Free Vibration of Modified Axially Moving Timoshenko Beams

Liang Jintao; Wang Ze; Guo Jiangyuan; Zhang Yanchao

doi:10.21656/1000-0887.460039

Volume 47 Issue 8

Aug. 2026

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Liang Jintao, Wang Ze, Guo Jiangyuan, Zhang Yanchao. Free Vibration of Modified Axially Moving Timoshenko Beams[J]. Applied Mathematics and Mechanics, 2026, 47(8): 1086-1092. doi: 10.21656/1000-0887.460039

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Free Vibration of Modified Axially Moving Timoshenko Beams

doi: 10.21656/1000-0887.460039

School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, P.R. China

Received Date: 2025-03-03
Rev Recd Date: 2025-10-20
Publish Date: 2026-08-01

Abstract

Abstract

The rotational inertia caused by the shear effect was considered, and a modified axial motion Timoshenko beam model was established under Newton's 2nd law in the material coordinate system. The natural frequencies of the system were solved, and the laws of the natural frequencies changing with parameters such as the beam length, the beam height and the axial velocity, were analyzed. The results obtained by this model were compared with those by the traditional axially moving Euler-Bernoulli beam theoretical model, the axially moving Rayleigh beam theoretical model and the axially moving Timoshenko beam theoretical model. The results show that, when the length-to-height ratio of the axially moving beam is greater than 10, the results obtained by the 4 models are consistent. When the length-to-height ratio is relatively small, the present results are basically consistent with those by the classical axially moving Timoshenko beam model. In addition, the rotational inertia caused by the shear effect has a greater impact on higher-order frequencies. Therefore, the influence of the moment of inertia due to the shear effect shall be considered in the dynamic analysis of axially moving beams.
- modified Timoshenko beam,
- shear effect,
- moment of inertia,
- free vibration,
- natural frequency

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References(16)

References

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