标题：A micro scale Timoshenko beam model based on strain gradient elasticity theory
作者：Wang, Binglei; Zhao, Junfeng; Zhou, Shenjie
作者机构：[Wang, Binglei; Zhao, Junfeng; Zhou, Shenjie] Shandong Univ, Sch Mech Engn, Jinan 250061, Shandong, Peoples R China.
通讯作者地址：[Zhou, SJ]Shandong Univ, Sch Mech Engn, Jingshi Rd 73, Jinan 250061, Shandong, Peoples R China.
来源：EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
关键词：Micro scale; Timoshenko beam; Size effect; Strain gradient
摘要：A micro scale Timoshenko beam model is developed based on strain gradient elasticity theory. Governing equations, initial conditions and boundary conditions are derived simultaneously by using Hamilton's principle. The new model incorporated with Poisson effect contains three material length scale parameters and can consequently capture the size effect. This model can degenerate into the modified couple stress Timoshenko beam model or even the classical Timoshenko beam model if two or all material length scale parameters are taken to be zero respectively. In addition, the newly developed model recovers the micro scale Bernoulli Euler beam model when shear deformation is ignored. To illustrate the new model, the static bending and free vibration problems of a simply supported micro scale Timoshenko beam are solved respectively. Numerical results reveal that the differences in the deflection, rotation and natural frequency predicted by the present model and the other two reduced Timoshenko models are large as the beam thickness is comparable to the material length scale parameter. These differences, however, are decreasing or even diminishing with the increase of the beam thickness. In addition, Poisson effect on the beam deflection, rotation and natural frequency possesses an interesting "extreme point" phenomenon, which is quite different from that predicted by the classical Timoshenko beam model. Crown Copyright (c) 2009 Published by Elsevier Masson SAS. All rights reserved.