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| Analysis of stability and critical flow velocity of 3D functionally gradient fluid-conveying pipeline with complex constraints |
| TANG Ye1,2, WANG Guo1, LI Ying3 |
| 1.School of Mechanical Engineering, Anhui Polytechnic University, Wuhu 241000, China;
2.Department of Mechanics, Tianjin University, Tianjin 300350, China;
3.School of Design, Anhui Polytechnic University, Wuhu 241000, China |
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Abstract Aiming at the failure or damage of the pipeline structure caused by multi-directional loads on the pipe conveying fluid in the harsh dynamic environment, a new type of fluid-conveying pipe composed by three directional functionally graded materials is proposed to improve the load endurance of the pipeline. Based on the Euler-Bernoulli beam theory, considering the coupling relationship between the fluid and the pipeline, Hamilton’s principle is used to establish the differential equation of motion of fluid-conveying pipes composed by three directional functionally graded materials under complex constraints. The differential quadrature method is employed to analyze variations of natural frequency of the fluid-conveying pipes composed by three directional functionally graded materials with the increase of fluid velocity. When the first-order natural frequency decreases to zero for the first time, the system is unstable, and the corresponding fluid velocity is determined to be the critical flow velocity. The effects of physical parameters such as complex constrained linear and torsional spring stiffness, axial, radial and circumferential functional gradient indexes on the vibration frequency and critical velocity of pipe conveying fluid are studied. The research results show that when the flow velocity is small, increasing the axial functional graded index and decreasing the radial and circumferential functional graded indexes will reduce the fundamental frequency of the system and increase the critical flow velocity, when the flow velocity is very large, the fundamental frequency will show the opposite trend with the change of the three-dimensional functional graded indexes. Increasing the three-dimensional functional graded indexes can reduce the second-order natural frequency. This shows that the stability of the pipe conveying fluid can be regulated by tuning the complex constraints and three-dimensional functional graded parameters.
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Received: 22 November 2021
Published: 15 May 2023
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