Size-dependent bending behavior of non-uniform beams resting on an elastic medium via modified couple stress theory

In this study, static analysis of variable cross-section embedded beams at micro scales is performed. It is considered that the microbeam is lying on Winkler foundation. Fundamental equations are obtained with the help of Euler-Bernoulli beam and modified couple stress theories. Four cases for the cross-section of cantilever microbeams as uniform, single tapered with variable width and constant height, single tapered with constant width and variable height, and double tapered with variable width and height are investigated. Displacements of embedded cantilever microbeams are obtained by Rayleigh-Ritz method for various taper ratios. The effects of small-scale parameter, Winkler parameter, tapering case, and taper ratio on displacements are examined in detail. It is found that the microstructure effect and tapering cases may play important roles in the displacements of microbeams.