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The Quarterly Journal of Mechanics and Applied Mathematics 2003 56(4):493-512; doi:10.1093/qjmam/56.4.493
© 2003 by Oxford University Press
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The Kinematics of Fibre-Reinforced Fluids. An Integrable Reduction

W. K. Schief1 and C. Rogers1

( 1 School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia )

A geometric formulation previously adopted in hydrodynamics and soliton theory is used here to investigate the kinematic conditions attendant upon the motion of an ideal fibre-reinforced fluid. Conditions are established for the existence of multiple-fibre configurations. Kinematically admissible spatial motions are obtained in which the fibres are geodesic windings on nested toroidal surfaces. In the case of purely planar motion, it is shown that the kinematic relations reduce to a third-order nonlinear equation. Remarkably, this admits a reduction to a solitonic system which is related to the classical sine-Gordon equation. The kinematic conditions in this case possess a duality property.

Received 10 October 2002. Revised 7 February 2003.


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Home page
 Q J Mechanics Appl MathHome page
W. Schief, C Rogers, and S Murugesh
On the kinematics of 2+1-dimensional motions of a fibre-reinforced fluid. Integrable connections
Q J Mechanics Appl Math, February 1, 2007; 60(1): 49 - 64.
[Abstract] [Full Text] [PDF]


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