Thermal and Small-Scale Effects on Vibration of Embedded Armchair Single-Walled Carbon Nanotubes

Abstract

The non-local Timoshenko beam theory has been implemented to investigate the free vibration of armchair single-walled carbon nanotubes embedded in elastic medium including the thermal effects. The mechanical properties of nano-composite (carbon nanotubes and polymer matrix) are treated as functions of temperature change and the analytical solution is derived according to the governing equations of non-local Timoshenko beam models. The equivalent Young’s modulus and shear modulus for armchair single-walled carbon nanotubes are derived using an energy-equivalent model. Influence of small-scale coefficient, vibrational mode number, matrix of nano-composite and aspect ratio on the frequency ratio of the armchair single-walled carbon nanotubes including the thermal effect are studied and discussed. The research work reveals the significance of the small-scale coefficient, the vibrational mode number, the elastic medium and the aspect ratio on the frequency ratio. It is also demonstrated that some properties of free vibrations of single-walled carbon nanotubes are dependent on the change of temperature.