Wave-based method for longitudinal vibrational analysis of irregular single-walled carbon nanotube with elastic-support boundary conditions

Abstract

The longitudinal vibrationnal analysis of an irregular single-walled carbon nanotube (ISWCNT) with elastic boundary restraints along its ends is invistigated in this study. The Flügge’s principle is employed to model the ISWCNT and the wave propagation approach is utilized to evaluate the natural frequncy of longitudinal vibration of ISWCNT. The boundary conditions and governing equations are formulated based on Flügge’s model. An exact solution is presented in the axial direction and the MATLAB R2013a Software is hired to present a numerical solution for the longitudinal vibration. A novel equation of motion and frequancy equation are derived for vibrational analysis of ISWCNT under the elastic-support boundary conditions in the longitudinal direction and the impacts of surface irregularity parameter are investigated to find a better profile for irregularity varation to maximize the vibration stability of ISWCNTs. It is concluded that, the irregular single-walled carbon nanotubes or those whose natural frequencies decrease from the large irregularity parameter to the small irregularity parameter of SWCNTs are not optimum designs to build appropriate nanodevices for various applications. In addition, it is observed that to improve the vibration stability of ISWCNTs, it is better to decrease surface irregularity from the large to the small irregularity parameter. Results of this work can be utilized to provide optimum designs for nanodevice in which ISWCNT is common nanocomposite structural element.