基于同伦分析法的FGM输流管非线性频率分析

周杰; 常学平; 李映辉; 邵永波

doi:10.21656/1000-0887.430296

基于同伦分析法的FGM输流管非线性频率分析

doi: 10.21656/1000-0887.430296

1.
西南石油大学机电工程学院，成都 610500
2.
西南交通大学力学与航空航天学院，成都 610031
3.
西南石油大学土木工程与测绘学院，成都 610500

基金项目: 国家自然科学基金（51674216）

详细信息

作者简介:
周杰（1997—），男，硕士生（E-mail：17713653269@163.com）

常学平（1977—），男，副教授，博士（通讯作者. E-mail：xuepingch0952@sina.com）

中图分类号: O322
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- 被引次数: 0
出版历程
- 收稿日期: 2022-09-27
- 修回日期: 2023-01-05
- 网络出版日期: 2023-02-02
- 刊出日期: 2023-02-15

Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method

1.
School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, P.R.China
2.
School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China
3.
School of Civil Engineering and Geomatics, Southwest Petroleum University, Chengdu 610500, P.R.China

摘要

摘要:
该文基于同伦分析法研究了广义边界条件下含孔隙功能梯度材料(FGM)输流管道的非线性振动。基于FGM的幂律分布规律和Voigt模型来描述具有孔隙的FGM管道的材料特性。基于Euler-Bernoulli梁理论和von Kármán非线性理论，利用Hamilton变分原理，建立了含孔隙功能梯度流体输送管道的动力学控制方程和广义边界条件。采用同伦分析法求解了广义边界条件下的功能梯度流管道的非线性振动特性。数值结果表明：平移弹簧对失稳的临界流速影响不明显，而扭转弹簧则提高了失稳的临界流速，使系统更加稳定；在非线性系统中，黏弹性系数不会改变失稳临界流速；管道长度、幂律指数和孔隙率都会对FGM多孔输流管道的非线性自由振动有明显的影响。
- 同伦分析法 /
- 广义边界条件 /
- 非线性振动 /
- 孔隙率 /
- 输流管道
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.
- homotopy analysis /
- generalized boundary condition /
- nonlinear vibration /
- porosity /
- conveying pipe

HTML全文

图 1 广义边界条件下输送流体的管道示意图

Figure 1. Schematic diagram of a pipeline conveying fluid under generalized boundary conditions

下载: 全尺寸图片幻灯片

图 2 不同幂律指数下非线性频率随流速的变化

Figure 2. Variations of nonlinear natural frequencies with the fluid velocity under different power law indices

下载: 全尺寸图片幻灯片

图 3 不同孔隙率下非线性频率随流速的变化

Figure 3. Variations of nonlinear natural frequencies with the fluid velocity under different porosities

下载: 全尺寸图片幻灯片

图 4 不同黏弹性系数下非线性频率随流速的变化

Figure 4. Variations of nonlinear natural frequencies with the fluid velocity under different viscoelastic coefficients

下载: 全尺寸图片幻灯片

图 5 不同支撑平移弹簧刚度下非线性频率随流速的变化

Figure 5. Variations of nonlinear natural frequencies with the fluid velocity under different support spring stiffnesses

下载: 全尺寸图片幻灯片

图 6 不同扭转弹簧刚度下非线性频率随流速的变化

Figure 6. Variations of nonlinear natural frequencies with the fluid velocity under different rotating spring stiffnesses

下载: 全尺寸图片幻灯片

图 7 不同初始振幅下非线性频率随流速的变化

Figure 7. Variations of nonlinear natural frequencies with the fluid velocity under different initial amplitudes

下载: 全尺寸图片幻灯片

图 8 不同幂律指数下非线性频率随流体密度的变化

Figure 8. Variations of nonlinear natural frequencies with the fluid density under different power law indices

下载: 全尺寸图片幻灯片

图 9 不同孔隙率下非线性频率随流体密度的变化

Figure 9. Variations of nonlinear natural frequencies with the fluid density under different porosities

下载: 全尺寸图片幻灯片

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