Determination of Natural Frequency and Critical Velocity of Inclined Pipe Conveying Fluid under Thermal Effect by Using Integral Transform Technique

This study proposes an analytical solution of natural frequencies for an inclined fixed supported Euler-Bernoulli pipe containing the flowing fluid subjected to thermal loads. The integral transform technique is employed to obtain the spatial displacement-time domain response of the pipe-fluid system. Then, a closed-form analytical expression is presented. The effects of various geometric and system parameters on the vibration characteristics of pipe-fluid system with different flow velocities are discussed. The results illustrate that the proposed analytical solution agrees with the solutions achieved in previous works. The proposed model predicts that the pipe loses the stability by divergence with the increasing flow velocity. It is evident that the influences of inclination angle and temperature variation are dramatically increased at a higher aspect ratio. Additionally, it is demonstrated that the temperature variation becomes a more harmful effect than the internal fluid velocity on the stability of the pipe at elevated temperature.