Using Couple stress Theory for Transverse Vibrations of Cracked Nanobeams

The aim of this paper is to study the transverse frequency of a cracked nanobeam. The frequency equation of the nanobeam with simple support beam is derived base on the couple stress theory. This model promotes a discontinuity in bending slope, which is proportional to the second derivative of the displacements. Frequency equation of crackednanobeam is derived and the natural frequencies for different crack positions and beam length are calculated. According to the equation, it can be found that the effects of the crack parameter and crack location on the transverse frequency of the cracked nanobeam are significant. The frequency decreases with an increase of the crack parameter. Some numerical example is done to show these effects on natural frequencies. The results are compared with some data available in the literature and show good agreement.

کلیدواژه ها:

cracked nanobeam ، natural frequency ، couple stress theory