标题：The size-dependent natural frequency of Bernoulli-Euler micro-beams
作者：Kong, Shengli; Zhou, Shenjie; Nie, Zhifeng; Wang, Kai
作者机构：[Kong, Shengli; Zhou, Shenjie; Nie, Zhifeng; Wang, Kai] Shandong Univ, Sch Mech Engn, Jinan 250061, Peoples R China.
通讯作者地址：[Zhou, SJ]Shandong Univ, Sch Mech Engn, Jinan 250061, Peoples R China.
来源：INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
关键词：strain gradient; Bernoulli-Euler beam; size effect; natural frequency
摘要：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.