Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-06-03T15:09:29.110Z Has data issue: false hasContentIssue false
  • English
  • Français

Elastic waves in a prestressed Mooney material

Published online by Cambridge University Press:  17 April 2009

J.A. Belward
J.A. Belward
Affiliation:
University of Queensland, St Lucia, Queensland.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The dynamic response of a prestressed incompressible Mooney material is studied by investigating plane wave propagation and the response of the material to impulsive lines of force. The choice of an initial deformation which is axially symmetric gives a particularly simple form for the secular equation for the plane wavefront velocities. The speeds of propagation and the amplitudes of the two permissible transverse waves are found and necessary and sufficient conditions for there to exist two real wave speeds in all directions are established. The simple form of the secular equation enables the response of the material to concentrated disturbances to be readily solved using Fourier transforms. The motions caused by a line of impulsive forces is examined in some detail.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 1 , August 1972 , pp. 135 - 160
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Ericksen, J.L., “On the propagation of waves in isotropic incompressible perfectly elastic materials”, J. Rational Mech. Anal. 2 (1953), 329–337.Google Scholar
[2]Flavin, J.N., Green, A.E., “Plane thermo-elastic waves in an initially stressed medium”, J. Mech. Phys. Solids 9 (1961), 179–190.CrossRefGoogle Scholar
[3]Gelfand, I.M. and Shilov, G.E., Generalized functions, Vol. 1 (translated by Saletan, Eugene. Academic Press, New York, London, 1964.Google Scholar
[4]Gradshteyn, I.S., Ryzhik, I.M., Table of integrals, series, and products, 4th ed. (translated by Technica, Scripta, Inc. Academic Press, New York, London, 1965).Google Scholar
[5]Knowles, James K., “Large amplitude oscillations of a tube of incompressible elastic material”, Quart. Appl. Math. 18 (1960), 71–77.CrossRefGoogle Scholar
[6]Manacorda, T., “Sulla propagazione di onde ordinarie di discontinuità nella elasticità di secondo grado per solidi incomprimibili”, Riv. Mat. Univ. Parma 10 (1959). 19–33.Google Scholar
[7]Truesdell, C., Noll, W., “The non-linear field theories of mechanics”, Handbuah der Physik, Band III/3 (Springer-Verlag, Berlin, Heidelberg, New York, 1965).Google Scholar