标题：Nonlinear microbeam model based on strain gradient theory
作者：Junfeng Zhao;Shenjie Zhou;Binglei Wang;Xiping Wang
作者机构：[Zhao, J] School of Civil Engineering, Shandong University, Jinan, Shandong 250061, China, School of Mechanical Engineering, Shandong University, Jina 更多
通讯作者地址：[Zhao, JG]Shandong Univ, Sch Civil Engn, Jinan 250061, Shandong, Peoples R China.
来源：Applied mathematical modelling
关键词：Nonlinear microbeam;Strain gradient theory;Static deformation;Post-buckling;Free vibration
摘要：The nonlinear governing equation of microbeam based on the strain gradient theory is derived by using a combination of the strain gradient theory and the Hamilton\'s principle, and the nonlinear static bending deformation, the post-bucking problem and the nonlinear free vibration are analyzed. The nonlinear term in the nonlinear governing equation is associated with the mean axial extension of the microbeam. The static bending deformation of the clamped-clamped microbeam subjected to transverse force, the critical buckling loads and the nonlinear frequencies of the simple supported microbeam with initial lateral displacement are discussed. It is shown that the size effect is significant when the ratio of characteristic thickness to internal material length scale parameters is approximately equal to one or two, but is diminishing with the increase of the ratio. The results also indicate that the nonlinearity has a great effect on the static and dynamic behavior of microbeam. To attain accurate and reliable characterization of the static and dynamic properties of microbeam, therefore, both the micro structure dependent parameters and the nonlinear term have to be incorporated in the design of micro structures in MEMS or NEMS.