热环境中超临界黏弹性输流管道自由振动分析

Based on the Euler-Bernoulli beam theory, the current work investigates the free vibration of a supercritical pipe conveying fluid in the thermal environment. Considering the temperature increment and the initial axial force, the partial-differential-integral governing equation for the transverse vibration of the simply supported pipe is established by the generalized Hamilton's principle. The non-trivial equilibrium configurations and corresponding critical flow velocities are obtained analytically, and verified by the differential quadrature element method (DQEM). Based on the complex mode method and the Galer-kin method, the natural frequencies of the supercritical pipe conveying fluid in the thermal environment are obtained. The results show that the larger the temperature increment is, the smaller the critical flow velocity will be, which also makes the pipe buckled more easily. But the supercritical natural frequencies become bigger at the same fluid velocity. The discussion also finds that the larger the initial tension is, the larger the critical flow velocity will be. Under this condition, the natural frequencies in the super critical region become smaller at the same flow velocity. This study provides guidance for the vibration design of pipes conveying fluid in the supercritical region under the thermal environment.