Free transverse vibrations of cracked nanobeams with surface effects

The flexural vibrations of cracked micro- and nanobeams in the presence of surface effects are studied. The cracked-beam model is set up by dividing the classical cracked beam element into two segments connected by a rotational spring located at the cracked section. This model promotes a discontinuity in bending slope, which is proportional to the second derivative of the displacements. Numerical examples demonstrate the effects of beam length, and crack position and severity on the calculated values of natural frequencies of an anodic alumina nanowire in the presence of surface effects. Limiting cases are considered and good agreements with the data available in the literature are obtained.