Size effect on transverse free vibrations of ultrafine nanothreads

Due to their unique properties and appealing applications, low dimensional sp³ carbon nanostructures have attracted increasing attention recently. Based on the beam theory and atomistic studies, this work carries out a comprehensive investigation on the vibrational properties of the ultrathin carbon nanothreads (NTH). Size effect is observed in transverse free vibrations of NTHs. To quantify such effects, the modified couple stress theory (MCST) is utilized to modify the Timoshenko beam theory. According to the first four order frequencies of NTHs from atomistic simulations, the critical length scale parameter of MCST is calibrated as 0.1 nm. It is shown that MCST has minor effect on the first four order modal shapes, except for the clamped boundary. MCST makes the modal shapes at the clamped boundary closer to those observed in atomistic simulations. This study suggests that to some extent the MCST-based Timoshenko beam theory can well describe the transverse vibration characteristics of the ultrafine NTHs, which are helpful for designing and fabricating the NTH-based nanoscale mechanical resonators.