Parametric excitation of higher-order electromechanical vibrations of carbon nanotubes

The eigenfrequencies of electromechanical vibrations of carbon nanotubes (CNT), rooted in a metallic base and subjected to longitudinal dc and radio frequency (rf) electric field, depend on the amplitudes of the fields. When the driver rf frequency equals the sum of frequencies of two normal modes of CNT (=ωs+ωr), parametric excitation of the two vibrations occurs and the growth rate of parametric instability scales linearly with the amplitude of the rf field. The growth rate decreases with the order of the excited mode. Resonant excitation also occurs when 2=ωs+ωr, however, in this the growth rate goes as the square of the rf amplitude.