标题：Static and dynamic analysis of micro beams based on strain gradient elasticity theory
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;; Non-classical boundary conditions
摘要：The static and dynamic problems of Bernoulli-Euler beams are solved analytically on the basis of strain gradient elasticity theory due to Lam et al. The governing equations of equilibrium and all boundary conditions for static and dynamic analysis are obtained by a combination of the basic equations and a variational statement. Two boundary value problems for cantilever beams are solved and the size effects on the beam bending response and its natural frequencies are assessed for both cases. Two numerical examples of cantilever beams are presented respectively for static and dynamic analysis. It is found that beam deflections decrease and natural frequencies increase remarkably when the thickness of the beam becomes comparable to the material length scale parameter. The size effects are almost diminishing as the thickness of the beam is far greater than the material length scale parameter. (c) 2008 Elsevier Ltd. All rights reserved.