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.

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Articles you may be interested inSize effects on electromechanical coupling fields of a bending piezoelectric nanoplate due to surface effects and flexoelectricity

This article deals with free vibration of circular nanoplates with consideration of surface properties due to high surface to volume ratio. Classical laminated plate is employed with inclusion of surface elasticity and surface residual stress effects. Solution of the resulting differential equation leads to size dependent behavior of natural frequencies and mode shapes of vibration to be demonstrated. Deviation of the results from conventional theories is shown to be due to changes in the arguments of Bessel functions in the corresponding characteristic equations.