Study on Natural Vibration Characteristics of Bidirectional Functionally Graded Material Beams With Cracks and Geometric Imperfections

SHI Yinghui; TANG Huaiping; ZHAO Yingzhi

doi:10.21656/1000-0887.450213

Volume 46 Issue 9

Sep. 2025

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SHI Yinghui, TANG Huaiping, ZHAO Yingzhi. Study on Natural Vibration Characteristics of Bidirectional Functionally Graded Material Beams With Cracks and Geometric Imperfections[J]. Applied Mathematics and Mechanics, 2025, 46(9): 1147-1157. doi: 10.21656/1000-0887.450213

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Study on Natural Vibration Characteristics of Bidirectional Functionally Graded Material Beams With Cracks and Geometric Imperfections

doi: 10.21656/1000-0887.450213

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

Funds:

The National Science Foundation of China(51778548)

Received Date: 2024-07-15
Rev Recd Date: 2025-06-07

Available Online: 2025-10-17

Abstract

Abstract

Based on the Timoshenko beam theory, in view of geometric imperfections and cracks, the governing equations for bidirectional functionally graded beams were derived under the Hamiltonian principle. The cracked section was modeled with a massless elastic rotational spring, and the governing equations were solved with the differential quadrature method. The effects of geometric imperfection types, geometric imperfection dimensionless vibration amplitudes, crack depths, and other factors on the dimensionless frequencies were explored. The results show that, for a certain axial functional gradient index value, the dimensionless fundamental frequency increases with the dimensionless amplitude of the geometric imperfection, and decreases with the of crack depth. Moreover, the influence of the global imperfection on the dimensionless fundamental frequency is greater than the sine imperfection.
- bi-directional functionally graded beam,
- geometric imperfection,
- crack,
- massless elastic rotational spring,
- differential quadrature method

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References(26)

References

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