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Dynamic modeling and analysis of rotating FG beams for capturing steady bending deformation

机译：旋转FG梁捕获稳定弯曲变形的动态建模与分析

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摘要

A dynamic analysis of rotating functionally gradient (FG) beams is presented for capturing the steady bending deformation by using a novel floating frame reference (FFR) formulation. Usually, the cross section of bending beams should rotate round the point at the neutral axis while centrifugal inertial forces are supposed to act on centroid axis. Due to material inhomogeneity of FG beams, centroid and neutral axes may be in different positions, which leads to the eccentricity of centrifugal forces. Thus, centrifugal forces can be divided into three componets: transverse component, axial component and force moment acting on the points of the neutral axis, in which transverse component and force moment can make the beam produce the steady bending deformation. However, this speculation has not been presented and discussed in existing literatures. To this end, a novel FFR formulation of rotating FG beams is especially developed considering centroid and neutral axes. The FFR and its nodal coordinates are used to determine the displacement field, in which kinetic and elastic energies can be accurately formulated according to centroid and neutral axes, respectively. By using the Lagrange's equations of the second kind, the nonlinear dynamic equations are derived for transient dynamics problems of rotating FG beams. Simplifying the nonlinear dynamic equations obtains the equilibrium equations about inertial and elastic forces. The equilibrium equations can be solved to capture the steady bending deformation. Based on the steady bending state, the nonlinear dynamic equations are linearized to obtain eigen-frequency equations. Transient responses obtained from the nonlinear dynamic equations and frequencies obtained from the eigen-frequency equations are compared with available results in existing literatures. Finally, effects of material gradient index and angular speed on the steady bending deformation and vibration characteristics are investigated in detail.
机译：通过使用新颖的浮动帧参考（FFR）制剂，提出了一种旋转功能梯度（FG）光束的动态分析。通常，弯曲梁的横截面应在中性轴处的点旋转，而离心惯性力应该在质心轴上作用。由于FG梁的材料不均匀性，质心和中性轴可能处于不同的位置，这导致离心力的偏心率。因此，离心力可以分成三个组件：横向部件，轴向部件和作用在中性轴的点上的力矩，其中横向部件和力矩可以使梁产生稳定的弯曲变形。但是，在现有的文献中尚未介绍和讨论这种猜测。为此，考虑到质心和中性轴，特别开发了旋转FG梁的新型FFR配方。 FFR及其节点坐标用于确定位移场，其中分别可以根据质心和中性轴精确配制动力学和弹性能量。通过使用第二种的拉格朗日的等式，导出非线性动态方程用于旋转FG梁的瞬态动力学问题。简化非线性动态方程获得关于惯性和弹性力的平衡方程。可以解决平衡方程以捕获稳定的弯曲变形。基于稳定的弯曲状态，非线性动态方程被线性化以获得特征频率方程。将从非线性动态方程获得的瞬态响应和从eIGEN频率方程获得的频率进行比较，其可用导致现有文献中的结果。最后，详细研究了材料梯度指数和角度速度对稳定弯曲变形和振动特性的影响。

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  • 来源
    《Applied Mathematical Modelling》 |2020年第12期|498-517|共20页
  • 作者

    Yuanzhao Chen; Xian Guo; Dingguo Zhang; Liang Li;

  • 作者单位

    School of Mechanical and Transportation Engineering Guangxi University of Science and Technology Liuzhou 545006 China School of Sciences Nanjing University of Science and Technology Nanjing 210094 China;

    School of Sciences Nanjing University of Science and Technology Nanjing 210094 China;

    School of Sciences Nanjing University of Science and Technology Nanjing 210094 China;

    School of Sciences Nanjing University of Science and Technology Nanjing 210094 China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Rotating FG beams; Centroid and neutral axes; Steady bending deformation; Vibration characteristics;

    机译：旋转FG梁;质心和中性轴;稳定弯曲变形;振动特性;

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