Free Vibration of Modified Axially Moving Timoshenko Beams
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摘要: 考虑了剪切效应引起的转动惯量，应用物质坐标系下的Newton第二定理建立了修正的轴向移动Timoshenko梁模型. 求解了系统的固有频率，并分析了固有频率随梁长、梁高、轴向速度等参数变化的规律. 并将该文模型得到的结果与传统的轴向移动Euler-Bernoulli梁理论模型、轴向移动Rayleigh梁理论模型和轴向移动Timoshenko梁理论模型的结果进行对比. 结果表明：当轴向移动梁的长高比大于10时，四种模型得到的结果一致. 当长高比较小时，该文的结果与经典的轴向移动Timoshenko梁模型基本一致. 此外，剪切效应引起的转动惯量对高阶频率的影响更大. 因此，在轴向移动梁的动力学分析中应加以考虑剪切效应引起的转动惯量的影响.
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关键词:
- 修正Timoshenko梁 /
- 剪切效应 /
- 转动惯量 /
- 自由振动 /
- 固有频率
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.-
Key words:
- modified Timoshenko beam /
- shear effect /
- moment of inertia /
- free vibration /
- natural frequency
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图 2 不同梁长高比条件下四种轴向移动模型的一阶固有频率
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 2. The 1st-order natural frequencies of 4 models with different beam length-height ratios
图 3 不同梁高度条件下四种轴向移动模型的一阶固有频率
Figure 3. The 1st-order natural frequencies of 4 models with different beam heights
图 4 不同轴向速度条件下四种轴向移动模型的一阶固有频率
Figure 4. The 1st-order natural frequencies of 4 models with different axial velocities
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