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Mode localization phenomenon of functionally graded nanobeams due to surface integrity
International Journal of Mechanics and Materials in Design ( IF 3.7 ) Pub Date : 2018-10-28 , DOI: 10.1007/s10999-018-9421-x
Mohamed Shaat

This is the first study on the mode localization and surface stress-based deflection phenomena of functionally graded (FG) nanobeams due to surface integrity. A new model for FG nanobeams with engineering surfaces is developed. The engineering surface is considered a different material phase with a surface texture (i.e. waviness and roughness). The initial curvatures of cantilever, simple supported, and clamped–clamped FG nanobeams due to surface residual stresses are determined. It is revealed that the initial curvature increases with an increase in the slope of the surface texture and/or a decrease in the surface roughness. Moreover, the natural frequencies and mode shapes of FG nanobeams are derived depending on the surface’s texture and mechanical properties. It is observed that natural frequencies of FG beams may decrease or increase due surface roughness. Thus, as a first prospect, the surface roughness allows the vibration energy to propagate over the beam length and hence its natural frequency decreases resulting in a zero-frequency mode. As for the other prospect, surface roughness inhibits the propagation of the vibration energy through the beam length leading to a mode localization and an increase in the natural frequency.



中文翻译:

由于表面完整性而导致的功能梯度纳米束的模式定位现象

这是对功能梯度(FG)纳米光束由于表面完整性而产生的基于模式应力和基于表面应力的偏转现象的首次研究。开发了具有工程表面的FG纳米束的新模型。工程表面被认为是具有表面纹理(即波纹度和粗糙度)的不同材料相。确定了由于表面残余应力而导致的悬臂,简单支撑和夹固FG纳米束的初始曲率。揭示出初始曲率随着表面纹理的斜率的增加和/或表面粗糙度的减小而增加。此外,FG纳米束的固有频率和众数形状取决于表面的纹理和机械性能。可以观察到,由于表面粗糙度,FG光束的固有频率可能会降低或增加。因此,作为第一前景,表面粗糙度允许振动能量在光束长度上传播,因此其固有频率降低,从而导致零频率模式。至于另一个前景,表面粗糙度抑制了振动能量在光束长度上的传播,从而导致了模式定位和固有频率的增加。

更新日期:2018-10-28
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