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Title: Anti-symmetric motion of a pre-stressed incompressible elastic layer near shear resonance
Authors: Pichugin, AV
Rogerson, GA
Keywords: Pre-stress;Elastic plates;Dispersion;Shear resonance;Asymptotics
Issue Date: 2002
Publisher: Springer Verlag
Citation: Journal of Engineering Mathematics, 42(2): 181–202 (2002)
Abstract: A two-dimensional model is derived for anti-symmetric motion in the vicinity of the shear resonance frequencies in a pre-stressed incompressible elastic plate. The method of asymptotic integration is used and a second-order solution, for infinitesimal displacement components and incremental pressure, is obtained in terms of the long-wave amplitude. The leading-order hyperbolic governing equation for the long-wave amplitude is observed to be not wave-like for certain pre-stressed states, with time and one of the in-plane spatial variables swapping roles. This phenomenon is shown to be intimately related to the possible existence of negative group velocity at low wave number, i.e. in the vicinity of shear resonance frequencies.
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Dept of Mathematics Research Papers
Mathematical Sciences

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