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|Title:||On a Lamb-type problem for a bi-axially pre-stressed incompressible elastic plate|
|Publisher:||Oxford University Press|
|Citation:||IMA Journal of Applied Mathematics 71(2): 171-185|
|Abstract:||The far-field response of a bi-axially pre-stressed incompressible elastic plate, subjected to an instantaneous edge impulse loading, is studied using a refined long-wave low-frequency theory. The second-order correction introduced by the refined theory is demonstrated to smooth the discontinuity associated with one of the wave-fronts predicted by the leading order hyperbolic theory. The character of the so-called quasi-front is shown to depend greatly on both the material parameters and the pre-stress and may be either classical receding or advancing. Additionally, and in contrast to the analogous problem in linear isotropic elasticity, in a pre-stressed plate the dilatational quasi-front may propagate slower than the shear wave-front. This situation is demonstrated to lead to the formation of a head-wave quasi-front.|
|Description:||This is a pre-copy-editing, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The definitive publisher authenticated version J. D. KAPLUNOV AND A. V. PICHUGIN (2006). On a Lamb-type problem for a bi-axially pre-stressed incompressible, IMA Journal of Applied Mathematics. 71, 171−185. OUP, is available online at: http://dx.doi.org/10.1093/imamat/hxh097|
|Appears in Collections:||Dept of Mathematics Research Papers|
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