Abstract
After considering the shearing motion of a continuous medium, the equations of evolution for the jumps in velocity, acceleration and the deformation gradient across a propagating vortex sheet in the shearing motion are derived. These equations are used to calculate the speed of propagation of a vortex sheet into a medium in motion ahead of the wave, and to determine the jumps in the velocity and the deformation gradient when the medium is at rest ahead of the wave. To determine the jump in acceleration across the moving vortex sheet, it is found necessary to consider a special class of instantaneously linearly elastic materials, of which the finitely linear viscoelastic fluid is a special case. It is then shown that the acceleration behaves like a delta function across the singular surface, calling for a re-examination of the theory of singular surfaces. Connections with solutions to the Rayleigh problem are also explored.
Original language | English |
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Pages (from-to) | 725-739 |
Number of pages | 15 |
Journal | Journal de mecanique theorique et appliquee |
Volume | 4 |
Issue number | 6 |
Publication status | Published - 1985 |