Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method

ZHOU Jie; CHANG Xueping; LI Yinghui; SHAO Yongbo

doi:10.21656/1000-0887.430296

Volume 44 Issue 2

Feb. 2023

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Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(2): 191-200

ZHOU Jie, CHANG Xueping, LI Yinghui, SHAO Yongbo. Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method[J]. Applied Mathematics and Mechanics, 2023, 44(2): 191-200. doi: 10.21656/1000-0887.430296

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Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method

doi: 10.21656/1000-0887.430296

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

Received Date: 2022-09-27
Rev Recd Date: 2023-01-05

Available Online: 2023-02-02

Publish Date: 2023-02-15

Abstract

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

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References(33)

References

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