The Kinematics of Fibre-Reinforced Fluids. An Integrable Reduction

Authors: Schief W.K.; Rogers C.

Source: Quarterly Journal of Mechanics and Applied Mathematics, Volume 56, Number 4, November 2003 , pp. 493-512(20)

Publisher: Oxford University Press

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content

Abstract:

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.

Document Type: Research article

The full text electronic article is available for purchase. You will be able to download the full text electronic article after payment.

$40.22 plus tax

 

OR

Back to top

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content
Page Help Click here for Page Help
Shopping cart
Tools
Sign in






Need to register?
Sign up here
Text size: A | A | A | A