Dynamics of carbon nanotubes mass detection involving phonon-tunnelling dissipation

Nanomechanical (NEMS) resonators made from carbon nanotubes (CNTs) have emerged as ubiquitous devices for use in mass detection. Many oscillation behaviours of CNT mass detection have been theoretically studied by the continuum elastic model, albeit their performance is limited by deleterious effects of mechanical damping. Reported are the support-induced losses in generic mechanical resonators because of the tunnelling of mesoscopic phonons between the CNT and its supports. After formulating the problem, the resulting differential equations are solved analytically using the method of multiple scales, and a closed form solution is obtained. The results reveal that the Young´s modulus, density and geometric parameters of the CNT not only influence the resonant frequency shift and the system stiffness, but also affect the system vibration amplitude. Moreover, the effect of the supports material on the oscillation is discussed. Also, the phonon-tunnelling dissipation for dynamics of CNT mass detection is highlighted.