Free Vibration Analysis of Porous 2D Functionally Graded Material Microbeams on Winkler's Foundation

ZHAO Yingzhi; TANG Huaiping; LAI Zedong; ZHANG Jiajie

doi:10.21656/1000-0887.440050

Volume 44 Issue 11

Nov. 2023

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ZHAO Yingzhi, TANG Huaiping, LAI Zedong, ZHANG Jiajie. Free Vibration Analysis of Porous 2D Functionally Graded Material Microbeams on Winkler's Foundation[J]. Applied Mathematics and Mechanics, 2023, 44(11): 1354-1365. doi: 10.21656/1000-0887.440050

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Free Vibration Analysis of Porous 2D Functionally Graded Material Microbeams on Winkler's Foundation

doi: 10.21656/1000-0887.440050

School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China

Received Date: 2023-02-27
Rev Recd Date: 2023-04-03
Publish Date: 2023-11-01

Abstract

Abstract

Based on the modified couple stress theory and the Timoshenko beam theory, the governing equations for free vibration of porous 2D functional graded material (FGM) on Winkler's foundation were derived under Hamilton's principle. The differential quadrature method was used to obtain the numerical solutions of the vibration frequencies and fundamental mode shapes of microbeams with both ends clamped (C-C) and simply supported (S-S). The improved stiffness matrix was used to greatly improve the calculation efficiency. The proposed model was degenerated to the macro and micro 2D-FGM models, which were compared with those in previous literatures for validation. The results show that, the present mathematical model is suitable for different types of 2D material distributions. The dimensionless frequencies increase with the dimensionless elastic modulus of Winkler's foundation. Under a certain dimensionless elastic foundation modulus, the dimensionless frequencies decrease with the functionally graded index, the axial functionally graded index and the porosity. The effect of the material variation on the mode shape increases with the mode number. For the same parameter, the dimensionless frequencies of the beam with uniform porosity distribution are slightly lower than those with linear porosity distribution.
- modified couple stress theory,
- porosity,
- Winkler's foundation,
- 2D functionally graded material,
- differential quadrature method

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References(31)

References

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