Effect of ideal fluid and viscous fluid on stability of elastic beam subjected to confined annular flow

Abstract

In this paper, dynamic stability analysis methods of a beam subjected to a confined annular axial flow are dealt with. Such structures are submarine resources production pipeline, reactor core structures of nuclear power plants, high-speed trains passing thorough a tunnel, a piping system in the field of ocean mining, and so on. The relation between the annular axial flow velocity and the unstable dynamics of structures are clarified. We have compared two analysis methods which can evaluate the dynamic instability of such structures. In first analysis method, the fluid is treated as viscous fluid, and is governed by the Navier-Stokes equation, and the beam structure is treated as the Euler-Bernoulli beam. This is called as the viscous fluid solution namely NS solution hereafter. In second analysis method reported by (Rinaldi and Paidoussis, 2012), the fluid is treated as ideal fluid. Then the viscosity effect is added to the equation of motion. This is called as the ideal fluid solution namely R&P solution hereafter. The complex eigenvalue analysis of the fluid structure coupled equation of motion is performed in order to clear up the dynamic instability. Performing the parametric studies, the comparison between both solutions is investigated. When the fluid viscosity becomes large, the difference in the critical velocity between the viscous fluid solution namely NS solution and the ideal fluid solution namely R&P solution is found to be generated. The destabilization effect appears due to the fluid viscosity force terms of the added stiffness of the fluid-structure coupled equation only in the viscous fluid solution.