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首页> 外文期刊>Proceedings of the institution of mechanical engineers >Modified couple stress-based free vibration behavior of pre-twisted tapered BFGM rotating micro beam considering spin-softening and Coriolis effects
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Modified couple stress-based free vibration behavior of pre-twisted tapered BFGM rotating micro beam considering spin-softening and Coriolis effects

机译：考虑自旋软化和科里奥利效应的预扭锥形BFGM旋转微梁基于耦合应力的修正自由振动特性

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摘要

An improved mathematical model of pre-twisted tapered rotating micro beams made of bidirectional functionally graded material (BFGM) is presented to study its free vibration behavior. The effects of spin-softening and Coriolis acceleration are incorporated, and modified couple stress theory is employed to address the size effect. The mathematical formulation is based on first-order shear deformation theory and is developed in a global non-inertial frame incorporating appropriate transformations between the global inertial frame and the local non-inertial frame. Two different but interrelated steps are employed, where the first step determines the centrifugally deformed configuration using minimum potential energy principle, and the second step determines the free vibration behavior through tangent stiffness of the deformed rotating beam using Hamilton's principle. The direct use of tangent stiffness considers the centrifugal stiffening effect through von Karman non-linearity and bypasses the need of strain energy functional for the vibrating beam. The governing equations are transformed to an eigenvalue problem through state-space approach and solved following Ritz method. The effects of spin-softening, Coriolis acceleration, and pre-twist angle are shown and discussed. The effects of different parameters such as size-dependent parameter, aspect ratio, material gradation indices, operating temperature, FGM constituent, taperness parameters, and slender parameter are discussed.
机译：提出了一种由双向功能梯度材料（BFGM）制成的改进的预扭锥形旋转微梁数学模型，以研究其自由振动行为。结合了自旋软化和科里奥利加速度的影响，并采用改进的耦合应力理论来解决尺寸影响。该数学公式基于一阶剪切变形理论，并且是在全局非惯性框架中开发的，该框架在全局惯性框架和局部非惯性框架之间进行了适当的转换。使用两个不同但相互关联的步骤，其中第一步使用最小势能原理确定离心变形的构型，第二步使用汉密尔顿原理通过变形的旋转梁的切线刚度确定自由振动行为。切线刚度的直接使用考虑了通过von Karman非线性产生的离心刚度效果，并且绕开了对振动梁起作用的应变能的需求。通过状态空间方法将控制方程转化为特征值问题，并按照Ritz方法求解。显示并讨论了自旋软化，科里奥利加速度和预扭转角的影响。讨论了不同参数的影响，例如尺寸相关参数，长宽比，材料渐变指数，工作温度，FGM成分，锥度参数和细长参数。

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