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首页> 外文期刊>Applied Mathematical Modelling >Free vibration, buckling and dynamic stability of bi-directional FG microbeam with a variable length scale parameter embedded in elastic medium
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Free vibration, buckling and dynamic stability of bi-directional FG microbeam with a variable length scale parameter embedded in elastic medium

机译：可变长度比例参数嵌入弹性介质中的双向FG微梁的自由振动，屈曲和动态稳定性

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In this paper, size dependent free vibration, buckling and dynamic stability of bi-directional functionally graded (BDFG) microbeam embedded in elastic medium are investigated. The material properties vary along both thickness and axial directions. In particular, the material length scale parameter of microbeam is considered as a function of spatial coordinates and varies with the material gradient parameters. The system of differential equations with variable coefficients governing the motion of BDFG microbeam is derived employing Hamilton's principle, the modified couple stress theory and third-order shear deformation beam theory. The differential quadrature method (DQM) is utilized to solve the static and dynamic problem. Three different models evaluating the material length scale parameter of BDFG microbeam are presented for comparison. Parametric studies are carried out to show the influence of gradient parameters, size effect, stiffness of elastic medium on the free vibration, buckling and dynamic stability characteristic of BDFG microbeam. Results show that the variation of material length scale parameter should be considered in the analysis of BDFG microbeam. (C) 2018 Elsevier Inc. All rights reserved.
机译：本文研究了嵌入弹性介质中的双向功能梯度（BDFG）微束的尺寸依赖性自由振动，屈曲和动态稳定性。材料特性沿厚度和轴向均变化。特别地，微束的材料长度尺度参数被认为是空间坐标的函数，并且随材料梯度参数而变化。利用汉密尔顿原理，修正耦合应力理论和三阶剪切变形梁理论，推导了变系数微分方程组控制BDFG微梁的运动。微分求积法（DQM）用于解决静态和动态问题。提出了三种不同的评估BDFG微束材料长度尺度参数的模型进行比较。进行了参数研究，以显示梯度参数，尺寸效应，弹性介质的刚度对BDFG微梁的自由振动，屈曲和动态稳定性特征的影响。结果表明，在BDFG微束分析中应考虑材料长度尺度参数的变化。 （C）2018 Elsevier Inc.保留所有权利。

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