Figure 1

(Color online) The thermal vibrational spectrum for (a) a 50 nm CNT at $T=300\text{K}$ and (b) a 20 nm CNT at $T=700\text{K}$. The range of the axes in both plots is the same to facilitate comparison. In addition to the MD results, we display results from the Timoshenko and Euler Bernoulli beam theory. For the Timoshenko results, the width of the impulse is the error in the frequency prediction that results from uncertainty in estimating the flexural rigidity $EI$. The total intensity is the sum over the spectral intensity of the peak.Reuse & Permissions

Figure 2

(Color online) The thermal vibration width in nanometer squared versus temperature in Kelvin for a 20 nm tube. A best-fit line from a weighted least-squares analysis gives an intercept of $1.6608\times {10}^{-4}{\text{nm}}^2$ with an error of $1.4724\times {10}^{-3}{\text{nm}}^2$, confirming the linear hypothesis in Eq. (3). The best-fit line shown in the figure is constrained to have zero intercept.Reuse & Permissions