Fluid-structure interactions of internal pressure pipeline using the hierarchical finite element method

Abstract

We study the influence of the fluid with the structure in vibration between fluid and structure of a cylinder of circular section granted by the phenomenon of the interaction fluid structure of a conditioned flow of laminar nature and incompressible in the form of the macrostructure. These two phenomena by the mechanical relations of stresses according to displacements, modelled by a cylinder. The analysis of the vibrations of cylinders filled with fluid is studied with limiting conditions of fluid and the solid with the coupling conditioned by its limits of action-reaction in forces. The problem of the cylindrical pipe is formulated by deriving the deformation and the kinetic energies of the vibrating cylinder with and its fluid to have different natural frequencies, we use the principle of Hamilton change the problem in the expression of the equation cylindrical differential which gives three displacement functions in a system of partial differential equations of the cylindrical coordinate of circular section which meet the limiting conditions imposed at both ends. Let us apply the Navier-Stocks equation in cylindrical coordinates, with the fluid continuity equation, for the solid equation of mechanical behaviour of stresses in terms of displacement by strain. To obtain the results of natural frequencies we use the Galerkin method for solid and for Galerkin-time fluid. Where the liquid influences the inner surface of the circular cylinder, depending on the condition of the coupling that the stresses of the solid are equal to the stresses fluid. The modelling is done by a computer language (MATLAB), the hierarchical finite element method is presented by a Legendre polynomial with double integral of Rodrigues, to arrive at the final formula of the mass-rigidity matrix, which dissects on three parts (fluid, coupling and structure). Based on a comparison with experimental results. We continue to study some geometrical and physical parameters which influence the natural frequencies, in a proportional or inversely proportional way.