Velocity gradient elasticity for nonlinear vibration of carbon nanotube resonators
In this study, for the first time, we investigate the nonlocality superimposed to the size effects on the nonlinear dynamics of an electrically actuated single-walled carbon-nanotube-based resonator. We undertake two models to capture the nanostructure nonlocal size effects: the strain and the velocity gradient theories. We use a reduced-order model based on the differential quadrature method (DQM) to discretize the governing nonlinear equation of motion and acquire a discretized-parameter nonlinear model of the system. The structural nonlinear behavior of the system assuming both strain and velocity gradient theories is investigated using the discretized model. The results suggest that nonlocal and size effects should not be neglected because they improve the prediction of corresponding dynamic amplitudes and, most importantly, the critical resonant frequencies of such nanoresonators. Neglecting these effects may impose a considerable source of error, which can be amended using more accurate modeling techniques.