Ogden, R. W. and Sotiropoulos, D. A.: On interfacial waves in pre-stressed layered incompressible solids. Proc. R. Soc., A 450, 319-341 (1995).
2. Rogerson, G. A. and Sandiford, K. J.: Flexural waves in pre-stressed incompressible elastic composites. Q. J. Mech. Appl. Math., 50, 597-624 (1997).
3. Rogerson, G. A.: Some asymptotic expansions of the dispersion relation for an incompressible, pre-stressed elastic plate. Int. J. Solids Struct., 34, 2785-2802 (1997).
4. Rogerson, G. A.: On the existence of surface waves and the propagation of plate waves in pre-stressed, fibre-reinforced composites. J. Mech. Phys. Solids, 46, 1581-1612 (1998).
5. Ogden, R. W. and Roxburgh, D. G.: The effect of pre-stress on the vibration and stability of elastic plates. Int. J. Eng. Sci., 30, 1611-1639 (1993).
6. Roxburgh, D. G. and Ogden, R. W.: Stability and vibration of pre-stressed compressible elastic plates. Int. J. Eng. Sci., 32, 427-454 (1994).
7. Sotiropoulos, D. A. and Sifniotopoulos, C. G.: Interfacial waves in pre-stressed incompressible elastic interlayers. J. Mech. Phys. Solids, 43, 365-387 (1995).
8. Connor, P. and Ogden, R. W.: The influence of shear strain and hydrostatic stress on stability and elastic waves in a layer. Int. J. Eng. Sci., 34, 375-397 (1996).
9. Dowaikh, M. A. and Ogden, R. W.: On surface waves and deformations in a pre-stressed incompressible elastic solid. IMA J. Appl. Math., 44, 261-284 (1990).
10. Dowaikh, M. A. and Ogden, R. W: On surface waves and deformations in a compressible elastic half space. Stability Appl. Anal. Continuous Media, 1, 27-45 (1991).
11. Chadwick, P.: Interfacial and surface waves in pre-strained isotropic elastic media. Z. Angew. Math. Phys., 46 (special issue), 51-71 (1995).
12. Connor, P. and Ogden, R. W.: The effect of shear on the propagation of elastic surface waves. Int. J. Eng. Sci., 33, 973-982 (1995).
13. Sheridan, P. M., James, F. O. and Miller, T. S.: Design of components. Engineering with Rubber (A. N. Gent ed) 209-235, Hanser, Munich, 1992.
14. Fu, Y. B. and Rogerson, G. A.: A non-linear analysis of instability of a pre-stressed incompressible elastic plate. Proc. R. Soc., A 446, 233-254 (1994).
15. Kaplunov, J. D., Kossovich, L. Yu. and Nolde, E. V.: Dynamics of Thin Walled Elastic Bodies, Academic Press, San Diego, 1998.
16. Kaplunov, J. D. and Markushevich, D. G.: Plane vibrations and radiation of an elastic layer lying on a liquid half-space. Wave Motion, 17, 199-211 (1993).
17. Kaplunov, J. D., Nolde, E. V. and Veksler, N. D.: Asymptotic formulae for the modal resonance of peripheral waves in the scattering of an obliquely incident plane acoustic wave by a cylindrical shell. Acustica, 80, 280-293 (1994).
18. Kaplunov, J. D.: Long wave vibrations of a thin body with fixed faces. Q. J. Mech. Appl. Math., 48, 311-327 (1995).
19. Rogerson, G. A. and Nolde, E. V.: Asymptotically approximate equations for dynamic flexural motion in a finitely deformed elastic layer. Proc. 1st Canadian Conf. on Nonlinear Solid Mechanics, 1, 79-88 (1999).
20. Achenbach, J. D.: An asymptotic method to analyse the vibrations of an elastic layer. Trans. ASME, J. Appl. Mech., 36, 65-72 (1969).
21. Goldenveiser, A. L.: An application of asymptotic integration of the equations of elasticity to derive an approximate theory for plate bending. Prikl. Mat. Mekh. (J. Appl. Math. Mech.), 31, 668-686 (1962).
22. Goldenveiser, A. L.: The principles of reducing three-dimensional problems of elasticity to two-dimensional problems of the theory of plates and shells. Applied Mechanics, Proc. 11th Int. Congress of Applied Mechanics, (H. Gortler ed) 306-311, Springer, Berlin, 1966.
23. Kaplunov, J. D.: Equations for high-frequency long-wave vibrations of an elastic layer lying on an acoustic half-space. Dokl. Akad. Nauk SSSR, 305, 1077-1081 (1989).
24. Kaplunov, J. D.: High-frequency stress-strain states of small variability in elastic shells. Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, 25, 147-157 (1990).
25. Berdichevskii, V. L.: High-frequency long-wave vibrations of plates. Dokl. Akad. Nauk SSSR, 236, 1319-1322 (1977).
26. Le, K. C.: High frequency vibrations and wave propagation in elastic shells: variational-asymptotic approach. Int. J. Solids Struct., 34, 3923-3939 (1997).
27. Ogden, R. W.: Non-linear Elastic Deformations, Ellis Horwood, New York, 1984.
28. Goldenveiser, A. L., Kaplunov, J. D. and Nolde, E. V.: On Timoshenko-Reissner type theories of plates and shells. Int. J. Solids Struct., 30, 675-694 (1993).