Nonlinear microbeam model based on strain gradient theory

The nonlinear governing equation of microbeam based on the strain gradient theo derived by using a combination of the strain gradient theory and the Hamilton's princ 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 associated with the mean axial extension of the microbeam. The static bending deformation of the clamped-clamped microbeam subjected to transverse force, the critical b ling loads and the nonlinear frequencies of the simple supported microbeam with ir lateral displacement are discussed. It is shown that the size effect is significant when 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 re, also indicate that the nonlinearity has a great effect on the static and dynamic behavior microbeam. To attain accurate and reliable characterization of the static and dyne properties of microbeam, therefore, both the micro structure dependent parameters the nonlinear term have to be incorporated in the design of micro structures in MEN NEMS. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.