LJKDeterministic Models and Algorithms: EDPMOISEMGMI Seminar

On Friday November 28 2014 at 10h00 in Salle 1  Tour IRMA

Seminary of Mr William KO (Simon Fraser University, Canada)

Parametric resonance in spherical immersed elastic shells

Summary

We perform a stability analysis for a fluidstructure interaction problem in which a spherical elastic shell or membrane is immersed in a 3D viscous, incompressible fluid. The shell is an idealized structure having zero thickness, and has the same fluid lying both inside and outside. The problem is formulated mathematically using the immersed boundary framework in which Dirac delta functions are employed to capture the twoway interaction between fluid and immersed structure. The elastic structure is driven parametrically via a timeperiodic modulation of the elastic membrane stiffness. We perform a Floquet stability analysis, considering the case of both a viscous and inviscid fluid, and demonstrate that the forced fluidmembrane system gives rise to parametric resonances in which the solution becomes unbounded even in the presence of viscosity. The analytical results are validated using numerical simulations with a 3D immersed boundary code for a range of wavenumbers and physical parameter values. Finally, potential applications to biological systems are discussed.
