A second order no-linear partial differential equation is worked out to describe the interaction of the flow with an elastic shell in large deformation domain. The model intends to describe the vibration of an aneurysm in arteries and veins. Two models are presented in this work. In the first one, the shell is inserted in otherwise rigid plane channel and in the second model the shell is inserted in otherwise rigid tube. In order to allow large displacement, the shell motion is described by Lagrangian variables. The steady version of the governing equation is a second order no-linear differential equation. A formal solution of the steady no-linear equation is obtained for plane channel model. It is shown that a steady solution exists only for some values of the dimensionless parameters ϕ and λ where ϕ is the ratio of transmural pressure to the elasticity coefficient and λ is the ratio of volume flux to the elasticity coefficient. The critical curve in the plan (ϕ,λ) for some control parameters are computed. Then, an unsteady solution of the no-linear unsteady equation is obtained numerically. It is found that the time signal prescribed by the unsteady no-linear solution depends strongly on the numerical values of the rheological parameters of the system. It is suggested that these signals could be used as a non invasive method in the diagnostic of the aneurysm when its vibration could be detected by a non invasive method. The linear analysis of the cylindrical geometry model shows that the aneurysm structure can be locked with heart pulse in a resonance frequency when the wall of the aneurysm becomes soft leading eventually to its rupture.

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