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Long wave motion in layered elastic media

Graham Rogerson (Keele University)

SES Medal Symposium in honor of D.J. Steigmann

Mon 2:40 - 4:00

MacMillan 115

The propagation of waves in a compressible pre-stressed elastic layered structure is considered, the structure being composed of 3 layers and symmetric about the mid-plane. The dispersion relation associated with traction free upper and lower boundaries is derived and long wave approximations, giving phase speed explicitly as a function of wavelength, are derived. A number of long wave regimes are analysed, forming analogues of classical being and extension, as well as shear and stretch resonance. By using the long wave dispersion approximations, the relative orders of displacement are established (relative to wave number) for each of these long wave regimes. In each case, appropriate scales for time and spatial variables are also introduced and a series of appropriate long wave models analogous the aforementioned classical theories, established.