Size-dependent post-buckling behaviors of geometrically imperfect microbeams

In this paper, the size-dependent buckling and post-buckling analysis of the imperfect microbeams is presented. By accounting the mid-plane stretching, the nonlinear integral partial-differential equation governing the transverse motion of the imperfect microbeam is derived employing Hamilton's principle. The modified couple stress theory is employed to capture the size effects of microbeams. The exact analytical solutions of the critical buckling load and the static response are acquired for the buckling problem of imperfect microbeams with different boundary conditions. Moreover, the dynamic behavior around the static configurations in the preand postbuckling domain is also investigated. It is found that the buckling of imperfect microbeam occurs through a saddlenode bifurcation, and the responses in postbuckling domain are asymmetrical. The numerical results are depicted to illustrate the influence of the dimensionless scale parameter and the imperfection amplitude on the circuital buckling load, static response and the dynamic properties of the imperfect microbeams.