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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 |
Issue 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: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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2001imajam.pdf | 334.24 kB | Adobe PDF | View/Open |
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