微纳米尺度下考虑表面效应的圆形薄板的位移解  

Displacement Solution of a Circular Thin Plate with Surface Effects at Micro / nanoscale

作　　者：姜礼鑫 林浩 曹高峰 刘建林[1] 

机构地区：[1]中国石油大学(华东)储运与建筑工程学院,山东青岛266580

出　　处：《鲁东大学学报（自然科学版）》2015年第4期301-305,312,共6页Journal of Ludong University:Natural Science Edition

基　　金：国家自然科学基金(11272357);山东省杰出青年自然科学基金(JQ201302)

摘　　要：基于Gurtin的表面弹性理论,综合考虑板的表面弹性和残余表面应力的影响,建立了微纳米尺度下薄板承受横向分布载荷的力学模型.然后以周边固支的圆板承受横向均布载荷为例,求得了残余表面应力为零、取正值和取负值时的挠曲线.最后对板的位移解进行了分析,阐明了残余表面应力对于其变形的影响.这些计算和分析丰富了传统固体力学的研究范畴,并且为研制微型传感器、微机电系统等提供了一定的参考.Based upon Gurtin＇ s theory of surface elasticity, the surface elasticity and residual surface stresswere both considered. As a result, the mechanical model of a thin plate under the action of the transverse dis-tributed load at micro/nanoscale was established. As a typical example, a circular plate under the action of thetransverse distributed load was analyzed, and the delfection curves when the redisual surface stress is zero, pos-itive and negative were solved respectively. Finally, these displacement solutions were discussed in detail, andthe effect of the residual surface stress on the deformation was addressed. These calculations and analyses haveenriched the scople of classical solid mechanics, and provided some references for the design of microsensorsand MEMS, etc.

关 键 词：表面残余应力 表面效应 BESSEL方程 位移 

分 类 号：O484.2[理学—固体物理]