Differential quadrature based nonlocal flapwise bending vibration analysis of rotating nanotube with consideration of transverse shear deformation and rotary inertia

This paper is concerned with the flapwise bending free vibration problem for rotating nanotubes. The small scale effect is taken into consideration based on nonlocal elasticity theory. In the nanotube model the effects of transverse shear deformation and rotary inertia are accounted. The nonlocal governing equations and the nonlocal boundary conditions are derived. These equations are solved analytically for the vibration frequencies of nanotubes via differential quadrature method. The vibration solutions obtained provide a better representation of the vibration behavior of short, stubby, nanotubes where the effects of small scale, transverse shear deformation and rotary inertia are significant. The effects of the nonlocal small scale parameter and the hub radii on the natural frequencies of the rotating carbon nanotube with respect to the rotating angular velocity are investigated in the present work. The results can provide useful guidance for the study and design of the next generation of nanodevices such as blades of a nanoturbine, nanogears, and nanoscale bearings, that make use of the vibration properties of rotating single-walled carbon nanotubes.

► The flapwise bending free vibration problem for rotating nanotubes is studied. ► In the nanotube model the effects of transverse shear deformation and rotary inertia are accounted. ► It is observed that as the nondimensional angular velocity increases the nondimensional fundamental frequency also increases. ► As the value of angular velocity, increases the difference between the frequencies by local and nonlocal models increases. ► In addition, as the distance of hubradius increases the value of frequency increases.