Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes

Vibration and buckling of in-plane loaded simply supported double-walled carbon nanotubes were investigated using the nonlocal Timoshenko-beam theory. The influence of in-plane loads on the natural frequencies was determined. The results show that while the natural frequencies decrease with increasing compressive in-plane loads, an increase in frequencies is observed for tension type of in-plane loads. Effects of in-plane loads are more pronounced for lower modes, and some mode changes are observed at critical in-plane loads. A comparison of nonlocal elasticity solutions with local elasticity solutions indicates that the nonlocal effects should be considered for higher modes of vibration of double-walled carbon nanotubes.