长沙理工大学学报（自然科学版）2026，Vol.23Issue(1)：174-183,10.DOI:10.19951/j.cnki.1672-9331.20220329002
含缺陷Timoshenko微梁的自由振动分析
Free vibration analysis of Timoshenko micro-beams with defects
摘要
Abstract
[Purposes]This paper aims to study the influence of thickness defects on the free vibration of micro-beams.[Methods]A thickness defect distribution function was introduced into the stiffness expression of Timoshenko beams.Then,based on the modified gradient elasticity theory,the governing equations for the free vibration of micro-beams were obtained by using Hamilton's principle.Finally,the equations were solved by using the Newmark-β method and the six-virtual-node finite difference method.[Results]The effects of defect depth,defect width,and defect location on the free vibration of micro-beams are mainly reflected in the amplitude and acceleration amplitude,while they have a minimal effect on the fundamental frequency.A smaller internal characteristic length parameter of the micro-beam means greater variation of the micro-beam amplitude with the defect width and depth.[Conclusions]If only the fundamental frequency of the free vibration of Timoshenko micro-beams is considered,the effect of thickness defects can be ignored.If its amplitude is considered,the effect of thickness defects cannot be ignored.关键词
Timoshenko微梁/缺陷/自由振动/尺寸效应/修正梯度弹性理论Key words
Timoshenko micro-beam/defect/free vibration/size effect/modified gradient elasticity theory分类
建筑与水利引用本文复制引用
彭斌峰,赵冰,陈健,彭旭龙,龙承运..含缺陷Timoshenko微梁的自由振动分析[J].长沙理工大学学报（自然科学版）,2026,23(1):174-183,10.基金项目
湖南省教育厅科学研究项目(优秀青年项目)(21B0315) （优秀青年项目）
