Viscous fluid-thin cylindrical elastic layer interaction: asymptotic analysis
Grigory P. Panasenko, Ruxandra Stavre · Applicable Analysis · 2014
This article represents a generalization of our previous work. We consider a periodic, non-steady, axially symmetric, creeping flow of a viscous incompressible fluid that fills a cylindrical elastic hollow tube. We study the interaction problem “viscous fluid-thin cylindrical elastic layer” when the thickness of the tube wall, , tends to zero, while the density and the Young’s modulus of the elastic material are of order and , respectively. We construct a complete asymptotic expansion when tends to zero. The error between the exact solution and the asymptotic one is evaluated in order to justify the asymptotic construction.