Vibrational analysis of initially stressed carbon nanotubes

In this paper an analytical method to investigate vibrational analysis of double-walled carbon nanotubes under initial compression stress. Simplified Flügge shell equations of motion are proposed as the governing equations of vibration for the carbon nanotubes. The nanotube structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. Vibration frequency equations in double wall carbon nanotubes are described through the effects of initial compression stresses. We investigate the influence of initial compression stress on the vibrational characteristics of carbon nanotubes based on the proposed theoretical approach. In this study, we consider the double-walled nanotubes with an inner diameter of 2.2 nm and an outer diameter of 3.0 nm. The theoretical investigation may give a useful reference for potential application and design of nanoelectronics and nanodevices.