Vibrational analysis of double-walled carbon nanotubes with inner and outer nanotubes of different lengths

In this study, the Euler–Bernoulli beam model is used to analyze the resonant vibration of double-walled carbon nanotubes (DWCNTs) with inner and outer nanotubes of different lengths. The resonant properties of DWCNTs with different inner and outer nanotube lengths are investigated in detail using this theoretical approach. The resonant vibration is significantly affected by the vibrational modes of the DWCNTs, and by the lengths of the inner and outer nanotubes. For an inner or outer nanotube of constant length, the vibrational frequencies of the DWCNTs increase initially and then decrease as the length of another nanotube increases. A design for nanoelectromechanical devices that operate at various frequencies can be realized by controlling the length of the inner and outer nanotubes of DWCNTs. This investigation may be helpful in applications of carbon nanotubes such as high frequency oscillators, dynamic mechanical analysis and mechanical sensors.