On the postbuckling and vibration of functionally graded porous microbeams with a variable material length scale parameter and rough surface

This study examines the postbuckling and vibration behaviors of functionally graded porous (FGP) microbeams with a spatially varying material length scale parameter (MLSP) and rough surface. A new model is developed to account for the coupled effects of both the variable MLSP and surface roughness. The material properties and MLSP of FGP microbeams are modeled as spatially varying functions governed by the material gradient parameter. Based on Euler beam theory, modified couple stress theory (MCST), and von-Kármán geometric nonlinearity, the governing equations and boundary conditions are derived using Hamilton’s principle. Closed-form solutions are then obtained for the postbuckling configuration and associated vibration characteristics of clamped–clamped FGP microbeams. Finally, the influences of surface roughness, MLSP, gradient index, porosity volume fraction, and beam thickness on the buckling and vibration behaviors are investigated. The results demonstrate that increasing the average roughness generally reduces the first two critical buckling loads, whereas increasing the average slope increases the first critical load but decreases the second one. The average slope can also distort the conventional postbuckling configuration. Moreover, the spatial variation of the MLSP has a pronounced influence on the size-dependent buckling and vibration responses, highlighting the necessity of incorporating both the variable MLSP and surface roughness for accurately predicting the mechanical behavior of FGP microbeams.