In practical operations of mechanical structures, it is not difficult to meet some large components such as helicopter rotors, gas turbine blades of marine engines, and rotating railway bridges, where these elements can be seen as beam models rotating around one fixed axis. Therefore, mechanical explorations of these structures with and without the effect of temperature will guide the design, manufacture, and use of them in practice. This is the first paper that uses the shear deformation theory-type hyperbolic sine functions and the finite element method to analyze the free vibration response of rotating FGM beams with initial geometrical imperfections resting on elastic foundations considering the effect of temperature. The material properties are assumed to be varied in the thickness direction of the beam based on the power law function and temperature changes The proposed theory and mathematical model are verified by comparing the results with other exact solutions. The numerical investigations have taken into account some geometrical and material parameters to evaluate the effects on the vibration behavior of the structure such as the rotational speed, temperature, as well as initial geometrical imperfections. The drawn comments have numerous scientific and practical implications for rotating beam structures.

中文翻译：

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在热环境中具有初始几何缺陷的弹性基础上旋转FG梁的自由振动研究

在机械结构的实际操作中，不难满足一些大型组件，例如直升机旋翼，船用发动机的燃气轮机叶片和旋转的铁路桥梁，其中这些元素可以看作是围绕一个固定轴旋转的梁模型。因此，在有或没有温度影响的情况下对这些结构进行机械探索将指导它们在实践中的设计，制造和使用。这是第一篇使用剪切变形理论类型的双曲正弦函数和有限元方法来分析旋转的FGM梁的自由振动响应的方法，考虑了温度的影响，这些FGM梁的初始几何缺陷位于弹性地基上。根据幂律函数和温度变化，假定材料特性在梁的厚度方向上发生变化。通过将结果与其他精确解进行比较，验证了所提出的理论和数学模型。数值研究已经考虑了一些几何和材料参数，以评估对结构振动行为的影响，例如转速，温度以及初始几何缺陷。所提意见对旋转梁结构具有许多科学和实践意义。数值研究考虑了一些几何和材料参数，以评估对结构振动行为的影响，例如转速，温度以及初始几何缺陷。所提意见对旋转梁结构具有许多科学和实践意义。数值研究考虑了一些几何和材料参数，以评估对结构振动行为的影响，例如转速，温度以及初始几何缺陷。所提意见对旋转梁结构具有许多科学和实践意义。