考虑小尺度效应的微圆轴扭转振动

在微机电系统中,微纳米构件常常表现出尺度效应。基于非局部弹性理论,建立了微圆轴的扭转振动模型,并结合3种常见的边界条件,给出了具体的算例。结果表明:对比于经典连续力学,非局部弹性理论预言的圆轴扭转振动固有频率下降,并且微圆轴的外特征尺度即横截面半径越小,二者相差越大;振动频率的阶数越高,影响也越明显。随着截面半径的增加,振动频率下降并且非局部尺度效应逐渐消失。同时考察了扭转振动的模态函数和相对转角,发现前者与经典弹性理论结果一致。此外还讨论了材料内禀尺度的选取问题,以数值算例证明了内禀尺度与材料晶格常数非常接近,晶格常数可近似用作微纳米力学中材料的内禀尺度参数。

Twisting vibration of micro circular shafts accounting for small scale effects

Micro/nano-components often exhibit size effects in micro-electro-mechanical systems.A torsional vibration model of micro circular shafts is established based on nonlocal elasticity theory in this paper.Concrete examples are presented for three kinds of boundary conditions.It is shown that according to nonlocal elasticity theory the predicted natural frequencies of the torsional vibration decrease in comparison with the results based on classical continuum mechanics,and the differences are much larger with a smaller external characteristic scale(such as radius of cross section) or for higher modal frequencies.Vibration frequencies decrease and the nonlocal scale effects disappear gradually with the increase of cross section radius.Vibration mode functions and relative rotation angles are also observed,of which the former are consistent with those predicted by classical continuum theory.Furthermore the selection of internal characteristic scale is discussed.A numerical example proves that lattice constant of material is very close to the scale mentioned,which may be approximately adopted as the internal characteristic scale in micro/nano-mechanics.