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Longitudinal and transverse instabilities of moving nanoscale beam-like structures made of functionally graded materials

机译：功能梯度材料制成的移动纳米级梁状结构的纵向和横向不稳定性

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摘要

A mathematical model is proposed to explore vibrations and instabilities of moving functionally graded (FG) nanobeams. It is assumed that the FG nanobeam moves with a constant velocity and its material properties vary continuously across the thickness according to a power-law relation. The longitudinal and lateral equations of motion of the moving nanostructure are extracted by employing the nonlocal Rayleigh beam model. Using Galerkin approach and admissible mode shapes, the longitudinal and transverse frequencies are calculated. The effects of the power-law index, small-scale parameter, length of the FG nanobeam, and its velocity on the frequencies and stability of the moving nanostructure are comprehensively addressed. Both divergence and flutter instabilities of moving FG nanobeams are discussed, and the roles of influential factors on such phenomena are explained.
机译：提出了一个数学模型来探索功能梯度（FG）移动的纳米束的振动和不稳定性。假设FG纳米束以恒定速度运动，并且其材料特性根据幂律关系在整个厚度上连续变化。通过使用非局部瑞利光束模型，提取了移动纳米结构的纵向和横向运动方程。使用Galerkin方法和允许的模态形状，可以计算纵向和横向频率。全面讨论了幂律指数，小尺度参数，FG纳米束的长度及其速度对移动纳米结构的频率和稳定性的影响。讨论了移动FG纳米束的发散和颤振不稳定性，并解释了影响因素对此类现象的作用。

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