A size-dependent Euler–Bernoulli beam model is developed to investigate the vibration characteristics of cracked nano-beams made of nanocrystalline materials. The proposed model incorporates a size-dependent micromechanical model and Mindlin's couple stress theory to model the beam material structure and size effects. The classical Mori-Tanaka micromechanics is modified to introduce the grain surface energy effects which are related to the grain size. In the context of the couple stress theory, a rotation gradient tensor is considered in the beam strain energy function to model the grain microrotation effects. The developed modeling package is then used to address the vibration characteristics of cracked nano-beams where the crack is represented as an equivalent torsional spring in the continuity equations. By converting the cracked beam to an equivalent infinite long plate under tension with an edge crack, the strain energy release rate due to the crack is derived accounting for the grain microrotation effects. After that, a crack severity factor that incorporates measures for the couple stress effects is derived. At the end, a parametric study is carried out illustrating the influences of the crack length, the crack location, the beam material structure, and the beam size on the cracked beam vibrational characteristics.

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