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A refined beam theory for bending and vibration of functionally graded tube-beams

机译：用于弯曲和振动功能梯度管梁的精细光束理论

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摘要

This paper presents a novel approach for analyzing transverse bending and vibration of functionally graded circular cylindrical tubes with radial nonhomogeneity. Different from the Euler-Bernoulli and Timoshenko theories of beams, a refined beam theory or third-order shear deformation beam theory for radially graded tubes is proposed, where warping, shear deformation and rotational moment of inertia of cross-section are all considered. The shear correction coefficient is not needed. Coupled governing equations for the deflection and rotation about the neutral axis of cross-section are derived from equilibrium equations, and then converted to a single fourth-order partial differential governing equation. The deflection and stress distribution for cantilever and simply-supported tubes are derived explicitly. The frequency equations for free flexural vibration of radially graded hollow cylinders with clamped-clamped, pinned-pinned, and clamped-free ends are obtained and the natural frequencies are calculated for different power-law gradients and various length/thicknesses ratios. The effects of radial gradient on the stress distribution and the natural frequencies are analyzed in detail.
机译：本文介绍了一种新的方法，用于分析具有径向非均匀性的功能渐进圆柱管的横向弯曲和振动。不同于梁的euler-bernoulli和梁的Timoshenko理论，提出了一种精炼光束理论或三阶剪切变形光束理论，用于径向分级管，其中横截面的翘曲，剪切变​​形和旋转力矩均考虑。不需要剪切校正系数。关于偏转和旋转的耦合控制方程围绕中性轴的横截面源自平衡方程，然后转换为单个四阶部分差分控制方程。明确地推导出悬臂和简单地支撑管的偏转和应力分布。获得具有夹紧夹紧，钉扎的空心圆柱体的自由弯曲振动的频率方程，并且针对不同的动力法梯度和各种长度/厚度比计算自然频率。详细分析了径向梯度对应力分布和自然频率的影响。

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