The size-dependent natural frequency of Bernoulli-Euler micro-beams
The size-dependent natural frequency of Bernoulli-Euler micro-beams
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DOI：
10.1016/j.ijengsci.2007.10.002
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发表时间：
2008-05-01
影响因子：
6.6
通讯作者：
Wang, Kai
中科院分区：
文献类型：
--
作者：
Kong, Shengli;Zhou, Shenjie;Wang, Kai
基于修正偶应力理论，对Bernoulli-Euler梁的动力学问题进行了解析求解。将修正偶应力理论的基本方程与汉密尔顿原理相结合，得到了平衡方程、初始条件和边界条件。求解了简支梁和悬臂梁的两个边值问题，分析了两种边界条件下梁的固有频率的尺寸效应。结果表明，新模型预测的梁的固有频率与梁的尺寸有关。当特征尺寸与内部材料长度尺度参数之比近似等于1时，新模型预测的固有频率与经典梁模型预测的固有频率之间的差异非常显著，但随着特征尺寸与内部材料长度尺度参数之比的增大而减小。(C)2008爱思唯尔有限公司保留所有权利。
The dynamic problems of Bernoulli-Euler beams are solved analytically on the basis of modified couple stress theory. The governing equations of equilibrium, initial conditions and boundary conditions are obtained by a combination of the basic equations of modified couple stress theory and Hamilton's principle. Two boundary value problems (one for simply supported beam and another for cantilever beam) are solved and the size effect on the beam's natural frequencies for two kinds of boundary conditions are assessed. It is found that the natural frequencies of the beams predicted by the new model are size-dependent. The difference between the natural frequencies predicted by the newly established model and classical beam model is very significant when the ratio of characteristic sizes to internal material length scale parameter is approximately equal to one, but is diminishing with the increase of the ratio. (C) 2008 Elsevier Ltd. All rights reserved.