Nonlinear behaviour and mass detection sensitivity of geometrically imperfect cantilevered carbon nanotube resonators

This study analyzes numerically the nonlinear static and dynamic behaviours as well as the mass detection sensitivity of a geometrically imperfect cantilevered carbon nanotube (CNT) resonator. More specifically, a new nonlinear model is developed for the cantilevered CNT nanoresonator, taking into account the effects of the initial curvature and cross-sectional area imperfection; furthermore, the new nonlinear model accounts for nonlinear damping and small-scale effects, employing the Kelvin–Voigt damping model and the modified couple stress-based elasticity theory, respectively. The electrostatic interactions in the CNT nanoresonator are modelled through use of a new electrostatic load model, previously developed by the authors. The nonlinear equation of motion of the geometrically imperfect cantilevered CNT nanoresonator is obtained making use of Hamilton's principle as well as the inextensibility condition. The electromechanical continuous model of the nanoresonator is reduced into a high-dimensional discretized model employing the Galerkin method. The discretized model, consisting of a set of coupled nonlinear ordinary differential equations, is solved numerically employing a continuation technique. The nonlinear behaviour of the nanoresonator is studied and the effect of different parameters on the static deflection and dynamic response is examined. Furthermore, the mass detection sensitivity of the nanoresonator is examined in detail and methods are proposed for enhancing the detection sensitivity.