Frequency analysis of nanotubes with consideration of surface effects

Consideration of surface effects in microscaled and nanoscaled materials is important for accurate prediction of their dynamic behavior. In this study, the Timoshenko beam model is modified to include the surface effects and used to analyze the vibration of nanotubes as well as calculate their natural frequencies. The thin surface layers have been taken into account for rotary inertia computation. Through an example it is shown that dynamic behavior of nanoscaled tubes with consideration of surface effects considerably deviates from the results obtained by classical theories. Plots illustrating such deviations are given to support the conclusions.