LJK-Deterministic Models and Algorithms: EDP-MOISE-MGMI 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 fluid-structure 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 two-way interaction between fluid and immersed structure. The elastic structure is driven parametrically via a time-periodic 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 fluid-membrane 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.