Vibration Analysis of Material Size-Dependent CNTs UsingEnergy Equivalent Model

This study presents a modified continuum model to investigate the vibration behavior of single andmulti-carbon nanotubes (CNTs). Two parameters are exploited to consider size dependence; one derived from theenergy equivalent model and the other from the modified couple stress theory. The energy equivalent model,derived from the basis of molecular mechanics, is exploited to describe size-dependent material properties such asYoung and shear moduli for both zigzag and armchair CNT structures. A modified couple stress theory is proposedto capture the microstructure size effect by assisting material length scale. A modified kinematic Timoshenko nanobeamincluding shear deformation and rotary inertia effects is developed. The analytical solution is shown andverified with previously published works. Moreover, parametric studies are performed to illustrate the influence ofthe length scale parameter, translation indices of the chiral vector, and orientation of CNTs on the vibrationbehaviors. The effect of the number of tube layers on the fundamental frequency of CNTs is also presented. Thesefindings are helpful in mechanical design of high-precision measurement nano-devices manufactured from CNTs.

Keywords:

Energy Equivalent Model , Modified Couple Stress Theory , Carbon Nanotube , Vibration of Timoshenko Nano Beam , Analytical Model