Natural frequency and stability analysis of a pipe conveying fluid with axially moving supports immersed in fluid

Structural model for a slender and uniform pipe conveying fluid, with axially moving supports on both ends, immersed in an incompressible fluid, is formulated. Free vibration and stability of the system are studied through numerical calculation. First, the equations of motion of the system are derived in an absolute coordinate system. An "axial added mass coefficient" is adopted to amend the forces caused by the external fluid. Boundary conditions are fixed by using coordinated conversion. Then, numerical results of the natural frequency are obtained via the Galerkin method, both for pinned-pinned and clamped-clamped supports. The critical speeds of supports and several instability types are discussed. Last, the effects of the system parameters on the dynamics and instability of the system are investigated.