Natural Frequencies, Critical Velocity and Equilibriums of Fixed-Fixed Timoshenko Pipes Conveying Fluid

In this paper, the free vibration characteristics of fixed-fixed Timoshenko pipe conveying fluid, including natural frequency, mode, critical velocity, bifurcation of static equilibrium configuration, are studied analytically and numerically. Based on the Timoshenko beam theory and generalized Hamilton principle, a vibration model of pipes conveying fluid with fixed-fixed boundary conditions is established. The analytical expressions of critical flow velocity and supercritical nontrivial static equilibrium configuration are derived. The natural frequencies are studied by the complex modal method (CMM) and the Galerkin truncation method (GTM). Moreover, the finite element method (FEM) is developed to deal with the influence of fluid velocity on the vibration characteristics of the pipe. The gyroscopic force caused by the fluid flow is equivalent to the damping matrix. It shows that the natural frequencies of the FEM agree well with the theoretical results of CMM and GTM in general. However, the developed FEM cannot reflect the influence of the fluid flow on the vibration mode of pipes. Furthermore, the free vibration characteristics of the pipe are significantly affected by the internal pressure of the pipe. [GRAPHICS] .