Abstract

The eigenfrequencies of bending vibrations are determined for wire with micro- and nanosize cross sections. The surface effects associated with an increase in the specific surface when reducing the cross-section area are taken into account. The first effect is induced by the difference in the elastic characteristics of the material of the surface layer and the bulk. The second effect is associated with the interaction between the excess pressure on the wire surface and the difference in the areas of convex and concave surfaces formed by the bending. The case of the wire hinged fastening at both ends is considered. The eigenfrequencies are determined in the linear and nonlinear formulations. The influence of surface effects and other input data on the eigenfrequencies is analyzed.

中文翻译：

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线微谐振器和纳米谐振器的频谱

摘要

确定具有微米和纳米尺寸横截面的线材的弯曲振动的本征频率。考虑到与减小横截面面积时比表面积增加相关的表面效应。第一效应是由表面层和块体的材料的弹性特性的差异引起的。第二个效果与金属丝表面上的过大压力与通过弯曲形成的凸面和凹面面积的差异之间的相互作用有关。考虑在两端用线铰接的情况。本征频率由线性和非线性公式确定。分析了表面效应和其他输入数据对本征频率的影响。