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

In this paper, the transverse vibration of cracked nano-beam has been studied based on modified couple stress theory. Crack is modeled by a rotational spring that creates a discontinuity. Frequency equations of cracked nano-beam with some typical boundary conditions are derived and the frequency parameter for different crack positions, crack parameter and length scale parameters value are calculated. According to the results, it can be found that the effects of the crack parameter and crack location on transverse frequency of the cracked nano-beam are significant. In addition, scale effect parameter is one of the important parameter in nanoscale that must be obtained. Finally, the results of special cases show good agreement with the results available in the literature.