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We propose a carbon nanotube oscillator that is composed of a cantilever inner tube and a short outer tube. When the inner tube vibrates, the centrifugal force and the van der Waals force drive the outer tube to oscillate along the inner tube, which means that the oscillator can simultaneously output two frequencies. The operation frequencies of the oscillator may be tunable in a wide range (from tens of gigahertz to more than 100 GHz) by controlling the initial conditions. The combination of tunability and high-frequency operation makes the oscillators promising for a variety of scientific and technological applications. A continuum model is presented to study the frequency properties of the oscillator. The model is validated by the molecular dynamics simulations.

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The continuous loading assumption is adopted in most present studies on the buckling of thin shells subjected to lateral loads, while the relationship between the finite number of loads and the lateral buckling remains unclear. In this work, we derive an analytic formula for the dependence of the critical buckling stress on the number of loads, which shows that the critical stress increases significantly with the increase of the load number and reaches a saturation value in the limit of large load number. Furthermore, the analytic formula reveals the dependence of the critical stress on the deviation of the radius in an imperfect shell. To verify the validity of the analytic formula, we perform molecular dynamics simulations to investigate the buckling of both perfect and imperfect single-walled carbon nanotubes under a finite number of lateral loads, where the analytic formula agrees with the simulation results. These results shall be valuable for understanding mechanical stability of elastic thin shells or nanoscale tubal structures subjected to discrete lateral loads.