使用多重束理论与不确定性考虑的旋转双向功能分级束的自由振动分析的比较研究
Moustafa S Taima1, Mohamed B Shehab1, Tamer A El-Sayed2
1Department of Mechanical Design, Faculty of Engineering, Mataria, Helwan University, P.O. Box 11718, Helmeiat-Elzaton, Cairo, Egypt.
Scientific reports
|October 20, 2023
概括
这项研究分析了由功能分级材料 (FGM) 制成的旋转,形梁的振动. 第三阶段剪切变形理论 (TSDT) 准确地预测了自然频率,超过了经典和第一阶段理论,特别是对于更厚的梁.
科学领域:
- 机械工程 机械工程
- 材料科学 材料科学 材料科学
- 振动分析 振动分析
背景情况:
- 功能分级材料 (FGM) 为高级应用提供可调节的特性.
- 旋转结构,如梁,经历复杂的动态行为受离心力的影响.
- 圆形几何形状和材料梯度显著影响结构振动特性.
研究的目的:
- 为了研究由FGMs制成的圆几何形状的旋转梁的自由振动.
- 为了比较Bernoulli-Euler (古典光束理论),蒂莫申科 (一阶剪切变形理论) 和雷迪 (三阶剪切变形理论) 在这些光束的建模中的准确性.
- 用概率方法分析参数不确定性对自然频率的影响.
主要方法:
- 使用虚拟能量的原理推导刚度和质量矩阵.
- 三种光束理论的应用:古典光束理论 (CBT),一级剪切变形理论 (FSDT) 和三级剪切变形理论 (TSDT).
- 参数不确定性 (旋转速度,材料特性,分布) 的纳入,使用以平均为中心的二次扰动方法和蒙特卡洛模拟.
主要成果:
- 与CBT相比,TSDT和FSDT与厚梁的3D有限元 (3D-FE) 模拟显示出更好的一致性.
- 随机材料属性导致CBT结果的偏差大于FSDT和TSDT.
- 与FSDT不同的是,TSDT提供了准确的预测,而不需要剪切校正系数.
结论:
- 第三级剪切变形理论 (TSDT) 在准确预测旋转的自然频率方面是卓越的.
- 该研究验证了与蒙特卡洛模拟和3D-FE分析对概率框架的验证.
- 了解材料分布,缩和旋转速度的影响对于设计FGM结构至关重要.
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