The Influence of shearing and rotary inertia on the resonant properties of gold nanowires

In a previous publication [ P. A. T. Olsson, J. Appl. Phys. 108, 034318 (2010) ], molecular dynamics (MD) simulations have been performed to study the resonant properties of gold nanowires. It has been documented in the aforementioned publication that the eigenfrequencies of the fundamental mode follows the continuum mechanically predicted behavior when Bernoulli–Euler beam theory is used, whereas the higher order modes tend to be low in comparison to Bernoulli–Euler beam theory predictions. In this work, we have studied the resonant properties of unstressed and prestressed nanowires to explain why the eigenfrequencies of the fundamental mode follows the behavior predicted by Bernoulli–Euler beam theory while those of higher order modes are low in comparison. This is done by employing Timoshenko beam theory and studying the nanowire deformations for different modes. We find good agreement between the MD results and Timoshenko predictions due to the increasing importance of shearing and rotary inertia for higher order resonant modes. Furthermore, we argue that this type of behavior is merely a geometric effect stemming from low aspect ratio for the considered structures as a converging type of behavior is found when the aspect ratios fall between 15 and 20. Finally, we have found that classical Timoshenko beam theory that neglects nanoscale surface effects is able to, simply through utilization of the size dependent Young’s modulus, capture the dynamic properties of the gold nanowires as calculated through MD.