Analysis of stability and critical flow velocity of 3D functionally gradient fluid-conveying pipeline with complex constraints

Here, aiming at problems of pipeline structure failure or damage caused by multi -directional load on pipe conveying fluid in harsh dynamic environment，a new 3 D functional gradient material was proposed to construct pipe conveying fluid to improve its load tolerance. Based on Euler-Bernoulli beam theory, considering interaction relation between fluid and pipe，dynamic differential equations of 3 D functionally gradient pipeline under complex constraints were established by using Hamilton variational principle. The differential quadrature method was used to solve the dynamic equations，and analyze natural frequency changes of 3 D functionally gradient pipeline vibration caused by increase in fluid flow velocity. It was known that when a pipe conveying fluid system' s first order natural frequency is reduced to 0，the corresponding fluid flow velocity is defined as the system ' s critical flow velocity. Effects of linear complex constraints and physical parameters of torsional spring stiffness as well as axial，radial and circumferential functional gradient indexes on natural frequencies and critical flow velocity of a flow-conveying pipeline system were studied. The study results showed that when flow velocity is smaller, increase in axial functional gradient index and decrease in radial and circumferential functional gradient indexes can reduce the system ' s fundamental frequency and increase its critical flow velocity ; when flow velocity is larger，the system ' s fundamental frequency has a reverse trend with changes of 3 D functional gradient indexes; increase in 3D functional gradient indexes can reduce the system' s second order natural frequency ; so，the stability of a fluid-conveying pipeline system can be controlled by adjusting its complex constraints and 3D functional gradient parameters. © 2023 Chinese Vibration Engineering Society. All rights reserved.