Vibration characteristics of zigzag and chiral functionally graded material rotating carbon nanotubes sandwich with ring supports

In this study, vibrations of rotating zigzag and chiral functionally graded carbon nanotubes with ring supports have been performed. To discretize the governing equations of current model, Galerkin’s method is utilized for frequency equations of single-walled carbon nanotubes. The unknown axial functions have been 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 the 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 the counterpart of length-to-radius ratio for rotating boundary conditions. The frequency phenomena have been observed to be 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.