Effect of Power Law-Index for Accurate Natural Frequencies of Rotating Isotropic SWCNTs with Ring Supports

Abstract

Vibration analysis of carbon nanotubes (CNTs) is very essential field owing to their many promising applications in tiny instruments. The unique and interesting properties of CNTs, particularly their mechanical and electrical features, have fascinated industries and researchers to implement CNTs for production of different electromechanical devices. Research on vibration behavior of CNTs was done for a few decades ago. Vibrations of isotropic rotating zigzag and chiral single-walled carbon nanotube (SWCNTs) with ring supports are established using the Love’s shell theory. To discretize the governing equations of current model, Galerkin’s method is utilized for frequency equations of single-walled carbon nanotubes (SWCNTs). The unknown axial functions have assumed by characteristic beam functions which fulfill boundary conditions applied at the tube ends. Effects of different parameters with ring supports on the fundamental natural frequencies versus ratio of length-to-radius, angular speed and height-to-radius ratio have been investigated. The frequencies curves decrease as the length-to-diameter ratio increases. With the increase of angular speed the frequency curve of backward waves increases and forward wave decreases for rotating zigzag and chiral tubes. On the other hand, the phenomena of frequency versus height-to-radius ratio are counterpart of length-to-radius ratio for rotating boundary conditions. The frequency phenomena have been observed very pronounced with ring support. Frequency value of C-C end condition is higher than those of C-F computations. The results of single-walled carbon nanotube are computed by using MATLAB software. To validate the accuracy of present model, the results have been compared with earlier modeling/simulations.