Free vibration analysis of Timoshenko pipes with fixed boundary conditions conveying high velocity fluid

Sever vibration will be induced due to the high flow velocity in the pipe. When the flow velocity exceeds the critical value, the static equilibrium configuration of the pipe loses its stability, and the vibration properties change accordingly. In this paper, the free vibration characteristics of the pipe with fixed-fixed ends are revealed in the supercritical regime. Based on the Timoshenko beam theory, the governing equations of the nonlinear vibration near the non-trivial static equilibrium configuration are established. The influences of system parameters on equilibrium configuration, critical velocity, and free vibration frequency is analyzed. The effects of supercritical velocity in different ranges on the natural frequencies are revealed. In addition, the comparison with the Euler-Bernoulli pipe model shows that the differences in critical velocity, equilibrium configuration, and frequency are still significant even the length-diameter ratio is large. The increase of the flow velocity reduces the difference of non-trivial static equilibrium configurations, but eventually aggravates the difference of natural frequencies. Within a certain supercritical velocity range, the vibration difference between the two pipe models is small, beyond this range, the vibration difference increases significantly.