Numerical Study of Static Instability of Pipe Conveying Incompressible Fluid under Different Boundary Conditions 

In this article, the influences of uniform velocity profile, mass ratio, length and Winkler elastic foundation on the static instability of pipe conveying incompressible fluid are investigated. The Euler-Bernoulli beam theory is employed to derive partial differential equation of pipes carrying fluid. The results were carried out using ANSYS Workbench program, where the analysis is based on the numerical solution; using Finite element method to formulate both the pipe structure and fluid flow equations. The numerical approach is based on some research and analytical models. The natural frequencies of the system are attained with respect to different boundary conditions, such as pinned-pinned ends, clamped-pinned ends and clamped-clamped ends. The numerical results show satisfactory agreement with the theory of many aspects of the pipe dynamical carrying incompressible fluid were observed numerically such as, the increase in flow velocity, mass ratio and length reduced from the rigidity of the system and consequently the proper modes. Winkler elastic foundation has a stabilizing effect on the system.