Size Effect on Free Transverse Vibration of Cracked Nano-beams using CoupleStress Theory

In this paper, the transverse vibration of cracked nano-beam has been studied based on modified couplestress theory. Crack is modeled by a rotational spring that creates a discontinuity. First, transversevibration equation of cracked nano-beam is derived along with its general response. Then, thefrequency parameters are calculated for different crack positions, different lengths of the beam,different length scale parameter, different crack properties, and some typical boundary conditions.Results indicate that the effects of the crack parameter and crack location on transverse frequency ofthe cracked nano-beam are quite significant. In addition, scale effect parameter is one of the importantparameters in nanoscale that must be taken into account. Finally, the results of special cases withsimple support boundary condition for classic and nonlocal theories are compared with those availablein the literature.