含缺陷Timoshenko微梁的自由振动分析OA

[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.