On postbuckling mode distortion and inversion of nanostructures due to surface roughness

Abstract

In this paper, we investigate the surface roughness-dependence of buckling of beam-nanostructures. A new variational formulation of buckling of Euler-Bernoulli rough beams is developed based on the Hamilton's principle. The equation of motion of the beam is obtained with a coupling term that depends on the beam surface roughness. Exact solutions are derived for the buckling configurations and the pre-buckling and postbuckling vibrations of simply supported structures. The derived solutions are used to comprehensively explain influence of surface roughness on buckling characteristics of micro/nano-beams. We reveal that the buckling configurations and postbuckling mode shapes are distorted due to surface roughness. Thus, the beam with a rough surface may exhibit a localized buckling configuration where the buckling energy is confined over a small portion of the beam. In addition, the postbuckling mode shape of simply supported beams with rough surfaces is applied load-dependent. We report a value of the applied axial load at which the postbuckling mode shape is completely distorted, and the beam exhibits a mode shape that is identical to its buckling configuration but with a different amplitude. For the first time, we reveal a postbuckling mode inversion due to surface roughness. We demonstrate that the postbuckling mode shape starts to exhibit an inverted form of its original shape at high load values. The findings presented in this study highlight new insights into buckling characteristics of micro/nano-beams.