2 p.m. - 3 p.m. Location: JO 4.614
Department of Mathematics/Chemical Engineering
University of Alberta
Exact geometric approach to the dynamics of tubes conveying fluid
We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. Using these methods, we obtain the fully three dimensional equations of motion. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross-section. We show some fully nonlinear solutions of the traveling wave types and discuss the results of experiments. Time permitting, we will also show how to derive a variational discretization of the dynamics based on the appropriate discretization of the fluid’s back-to-labels map, coupled with a variational discretization of the elastic part of the Lagrangian.
Sponsored by the Department of Mathematical Sciences