Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

Ogden, R.W. (2009) Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field. International Journal of Non-Linear Mechanics, 44(5), pp. 570-580. (doi:10.1016/j.ijnonlinmec.2008.11.017)

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Abstract

The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Ogden, R.W.
Subjects:Q Science > QA Mathematics
Q Science > QC Physics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:International Journal of Non-Linear Mechanics
Journal Abbr.:Int. J. Non-Linear Mech.
ISSN:0020-7462
ISSN (Online):1878-5638
Published Online:06 December 2008

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