Geometrically nonlinear dynamic behavior on detection sensitivity of carbon nanotube-based mass sensor using finite element method

The principle of mass detection using carbon nanotube (CNT) resonators is based on the detection of the resonant frequency shift due to an attached mass. Although CNT resonators can easily show a nonlinear oscillation behavior, there is a lack of studies on the influence of the design parameters and the nonlinear dynamic behavior on the detection sensitivity of CNT-based mass sensors. In addition, most of the finite element method (FEM) analysis models that are used to predict the resonant frequency shift due to attached masses have been implemented in the linear oscillation regime. In order to enhance the sensing performance of the CNT-based mass sensor, a parametric study of the resonant frequency shift is conducted herein with respect to the attached mass, the electrostatic force, the initial tension and the CNT length, using an FEM-based nonlinear analysis model. The FE model is applied to solve the nonlinear dynamic behavior of CNT resonators using direct time integration and the solution is verified by its comparison to the corresponding analytical solution that had been validated in previous studies. The analysis results of the nonlinear dynamic behavior of the CNT resonator indicate that the CNT length plays a key role in the detection sensitivity, and the amount of electrostatic force determines the linear or nonlinear oscillation behavior of the resonator. It is shown that the detection sensitivity can be improved using the nonlinear oscillation behavior and this improvement is more effective with longer CNTs. This study's results justify the possibility and validity of FEM use for the analysis of the nonlinear behavior of CNT resonators and elucidate the relationship between the design parameters and the nonlinear behavior of the CNT-based mass sensor in enhancing the sensing performance.