A bending quasi-front generated by an instantaneous impulse loading at the edge of a semi-infinite pre-stressed incompressible elastic plate

Journal of the Mechanics and Physics of Solids

Volumn 53, Issue 5, 2005, Pages 1079-1098

  Kaplunov, J D ^a   Pichugin, A V ^a,b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Matched asymptotic expansions; Plate; Plate bending; Pre stress; Quasi front

Indexed keywords

ACOUSTIC DEVICES; BENDING (DEFORMATION); ELASTICITY; FUNCTIONS; LOADING; PRESTRESSING; TENSORS; WAVEFRONTS;

CAUCHY STRESSES; IMPULSE LOADING; QUASI-FRONT; STRAIN ENERGY FUNCTIONS;

PLATES (STRUCTURAL COMPONENTS);

EID: 14544276293     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2004.12.002     Document Type: Article

References (22)

1. R. Burridge Lamb's problem for an anisotropic half-space Quart. J. Mech. Appl. Math. 24 1971 81 98
2. L. Cagniard Reflection and Refraction of Progressive Seismic Waves 1962 McGraw-Hill New York
3. J.D. Cole Perturbation Methods in Applied Mathematics 1968 Blaisdell Waltham MA, Toronto, London
4. A.T. De Hoop A modification of Cagniard's method for solving seismic pulse problems Appl. Sci. Res. Sect. B 8 1960 349 356
5. A. De Morgan The Differential and Integral Calculus 1842 Robert Baldwin London
6. I. Emri, J.D. Kaplunov, and E.V. Nolde Analysis of transient waves in thin structures utilising matched asymptotic expansions Acta Mechanica 149 2001 55 68
7. A.L. Goldenveizer, J.D. Kaplunov, and E.V. Nolde On Timoshenko-Reissner type theories of plates and shells Int. J. Solids Struct. 30 1993 675 694
8. I.S. Gradshteyn, and I.M. Ryzhik Table of Integrals, Series, and Products 1980 Academic Press San Diego, New York, London, Sydney, Tokyo
9. K.F. Graff Wave Motion in Elastic Solids 1991 Dover New York
10. J.D. Kaplunov, L.Y. Kossovich, and E.V. Nolde Dynamics of Thin Walled Elastic Bodies 1998 Academic Press New York
11. 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. Ser. A 456 2000 2589 2610
12. Y.D. Kaplunov, and E.V. Nol'de Lamb problem for a generalized plane stress state Sov. Phys. Dokl. 37 1992 88 90 (transl. from Dokl. Akad. Nauk, 322, pp. 1043-1047)
13. Y.D. Kaplunov, and Y.V. Nol'de A quasifront in the problem of the action of an instantaneous point impulse at the edge of a conical shell J. Appl. Maths Mech. 59 1995 773 780 (transl. from Prikl. Mat. Mekh., 59, pp. 803-811)
14. H. Lamb On the propagation of tremors over the surface of an elastic solid Phil. Trans. Roy. Soc. Ser. A 203 1904 1 42
15. R.W. Ogden Non-linear Elastic Deformations 1984 Ellis Horwood New York
16. R.W. Ogden, and D.G. Roxburgh The effect of pre-stress on the vibration and stability of elastic plates Int. J. Eng. Sci. 31 1993 1611 1639
17. G.I. Petrashen', G.I. Marchuk, and K.I. Ogurtsov On Lamb's problem for a half-space Uchenie Zapiski LGU, Ser. Matem. Nauk 135 21 1950 71 118 (in Russian)
18. Pichugin, A.V., 2002. Ph.D. Thesis. University of Salford.
19. A.V. Pichugin, and G.A. Rogerson An asymptotic membrane-like theory for long-wave motion in a pre-stressed elastic plate Proc. Roy. Soc. Lond. Ser. A 458 2002 1447 1468
20. R. Skalak Longitudinal impact of a semi-infinite circular elastic bar ASME J. Appl. Mech. 34 1957 59 64
21. V.I. Smirnov, and S.L. Sobolev On application of the new method to investigation of elastic vibrations in axially-symmetric spaces Tr. Seismol. Inst. AN SSSR 29 1933 43 51 (in Russian)
22. J.R. Willis Self-similar problems in elastodynamics Phil. Trans. Roy. Soc. Lond. Ser. A 274 1973 435 491