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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/1573

Title: A two-dimensional model for extensional motion of a pre-stressed incompressible elastic layer near cut-of frequencies
Authors: Pichugin, AV
Rogerson, GA
Keywords: Asymptotic analysis
Elasticity
Pre-stress
waves
Publication Date: 2001
Publisher: Oxford University Press
Citation: IMA Journal of Applied Mathematics, 66(4): 357-385
Abstract: A two-dimensional model for extensional motion of a pre-stressed incompressible elastic layer near its cut-off frequencies is derived. Leading-order solutions for displacement and pressure are obtained in terms of the long wave amplitude by direct asymptotic integration. A governing equation, together with corrections for displacement and pressure, is derived from the second-order problem. A novel feature of this (two-dimensional) hyperbolic governing equation is that, for certain pre-stressed states, time and one of the two (in-plane) spatial variables can change roles. Although whenever this phenomenon occurs the equation still remains hyperbolic, it is clearly not wave-like. The second-order solution is completed by deriving a refined governing equation from the third-order problem. Asymptotic consistency, in the sense that the dispersion relation associated with the two-dimensional model concurs with the appropriate order expansion of the three-dimensional relation at each order, is verified. The model has particular application to stationary thickness vibration of, or transient response to high frequency shock loading in, thin walled bodies.
URI: http://bura.brunel.ac.uk/handle/2438/1573
DOI: http://dx.doi.org/10.1093/imamat/66.4.357
Appears in Collections:Mathematics
Information Systems and Computing
School of Information Systems, Computing and Mathematics Research Papers

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