A new electrostatic load model for initially curved carbon nanotube resonators: pull-in characteristics and nonlinear resonant behaviour

A new nonlinear electrostatic load model for initially curved clamped–clamped carbon nanotube (CNT) resonators is developed in this study. In particular, first a 3D finite element analysis is performed in order to obtain the electrostatic force distribution on a clamped–clamped CNT resonator (with and without initial curvature). A nonlinear model for the electrostatic load is then developed based on the 3D finite element analysis results. Based on the newly developed electrostatic load model, the nonlinear equations of motion of the initially curved CNT resonator are derived employing Hamilton’s principle together with the modified couple stress theory. Moreover, the Kelvin–Voigt viscoelastic model is employed to model the energy dissipation. The new nonlinear model of the system, consisting of two strongly nonlinear coupled partial differential equations, is discretized into a set of nonlinear ordinary differential equations via Galerkin’s technique, and solved employing the pseudo-arclength continuation method. The numerical results are obtained for both static and dynamic cases, with special focus on the static pull-in behaviour and on the effects of the newly developed electrostatic load model, viscoelasticity, initial curvature, and length-scale parameter on the nonlinear resonant response.