| Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method北大核心CSCD |
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| 引用本文： | 周杰,常学平,李映辉,邵永波.Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method北大核心CSCD[J].应用数学和力学,2023,44(2):191-200. |
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| 作者姓名： | 周杰 常学平 李映辉 邵永波 |
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| 作者单位： | 1.西南石油大学 机电工程学院，成都 610500 |
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| 基金项目： | 国家自然科学基金（51674216） |
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| 摘 要： | Based on the homotopy analysis method, the nonlinear vibration of porous functionally graded material (FGM) conveying pipes under generalized boundary conditions was studied. Based on the power-law distribution of the FGM and the Voigt model, the physical properties of the porous pipe material were described. Under the Euler-Bernoulli beam theory and the von Kármán nonlinear theory, and by means of Hamilton’s variational principle, the dynamic control equations and generalized boundary conditions for porous FGM conveying pipes were established. The homotopy analysis method was used to solve the nonlinear vibration characteristics of the porous FGM conveying pipe under generalized boundary conditions. The numerical results show that, the translation spring has little effect on the critical velocity of instability, while the rotation spring increases the critical velocity of instability, making the system more stable; in the nonlinear system, the viscoelastic coefficient does not change the critical velocity; the pipe length, the power-law exponent and the porosity all influence the nonlinear free vibration of the porous FGM conveying pipe. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.
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| 关 键 词： | 同伦分析法 广义边界条件 非线性振动 孔隙率 输流管道 |
| 收稿时间： | 2022-09-27 |
Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method |
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| Zhou J.,Chang X.,Li Y.,Shao Y..Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method[J].Applied Mathematics and Mechanics,2023,44(2):191-200. |
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| Authors: | Zhou J Chang X Li Y Shao Y |
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| Institution: | 1.School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, P.R.China2.School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China3.School of Civil Engineering and Geomatics, Southwest Petroleum University, Chengdu 610500, P.R.China |
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| Abstract: | Based on the homotopy analysis method, the nonlinear vibration of porous functionally graded material (FGM) conveying pipes under generalized boundary conditions was studied. Based on the power-law distribution of the FGM and the Voigt model, the physical properties of the porous pipe material were described. Under the Euler-Bernoulli beam theory and the von Kármán nonlinear theory, and by means of Hamilton’s variational principle, the dynamic control equations and generalized boundary conditions for porous FGM conveying pipes were established. The homotopy analysis method was used to solve the nonlinear vibration characteristics of the porous FGM conveying pipe under generalized boundary conditions. The numerical results show that, the translation spring has little effect on the critical velocity of instability, while the rotation spring increases the critical velocity of instability, making the system more stable; in the nonlinear system, the viscoelastic coefficient does not change the critical velocity; the pipe length, the power-law exponent and the porosity all influence the nonlinear free vibration of the porous FGM conveying pipe. |
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| Keywords: | conveying pipe generalized boundary condition homotopy analysis nonlinear vibration porosity |
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