Selective Excitations of Transverse Vibrational Modes of a Carbon Nanotube through a “Shuttle-Like” Electromechanical Instability

Figure 3

(Color online) Regions of instability in the parameter plane ($z_0\text{,}$${\mathrm{\Gamma }}_0^{*}(d)$) for the first three bending modes when the inverse characteristic time of the nanotube mechanical response to the external force is larger than the frequencies of the nanotube vibrational modes, $1/\tau =10{\omega }_1$. The regions computed from the real part of the analytic expression (7) (solid lines) are compared with the results obtained by the numerical solution of the linearized equations of motion (markers). The region of instability for the first mode includes all the values of ($z_0\text{,}$${\mathrm{\Gamma }}_0^{*}(d)$) for which the other modes are unstable; therefore no selective excitation can be attained in this regime. The other relevant parameters are $eℰ/(m\lambda {\omega }_1^2)=0.1\text{,}$${\mathrm{\Gamma }}_{\text{NT-L}}=5{\omega }_1\text{,}$$Y=10^{-3}$.